Caught Up in the Craze

Poker Talk at Swarthmore

2012-01-24T08:59:00.000-08:00

I've been invited by the Swarthmore College math department (from which I graduated) to give a talk about how mathematics is used in poker. The talk will be February 14th and should be added to this page in a few weeks. This colloquium series is open to the public, so feel free to show up if you like. Of course, this is my first attempt at giving such a talk, and in fact it is the first talk of any sort I've given since college, so it might not be very polished. That said, I'm working hard to make it interesting and engaging. I will be drawing inspriation mostly from The Mathematics of Poker by Chen and Ankenman and also Introduction to Probability with Texas Hold'em Examples by Frederic Paik Schoenberg.

I'm planning to argue for focusing on EV for strategic purposes and then do some analysis of abstract simple forms of poker like the [0,1] and AKQ games analyzed in The Mathematics of Poker. The audience will be mathematicians who are not necessarily familiar with poker, so I will discuss pot odds and equity using a [0,1] game example. I will introduce game theory and solve a simple no-fold [0,1] game and a full-street AKQ game that will yield the optimal bluffing to betting ratio. I will then shift away from game theory and look at an example of using Bayes' rule to model an opponent's strategy. At the end I plan to list several other aspects of poker that can be interesting to analyze mathematically, but I won't do any of this analysis for the talk (unless I am underestimating my timing, which is unlikely... more likely, I'll have to cut out something like the no-fold [0,1] analysis). These other topics include bankroll strategy, game selection, tournament theory, online data mining, and the metagame. Also, I will allude to the sort of structured hand analysis and concept analysis that I have done here on the blog in past years. All this is supposed to fit into 45 minutes, so I will be doing a lot of rehearsing and tweaking in the next few weeks.

*****

I am quoted in the Intro to Probability book by Schoenberg (a friend and commenter on this blog) criticizing Sklanksy's "Fundamental Theorem of Poker." Beyond that, the book's examples are much more interesting to me as a mathematically-inclined serious poker player than I expected. I would recommend the book to anyone who fits that description and also to statistics departments looking to attract more students to their introductory classes. (I can't imagine going through life without a basic understanding of statistical concepts - not the doing of statistics so much as the interpreting of statistics. "Statisteracy" is a term I recently learned and I think for the health of our society it needs to be an educational focus on par with numeracy... although a catchier word than "statisteracy" would be preferable.)

*****

I said earlier that I planned to apply to some statistics Master's programs. Instead, I applied to the following PhD programs:

Johns Hopkins Biostatistics
UPenn Wharton Statistics
George Washington Statistics
UMBC Statistics
U Maryland-College Park Applied Math & Statistics and Scientific Computation
U Maryland-College Park Economics
UMBC Statistics

*****

I have been playing much less poker than I expected. This is largely due to my applications taking longer than expected, but also, the games are tougher than I expected and I've mostly been losing. Last year was my first losing year, but I played less all year than I used to in a normal month. I haven't played at all this year, although I have been invited to a low-stakes home game next month.

Hollywood Casino at Charles Town

2011-09-07T12:04:00.000-07:00

I've completed the move to Mt Airy, Maryland, and Calvin is in a daycare center that he seems to like, so I have a bit of time to give my adoring fans an update.

I'm going to apply to Master's programs in statistics, applied math, or biostatistics, planning to start in Fall 2012. I'm not sure what to do in the meantime, but I do have one better-than-expected option. Hollywood Casino in West Virginia, less than an hour away, is much nicer than I expected. I was imagining something akin to Hollywood Park Casino, due to the fact that it's on a racetrack and in West Virginia (which I unfairly imagined as being rather run-down). Also, it's similar name encouraged the comparison. The fact that their HR department was unfamiliar with the term "poker prop" did not seem to bode well, either.

In actuality, the casino seems new and the casino floor has the feel of an upscale Vegas casino, a la the Wynn. One drawback is that it feels even more packed with loud slot machines, but it's not too hard to get past those and to the poker room as long as I use the East entrance in the future. (Unaware of this, I used the West entrance on my visit.) When I finally made it to the poker room, it was packed. This was an overcast Saturday afternoon, so that was to be expected. I chatted with a floorman, who told me they have thirty tables, and there were usually wait lists on the weekends. They had discussed expanding downstairs, but that would have displaced some valuable slot machines. That's probably okay, though, because I am more likely to go during the week, when he said they usually only have about 20 tables running. The poker room shares an entrance with the stands for the racetrack, which could cause some unexpected disturbances. Their biggest game is a 5-10 NLH $300 minimum buy-in game, which is very similar to the game I got very used to at the Bike last year. Occasionally they have a 10-20 NLH game, too. They also had some PLO games running, which is also supposedly becoming more popular in Los Angeles.

I asked the floor man about props, and I was surprised to find that he had never heard of them. When I explained them, he assured me that they have none of them and that employees are not even allowed to play at the casino. Oh well.

In other news, friend and occasional commenter Rick Schoenberg has an awesome-looking textbook coming out in December called Introduction to Probability with Texas Holdem Examples. Reading the blurb makes me want to go back and review some of those concept analyses I wrote two years ago. That will have to wait until several other projects are finished, I'm afraid.

Moving to Maryland

2011-05-09T08:19:00.000-07:00

The Los Angeles era is almost over (for me, anyway). Brigid got a good job out in Mt. Airy, MD, so we'll be moving there this summer. The closest poker room, I think, will be "Hollywood Casino" in Charles Town, West Virginia. It's actually not very far from Mt Airy, but this still probably means my poker career is over or at least on hiatus. Although poker has treated me pretty well financially the past few years, I haven't really felt passionate about it. Even moving up in stakes after I got laid off didn't help. I've already stopped playing poker except on rare occasions, instead watching little Calvin and investigating my other options.

I've mentioned my interest in trying something else several times on this blog (I did well on the LSAT in February), so this is could work out well. I'll likely go back to school, but not until fall 2012, so I'll pursue some other projects in the meantime. I'll use this blog as well as my twitter feed to give any substantial updates, but don't expect regular posts (or tweets) for a while.

Online Poker Indictments

2011-04-15T17:08:00.000-07:00

I haven't been playing or thinking much about poker recently, but there is some big news in the poker world today.

If this were just a cultural decision made for the societal good, I would be upset but ultimately okay with it from a political standpoint. It will be interesting to see what we learn in the coming weeks about the sort of political maneuverings that might have been going on behind the scenes. Brick and mortar casinos in particular might have some incentive to try to take down the online poker sites (now that those sites have done their job in creating so many new poker players fifteen years).

Live at the Bike

2011-03-08T12:25:00.000-08:00

My poker/wordswithfriends buddy Aaron (@ALLINAK) tells me that there was a pretty good 5-10NL game at the good 'ol Bicycle Casino yesterday. I had heard the game was dead; I wonder how they got that game going again, but it may be in part due to the Live at the Bike production. I just watched the first half of a $25-$50 NL session that made me really sad that they let me go. That was a juicy, juicy game, but it was much bigger than I'm used to playing. I also think playing on Live at the Bike could actually be help my game a bit, because the commentary is like free coaching. I think Nichoel is a good player, and I would certainly be interested to hear what she had to say about my game. Of course, the fact that anyone else can also watch me play would be a big downside.

I haven't been back to the Bike since being laid off. Considering how tough the Commerce's 10-20 game has been my past few sessions, I might find my way back to the Bike at some point. It just seems kind of wrong to be playing there without getting paid.

The (Poker) World in Turmoil

2011-02-24T14:33:00.000-08:00

After playing very little this year due to LSAT studying and visitors, I went to the Commerce yesterday and was filled in on some gossip. Haig Kalegian, the Bike's managing general partner, has supposedly been bought out by a group including Hashem Minaiy, the Bike's CEO. I know both of them a little bit, Haig better than Hashem. Meanwhile, several people tell me the Bike no longer runs the $500 NL game that I used to prop. This is particularly interesting to me because when I was laid off my supervisor told me they had a plan to keep the game going without me. I wonder if it was their plan all along to kill the game or if they just couldn't keep it going.

My winning streak ended in January... but it doesn't mean much since I only played seven hours.

Did you know there's a whole community living under Las Vegas?

Brigid should be finishing up her PhD soon (probably by the end of the year), so we may be on the move again as soon as September. Fortunately for me, poker rooms seem to be cropping up in the east as legislators look for new ways to bring in tax revenue. For example, there are big plans in Cleveland.

LAPC

2011-01-19T15:13:00.000-08:00

I knew it was starting soon, but I didn't realize the first event is today. The action at Commerce during this event is legendary, and I've been looking forward to getting in on it now that I'm not working.

I made the mistake of signing up to take the LSAT in a few weeks. I haven't taken any standardized tests in years, so I need to do some studying. I'll probably only play about once a week until after the test. At least the LAPC will still be going on a few weeks after the that. Maybe I'll even play a few tournaments.

I've Been Laid Off

2010-12-29T10:18:00.000-08:00

December 10 was my last day at the Bike. They offered me a position as a prop for the 8-16 limit and $80 NL games, which paid much less. I decided to strike out on my own, hopefully finding another similar propping job elsewhere. I really liked it at the Bike - good atmosphere, decent food, good relationships with most of the people there - and I had a pretty sweet deal, so I'm quite disappointed to be let go (despite having recently considered leaving).

In the past few weeks I've made my first trip to the Commerce in three years and my first ever trip to Hawaiian Gardens. My tentative plan is to play mostly 10-20 NL at the Commerce, probably three days a week, unless I can find another propping job. I played there on Monday, and the game seems just as beatable as the Bike's 5-10 NL, so I think it should be good as long as I can take the swings. Compared to most poker players, I'm quite good at dealing emotionally with swings, but I think it will be a lot harder if I'm playing less often, especially considering the higher stakes.

Hawaiian Gardens seems like the most likely casino to be hiring these days, but they don't pay as much and I would probably have to work overnight. On December 4, three days after I was told I was being laid off, I went to Hawaiian Gardens for the first time to check it out. There were a ton of games going, mostly low limit, but they also had two 5-10 NL games, which is more than the Bike usually has. The games were pretty good, and the food excellent, but the atmosphere is rather chaotic. I think it might be draining to work there forty hours a week.

With my free time I might try to do some poker studying, in which case I'll have some fodder for some analysis on the blog.

Winning Streak Stays Alive

2010-11-04T09:42:00.000-07:00

I haven't had a losing month since September 2009 (-$415), and in fact have won at least $1500 each month. When I posted last time, I was up about $2200 with only four days to go in October. I lost almost all of that in the first three days of that week, and was up $84 going into Friday. I try to make a point of not worrying about streaks or short term wins or losses because they can only interfere with the ultimate goal of making optimal decisions on each hand, but the streak was on my mind since I had written about it the previous week. Anyway, I had a big day on Friday, and won just over $3000 for the month. Streak stays alive! I will probably not update on this regularly because I don't want it to interfere with my play.

Rumor has it that the Live at the Bike game is set to resume next week. A section of the Plaza (the poker section where I play) has been cordoned off with a table that will be fitted with hole cams. I don't know why the Live at the Bike was shut down a few years ago, but it really seems like a great idea: people will find the live feed on the internet and learn about the Bike, and lots of people will probably show up just for the novelty of playing in a "televised" game. I'm not thrilled with the idea of being filmed and my cards being broadcast, but if that's what brings in the customers, I'm all for it.

Supposedly on Thursdays we'll also have a "2-11" game in the Plaza, played $100-$300 buyin NL for high only. I'll need to do some strategy analysis if I play. 2-11 is basically a variant of Omaha, and I don't even really know Omaha strategy very well. I guess nobody really knows 2-11 strategy yet, but good Omaha players might have a head start.

I've mentioned before that it might become awkward if people at the casino found my blog. This has happened, but not in quite the why I envisioned. I thought the awkwardness would be among the players, who I occasionally write about. Instead, one of my supervisors found the blog! She called me into her office to let me know it's being monitored, but it seems like they are pretty much okay with it.

Still Slow at the Bike, But Plenty Is Going On

2010-10-23T20:27:00.000-07:00

After having my most profitable month ever in September (ignoring jackpot winnings), I'm at some risk of having my first losing month in over a year. I'm up so far this month, but only a little and I could easily lose it if my last week of October goes poorly. Not bad considering I had five losing months in 2009. My win rate this year (playing mostly NL) is three times that of last year (playing mostly limit), and despite an initial jump in volatility, overall my hourly standard deviation this year has been only 10% higher than last year. Of course, avoiding having any losing months is not the object of poker, but it's nice to see all the black in my spreadsheet.

I went to Vegas two weeks ago to visit the In-Laws. It turned out to be a good venue for a mini reunion. I stopped by several poker rooms, and it was all very, very slow. The Mirage was almost completely dead around noon on a Sunday.

Things have gotten pretty slow at the Bike recently, particularly for my regular $500 NL game, which I played for only eleven hours in four days this week. However, they have had two or three 20-40 limit games going most days (thanks mostly to a new crop of flexible, low wage, silent props and a promotion giving players $5-$10 per hour, depending on the time of day), and often a 50-100 mix game, which includes Badeuci and Badacey, mixes of Badugi with 2-7 lowball or A-5 lowball, respectively.

I met Pinkerton, one of this blog's occasional commenters. He introduced himself after we'd been chatting for quite a while without my realizing who he was. This was the second time a reader has introduced himself at the casino, and in both cases they were reasonably discreet about it. As I told Pinkerton, it might become awkward for me if the existence of this blog became common knowledge at the Bike.

The day I met Pinkerton I also met Charles Lei, an online pro and poker teacher at dragthebar.com. He made the mistake of saying "nice hand" to a player after this player beat the volatile Vinny Vinh in a pot. Vinny took offense and harrassed Charles a bit. I stood up for Charles, telling Vinny I didn't think Charles had done anything wrong. Hours later, Vinny retaliated by calling the floorman immediately after I got up for a bathroom break, telling him I had been away for hours and that the f-ing props think they can do whatever they want and still get a paycheck (another player told me about this later). The other players stood up for me, but the dealer agreed with Vinny (!), so I returned to find my chips picked up and my seat taken by a new player. Oh well. Good one, Vinny! You got me. Anyway, Charles has been discussing hands and players with me every day since then, which is nice for me because he has refined his game pretty well and has some useful observations.

211 poker is returning at 2:11PM on Monday, only this time it will be played only for high, both limit and no-limit. The game failed to catch on back in February 2009, when it was played as a high-low split pot game. I hope it catches on and brings some more people to the casino, but I just don't know if there's much of a market for a new game nowadays. Maybe they should wait until 2:11 on 2/11/2011.

Also rumored to be returning is Live at the Bike, which is an online video feed of actual cash game action at the Bike. Nichoel Peppe, whose position at the Bike I took after she left for Arizona, is likely returning to be a regular commentator on the program. Supposedly the high-stakes game that her husband was playing in Arizona broke after three of the regulars died of old age, so he and Nichoel recently moved back to Los Angeles. I think the Live at the Bike game will be at least 10-25 blinds. I'd like to try it, but it will be very awkward having cameras on both my cards and me.

My Blocking Bet is Disrespected

2010-09-18T21:47:00.000-07:00

Generally, I'm not a big proponent of the idea that you should try to think one "level" higher than your opponent, as is advocated in a lot of NLHE poker books, including a chapter called "Multiple Level Thinking" in No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller. Game theory takes care of this because it solves for the infinite-level. It cannot be out-thought; there is no higher level. Anyway, I had an interesting hand this week in which I ended up needing to think one level higher than my opponent. This is unusual. It only came up because my opponent and I have a rich history of hands against each other and because I made a weak play at one point in the hand that my opponent attempted to exploit. In fact, this opponent is the same player I named "X" in an earlier post, "Raising as a Bluff." Player X is a very good player. I know he has been paying special attention to my game for the past year, and he seems to pride himself on acting on his reads. I play a relatively predictable style; he knows this, and I know he knows this.

The reason my strategy is relatively predictable is that I usually try to play close to "optimally" in a game-theoretical sense. I don't go as far out of my way as most players do to mix up my play. If I truly played optimally, my strategy would not be exploitable (by definition), but, in practice, my play has many deviations from optimal, but intentional and (mostly) unintentional. One play I like to make that's probably not optimal is to make a small blocking bet when I'm out of position on the river and my opponent is likely to successfully bluff me out of the pot if I check. Once in a while I will make this same play with the near nuts. This makes it very expensive for my opponent to raise me as a bluff, and most people will just call me unless they have the nuts. I don't think player X has ever seen me make this type of blocking bet with the nuts, though. I know he has seen me do it a few times with medium-strong hands that cannot stand a raise.

On to the hand in question: Player X had about $1700 and I had him covered. I raised in early position with AsQh to $30 and got two callers, including player X.

Flop($100 pot): QcJh6c. I bet $65, X called.
Turn($230 pot): 4c. I checked, X bet $120, I called.
River($470 pot): 6h. I bet $160. My intention here is to force a cheap showdown. In my mind, X cannot be sure I didn't flop a set or two pair and then make a full house on the river. This should make it very dangerous for X to raise me here if he just has a flush. In truth, I probably would have bet a set on the turn even though the flush came in, but how could Player X be sure of this?

After I bet, player X says, "Really, Keith?" He thinks for 30 seconds and then raises to $660. My plan was to fold to a raise, but I stop to consider the circumstances. I have to call $500 more to win a pot that will be almost $1800 all told. If there's a 28% chance that X is bluffing, a call is profitable. I thought back over my play and realized that it was highly unlikely I would have a full house on the river here. Player X knows I couldn't have a hand like Q6 because I don't raise with that preflop, and he knows that if I had a set, I would have bet out on the turn. This means that my blocking bet was very transparently weak. My range here doesn't really include anything to scare my opponent. The truth is that he realized this before I did, and he had the guts to capitalize on it. However, I still had a chance to rectify the situation. I just had to think one level beyond X. When he raised me to $500, he could not have expected me to call. If he had a flush, he would have raised less or just called. I've seen him bluff with small pocket pairs before, and that is what I kind of expected him to have. I called and he showed me Td9d, a broken straight draw.

It occurs to me that most of my posts about hands involve my explaining how clever I was. Let me just acknowledge at this point that this is a result of severe selection bias. It's more fun for me to write about such hands, and I imagine it's more fun for you to read about them.

Slow Days at the Bike

2010-09-07T18:30:00.000-07:00

I changed my schedule; I still work four days, but now I work Mondays instead of Tuesdays in order to accommodate Calvin's daycare schedule. Yesterday, the $500 NL game never got started. This was the first time I've worked on a Monday since February, but this has never happened that I can remember on any day other than maybe once on Friday, which is always slow. Also, on Friday, the game didn't start until 6:45pm, 15 minutes before I go home. I've been playing Hi-Lo Stud (down about $500) and some $300-$500 buyin no-limit (up about $600). They did have a list for the $500NL game yesterday, and there were two $300-500 games going. Supposedly a lot of the regular players are at the Commerce for a holdem tournament series. I do hope the game kicks back up again soon, since I think it's the most profitable for me. Also, they might lay me off otherwise!

Meanwhile, people have been talking about the murder of a $20K jackpot winner on his way home from Hawaiian Gardens late Thursday or Friday night. The story is that the victim fought back against the thief and was hit by a car driven by the thief's accomplice. His girlfriend apparently escaped unharmed. There was some speculation at the casino that the girlfriend may have set him up.

This sort of thing is, of course, unfortunate, and for me it's also rather scary. I personally leave all but a few hundred of my cash at the casino each day, but I'm not sure a thief would realize I did this. It's not hard to recognize me as one of the regular players in the $500 NL game, and it might seem reasonable to assume I carry my entire bankroll with me. Indeed, I think there are a few people who do this. Unfortunately, this must make us all very tempting targets.

Preparing to Return

2010-08-30T12:04:00.000-07:00

After four weeks without poker, it can be a little hard to get back in the swing of things. You might think taking a month off would refresh my poker juices and have me chomping at the bit to get back to the tables, but the truth is I don't think about the game at all when I take time off. I'm going back to work in two days, though, so I figure I should get my mind back to thinking about poker a little. I'm a surprisingly good book called The Full Tilt Tournament Poker Strategy Guide, in which different authors each write one or more chapters. Authors include Chris Ferguson (which is why I got the book), Ted Forrest, Gavin Smith, and Howard Lederer. Although it is billed as a tournament guide, many of the chapters can be applied almost directly to cash games. I just finished a really useful chapter by Andy Bloch that includes lots of nifty charts. One of them completely trumps the interesting but completely impractical "Sklansky-Chubokov" numbers found in No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller. Bloch's numbers are similarly interesting and impractical, but slightly more practical and thus slightly more interesting. Basically, both try to give you an idea of when it's better to go all-in rather than fold if you are heads-up and your decision is binary (push or fold). Bloch's other charts include the win percentages of every hand when up against a random hand or a top 10% hand, as well as some other hand ranges.

Anyway, I'm hoping this book will pique my interest in returning to work on Wednesday.

Keeping the Props

2010-08-08T09:53:00.000-07:00

Last year I took almost three weeks off in August. This year I'm taking the whole month off. The Bike's big Legends tournament is in August, and they figure they don't need the props because they'll have plenty of players this month. The big news, though, is that we'll all be coming back at the end of the month. There had been rumors swirling since late June that we were being let go, and it was assumed that this would happen by August. In the middle of July, they called us to a meeting, and I think most people assumed we were going to be told when our last day was going to be. Instead, they told us we'd be keeping our jobs, but they wanted to emphasize some of the prop rules, such as no soft-playing and speaking only English at the table.

After the meeting, everything seems like it's back to normal, including the soft-playing and the Mandarin-speaking. The only thing that really changed is that a few props started looking for jobs at other casinos, and I suspect the Bike will lose at least one of their better props. It still seems like there's a decent chance the management will change its mind again and let us go in a few months. If they do, it wouldn't be a disaster for me; I could go back to playing on my own and take more time watching the baby. For the time being, I'm targeting September 1 as my return date.

Poker Ethics

2010-07-13T23:12:00.000-07:00

There was a doozy of an ethical dilemma last week at the poker table. I think I probably should have acted differently, but it's not entirely clear.

There are lots of rather subtle ethical dilemmas that come up in poker, and I am comfortable coming down on the side of keeping the game as pure as possible. Sometimes two players will collude, and this can run the gamut from the very subtle to blatant cheating. As an example of very subtle collusion, two friends at a table might agree to check whenever they are the only two left in a hand. This might seem harmless, but in some cases, one player might have a hand that he wants checked down and thus he might try to knock a third player out of the pot (or vice-versa, trying to keep a player in the pot). In the high-low stud game at the Bike, there is at least one player who takes advantage of one of his "friends" by doing this. Even if the players don't alter their decisions before the hand becomes heads-up, checking the hand down denies the other players the opportunity to gather information about how their opponents play. This isn't fair. I avoid even the subtlest collusion, but there are several players in my regular games who do this. I choose not to complain unless the collusion is at least slightly more egregious.

"One man to a hand" is a pretty well-known poker rule, but it is occasionally broken in subtle ways. Sometimes a player will show his hand to the guy sitting next to him. If this player then comments on the hand, saying, "that's an easy call," or something, this seems like a pretty clear violation of the rule, but it is very unlikely the hand would be called dead. I would still call the floorman over to make a decision. Then, if it happened a second time, maybe the hand would be called dead. Technically, nobody should be making any comment about someone's hand until it is face up on the table at showdown. Once the hand is revealed, anyone at the table can help the player and dealer to read it. Occasionally, I will notice a dealer mistake at showdown and point it out. I feel this is discretionary, but my default tends to be to point it out.

Last week, two players went all-in for about $600 each. One player, a regular who I know pretty well, had AQs and made a flush on a K7666 board. He put his hand face-up at showdown. The other player, new to the game, sat looking at his cards and the board in disgust for about 30 seconds before tossing his cards, face up, into the muck. He had AK for a full house. Although he clearly intended to concede the pot, he is technically the winner in this situation. However, the dealer immediately turned his cards face down and pushed the $1200 pot to the player with AQs. The player with AK remains oblivious to the fact that he had the best hand.

If the AK had belonged to a friend of mine, I would have called the floorman over, and most likely the player with AK would have been awarded the pot. Shouldn't I give a stranger the same courtesy? Certainly, my acquaintance with the AQs would have been disgusted with me, but, ethically, that should probably not be a concern of mine.

Potpourri

2010-07-05T11:27:00.000-07:00

It turns out that having a baby can distract me from some of my other projects, including blogging. Here are some things I've been meaning to mention for various periods of time.

In the "Asian Games" part of the Los Angeles casinos (which is where they have Pai Gao, Pan 9, Blackjack, and all the other non-poker games), since the casinos are not allowed to gamble against the players, one player plays as the "house," taking other players' bets like a Las Vegas casino would. The LA casinos simply take $5 or so each hand, as they do in poker. Instead of actual customers playing the role of "house," however, there is always an employee of a corporation. (The one at the Bike is run by the notorious "Corporation" Mike, among others.) You might think this sounds like an egregious exploitation of a loophole in the law, but I heard something even more remarkable: supposedly the corporations that work at Commerce Casino and Hawaiian Gardens are run by Hawaiian Gardens and Commerce, respectively. I'll try to get some verification on this, but in the meantime I will enjoy the idea that it might be true.

There is an episode of the TV show SportsNight in which many of the characters play poker. (Spoiler alert!) In the course of the game, the character Jeremy is winning big, while his girlfriend Natalie is losing. On the last hand, Jeremy bets big on the river, and tells Natalie something like, "I have you beat. If you trust me, you'll fold." Natalie calls and loses, and Jeremy feels like the relationship is on thin ice because of the lack of trust. Natalie apologizes. As a poker purist, I was disgusted by this. Here is how I saw it. First, Jeremy attempted to convince Natalie that he is willing to collude with her in the poker game. Trusting that her righteous boyfriend wouldn't be likely to stoop to that level (and that he wouldn't try testing her trust in such a crude way), Natalie disregarded his comment and called. Jeremy then took Natalie's money and received an apology. I don't get it. Jeremy was the one who was in the wrong!

The Bike employs "chip runners" to get chips for players at the table. To encourage tips, they make a point of telling players "good luck" when they give out the chips. One of the chip runners is a nervous old Asian woman who can be rather cloying in her attempts to make a good impression. I had to laugh when a player called her over with "Hey! Bad-Luck-Chip-Lady!"

Speaking of chips: As of May 1, casinos in Los Angeles will no longer accept chips from other casinos. Accepting competitors' chips had been standard practice, but supposedly there have been some counterfeit chips recently.

Speaking of counterfeits: Two popped up in our $500 NL game last month. A player used them to pay off a $200 river bet. The winning player was alerted by others at the table that the bills didn't look right, and he had them checked at the cage; the losing player then gave him another $200. Since then I've stopped keeping bills on the table, and I immediately change any bills I win.

Johnny Moss was the king of poker before Doyle Brunson. According to one of my colleagues at the Bike, he was also a cheater. Please take this with a grain of salt, but the story I heard from another prop goes as follows:

In those days, players used to take turns dealing, and several of the players in Johnny Moss's game were working together. We were playing hi-lo seven-card-stud, and the deuce of clubs opened. By the end of the hand, I had made three of a kind and a six for low. The other guy was drawing to a wheel. At the end, I showed my hand, and the other guy showed a wheel, but he had the deuce of clubs as one of his hole cards (the dealer had obviously slipped the previously folded card to him). I said, "How about I take this pot, and you guys can have the rest." The dealer simply pushed me the pot, and I left.

My June results through the 20th were fantastic, already a personal record for a single month. However, I lost a couple thousand in the last ten days.

UCLA Poker Panel and Another Poker Riddle

2010-05-31T21:56:00.000-07:00

Last week, as I mentioned, I went to see Chris Ferguson and Bill Chen at UCLA. The event was entertaining, as the panelists recounted anecdotes about Chris and joked about how he well-known he is. I had been hoping it would be more informative, perhaps with some online poker-data analysis or even a mathematical proof or two. However, nothing even approached that level, and it seemed like nobody there had ever even tried looking at online data. There was some discussion of the state of poker game theory and whether poker computer programs would ever be able to beat the best human players. Ferguson and Chen agreed that heads-up limit hold'em might be solved within ten years, and that computer programs might already be as good as people (only in heads-up limit hold'em), but it would be very hard to judge who is "best" unless many hundreds of thousands of hands were played. Chris's dad added that poker in general is unsolvable, since with more than two players, you can expect more than one equilibrium point (a well-known, general result of game theory). The event seemed to be at least partly for promotional purposes, as it was put online and Bill Chen made frequent book references, while the backdrop was initially a Full Tilt advertisement.

At the reception afterward, I didn't see Chris Ferguson, but I spoke a bit with Chris's dad and a bit more with Bill Chen. I asked Bill a little about his book, and jokingly asked when the sequel would be coming out. He said that they might be writing an example book where they look at 100 hands and analyze them with game theory. Sounds interesting. In order to slip away from my group of 3-4 people, Chen left us with the following riddle: if you hold 9333 in Omaha, what are 3 ways you can make the nuts? One way is to have 999 on the board (without a bigger quads or straight flush possible, of course). The other two are harder to see... as a group it took three of us a few minutes to figure them out, but none of us are Omaha players.

Here is the video of the event. I don't recommend viewing it, but I think it's about time for this blog to become a multimedia experience. I didn't watch most of it, but it seems to begin in the middle of Professor Tom Ferguson's tribute to his son.

Chairs, Dealers, Lawsuit, and the Full Tilt Book

2010-05-21T22:31:00.000-07:00

I like the atmosphere at the Bike. I think it's very player-friendly, especially in the Plaza section, where the food is free. However, I have to say that the chairs are mostly terrible. There are a few that are very comfortable, but about 80% of them are broken. Whenever a new player shows up at the casino, he complains about the chairs. Today someone said he felt like he was on a boat and was getting seasick. Instead of getting new chairs, the Bike has reupholstered some of the old ones, seemingly unaware that most of them were already broken and needed to be replaced. I'm afraid this means they have no intention of replacing them anytime soon.

The Commerce is getting over some more serious issues. I heard that ten out of eleven of their Dealer Coordinators were fired last month, and over one hundred dealers were suspended. Supposedly, most of the dealers were bribing the DC's in order to be put at the best tables (presumably, the tables with the best tippers).

The lawsuit against the Los Angeles casinos for their Jackpots has been thrown out by the judge. My understanding is that the jackpots are required to be "No Purchase Necessary" like any other sweepstakes. The casino does take out $1 per pot to fund the jackpot, but they offer people the opportunity to play for free. I've never seen it, but a friend told me he tried this out one day at the Bike. He and a couple other players sat at a table and were given tournament chips. Nine hands were dealt out, including to seats without any players. The flop, turn, and river were dealt, and if the jackpot was hit, the casino would pay out 10% of the jackpot at the normal ratios. So 5% would go to the losing hand, 2.5% to the winning hand, and the rest would share the other 2.5%. This was repeated ten times, and then the table broke. Seems pretty ridiculous to me, but that suffices to cover the casino legally.

I bought The Full Tilt Poker Strategy Guide: Tournament Edition. I was told that Chris Ferguson had some interesting things to say in the book (specifically, that it is worth avoiding difficult decisions, which I contradicted in my NLHE: TAP analyses). I thought it would be good to try to read Ferguson's arguments before I go to the event I mentioned in my previous post. Besides, the book got good reviews.

Chris Ferguson at UCLA

2010-05-17T23:23:00.000-07:00

A friend at UCLA just registered me for an event at UCLA with Chris Ferguson and several other people discussing "Math, Computer Science and Poker." Among the other panelists are Chris's father Tom Ferguson (one of Brigid's professors) and Bill Chen, author of The Mathematics of Poker.

I'm tempted to go back and look at my notes from Mathematics of Poker to try to come up with some intelligent questions. It might be more interesting to try to get opinions on more general poker theory, though. I don't really know if I'll get to ask any questions, but it should be pretty interesting.

Poker Future?

2010-05-10T15:36:00.000-07:00

I've been thinking vaguely about quitting my job or taking on further-reduced hours, which would force me to forfeit my insurance benefits. The main argument for reducing my hours is that it would give me more time to help out with the baby, which would allow Brigid to put some more time into her studies. If I were to do that, I might be better off just quitting my job altogether, because I would lose my benefits anyway, and the Bike's $500NL game has gotten much tougher in the past few weeks. This is likely a temporary situation, but it got me thinking about whether I could stand to move up in stakes. There is a regular $60-120 limit game at Commerce and occasional $100-200 games. If I use careful game selection, only playing when I know the game is juicy, I think I could probably crush these games. On the other hand, I would have to be willing to absorb some nasty swings. My guess is that, in the end, my win rate would be barely better than what I'm making now, taking my salary into account. My volatility would probably be nearly three times higher per hour. Adding to "volatility" is the fact that I really don't know what I would be getting into, so my expected win rate could be pretty much anything, potentially even negative (I think I would realize this and give up after a day or two). So, financially, I'm inclined to say it probably would not be worth it in the short term.

Of course, there are many other considerations beyond my short term financial well-being. For one thing, I think playing different and bigger games has the potential to make me a much better player, possibly increasing my long-term prospects. This argument is tempered by the fact that I think my current position playing $500NL is also very challenging and giving me some valuable experience. Another question that I think deserves consideration is: which would be more enjoyable? Well, it would certainly be nice to have my freedom back. My job is not particularly oppressive, but I do have a boss and hours and responsibilities. On the other hand, table selection is one of the least exhilarating aspects of being a poker player, and, for better or for worse, having a job largely removes this aspect. If I quit and try to prey on weak $100-$200 games, table selection will become my main occupation. I will probably want to give my phone number to some regulars or a floorman and try to persuade them to call me when the game is particularly good. I think there is something especially unsavory about being so explicit about preying on specific players. I'm reconciled to the fact that I don't add much to society when I play poker for a living, but I'm still not particularly proud of it. Playing high stakes would certainly be a bit more exciting, at least for a little while, but it would also be accordingly stressful. I find it a bit hard, psychologically, to shake off $3k losses, and these would be commonplace in a game as big as $100-200. Finally, I just don't like being at Commerce that much. The quieter atmosphere at the Bike is much preferable to me.

At this point, I think I'd prefer to keep my job even if I reduce my hours and lose my benefits. In year or so, I'll have a bigger decision to make as far as my career goes; Brigid will be finishing her PhD, and we might be moving out of L.A.

Philosophies on "Running it Twice"

2010-05-03T22:38:00.000-07:00

In the $500 NL game I play in, players are allowed to make a specific type of deal if they go all-in before the river: they can run the rest of the cards either two or three times and then split the pot in halves or thirds, respectively. The pieces of the pot are distributed according to who won each of the two or three iterations. (I gave an example in this post.)

It is strange and fascinating to listen to other players' philosophies on whether to make a deal and whether to run the board twice or three times. As far as I can see, there are only a few things that deserve any consideration:

1. What is my EV for each option? This can be answered mathematically: my EV is the same for all three options. This follows from the fact that EV(A+B) = EV(A)+EV(B), regardless of whether A and B are correlated. If we take A to be the first running of the cards, and B to be subsequent runnings of the cards, we can see that the EV does not depend on what type of deal we make.

2. What happens to my volatility for each option? This can also be answered mathematically: the volatility is lower if you run the board more times. This is the reason why running it more times might be worthwhile.

3. How much time is this going to take? If you are a winning player, you can lose money if too much time is wasted. Also, I would consider it bad table etiquette to needlessly waste the other players' time. Splitting the pot three ways can take a while. In fact, last week I won five-sixths of a pot because we ran the board three times and we chopped the last one, and this took a minute or two to sort out. Another thing that can waste time is the possibility that your opponent might take a while to decide whether to make a deal. I've seen such a decision take over five minutes.

4. How will this affect my table image? Being willing to run the board twice can change the way people play against me. The most significant difference is probably that some players may try to get all-in earlier in the hand in order to give themselves a chance to make a deal and chop the pot. They also may be more willing to call my all-in bets before the river. This is probably a good thing, since players are deviating away from trying to maximize their EV, but for certain players, it likely makes them play better (if they will now call with +EV hands that they would have otherwise folded).

Points 1 and 2 seem to me to be by far the most significant, but I also often consider point 3 and choose not to make a deal if the pot is small. I do this out of respect for the other players' time and because I figure it won't add too much volatility to my winnings. Point 4 is one I don't worry too much about, but it seems like it could be a reasonable consideration.

Most players know points 1 and 2 (minus the math), yet they often take longer than a minute to decide whether to make a deal. What could they be thinking about? Clearly it's not point 3 (time considerations), or they wouldn't waste everyone's time with their slow decisions. For most players, it's not point 4, either. The answer? Whim. This wouldn't be so bad if it weren't for the fact that they clearly consider these decisions to be excruciatingly important, and once they form their opinions on which option is best, they smugly ridicule players who make a different decision. Listening to them argue about it is like trying to watch one of those shows where pundits discuss politics. Nobody has any evidence to support their claims, but they are all quite satisfied in their certitude. For example:

"If I call a big bet with a draw, I'm trying to win the whole pot. Why run it twice? To get back half the pot? It's better to just fold and save your money than call and make a deal."

"If you initiate the thing, it's three times," meaning that if you put in the bet and are called, you should always run it three times, rather than twice.

Maybe I'll try to document more of these, but the point is that the decisions are made on a whim, and then supported with whatever "evidence" seems to fit.

The Week at the Bike

2010-04-05T15:19:00.000-07:00

I've been back to work for two weeks now (working only Tuesday - Friday). Transitioning back was easy. I realize I actually missed eating at the Bike - the food is quite good, but I get tired of it after a few weeks. A lot of the regulars in the game have good senses of humor, so it's fun to be part of that again, too. It also helps that I haven't yet had to play with "Corporation" Mike, who I find extremely unpleasant.

Early in the week I witnessed a pretty despicable angle shot and an interesting floor decision, which was explained to me the the next day. In this hand, Tony had the nuts on the river (a 7-high straight) and bet $400. His opponent, Jack, was on the far side of the table. Jack hemmed and hawed for a minute, counted out $400 in purple $25 chips, cupped his hand over the stack, and moved it forward. Tony quickly showed his hand, which is considered good etiquette when you are pretty sure you've won. In this case, however, he had been duped by Jack, who lifted his hand to reveal that there were no chips under it; he had left the stack back behind the line when he slid his hand forward. Jack had purposely used his arm and hand to block Tony's line of sight. Tony, obviously upset, argued that Jack should have to put the chips in. Jack defiantly refused, and the floorman John was called over. In my opinion, this is a difficult decision for the floorman (much more difficult than in the Diane situation). Technically, Jack did not move any chips forward, which is the usual standard. My expectation was that Jack would probably get to keep that $400, but clearly what he did was manipulative well beyond what is acceptable. The floorman couldn't decide what to do, so he took $400 from Jack and gave Tony the pot. He took the $400 with him as he went to go "check the cameras." Really, this was just a way to buy time before making a decision, since there was no argument about what had happened. While John was gone, Jack remained defiant, saying "I know it was wrong what I did, but I didn't move the chips forward so I don't have to put the money in!" Someone asked, "if you knew it was wrong, why'd you do it?" His explanation was comically lame: "I did it!" The floorman came back and gave the $400 to Tony after a little more protesting from Jack.

The next day I talked to John about the decision. He told me that the lead floorman watched the video with him, and told John: "Go out there and tell him he's a good magician. Give the money to Tony." I told John that I didn't mind the decision, but I didn't really understand what rule was being invoked. John came back a few minutes later with the (previously mythical) rulebook and said, "Rule #1."

I read rule #1, which went something like this: "The Bicycle Casino reserves the right to make any ruling that is in the best interest of the game, even if there is no explicit rule listed." That seems about right to me. There was at least one regular player who would have left if the decision had gone the other way, and I couldn't blame him for not wanting to play in a game where Jack was allowed to trick people like that.

On Wednesday night at 7 pm (exactly when my shift ends), there was a $50,000 freeroll tournament open to anyone who had at least 15 hours of play in the past month. Extra chips were given to people with 25 or 40 hours. (A similar promotion is in effect this month.) Usually, employees are not eligible for promotions, but for some reason we were allowed to participate in this one. I managed to get my card swiped 25 times, but I really didn't want to have to stick around for the eight hours it would have taken to win the tournament. My solution was to play hyper-aggressive at the beginning of the tournament. That way I could either go home or get a big stack and have a good chance at some money. At 7:40 I was in my car driving home.

On Friday I received some compliments and an interesting offer from Mario Esquerra, who is a semi-regular in our game. Mario is only okay in cash games, but he has an impressive tournament resume: over $1mil in total winnings, including a 3rd place finish in the WSOP main event in 1999. He's also captain of the Mexican team in World Team Poker. From previous conversations, I also know that he used to be a professional insurance fraud and subsequently became a born-again Christian. When he sat down on Friday, we were playing 5-handed, and he asked me, "when are you going to graduate?" I asked what he meant by that. "When are you going to play higher stakes? Your game is ready for you to be rich." A couple minutes into the conversation, he offered to coach me for two weeks. "All of my students have become millionaires." He listed Toto Leonidas among his disciples. He told me, "there is more money in this game than in the oil industry!" I haven't given him a definitive answer, but I think I'll decline. I'm curious, but I doubt he has much to tell me that I couldn't learn from a book or figure out for myself.

"Indian" Jay

2010-03-29T22:06:00.000-07:00

Perhaps the biggest donator in the Bike's $500 NL game is "Indian" Jay. According to Jay, he is actually Pakistani (which is probably true, but he also claims he gets his money from being a pimp, which I suspect is untrue). In any case, he's in his early 50's and gets his kicks by asserting verbal dominance over the table by insulting everyone, making vulgar jokes, and making ridiculous overbets to give people difficult decisions.

Many players like to sit to Jay's left, following the conventional wisdom that you should sit to the left of weak, loose players, because you will get to act after them on every street in every hand, giving you the best chance to win their chips. While this is probably true in moderate cases, especially if the weak player is passive, I think this logic is far too simplistic in extreme cases such as Jay, who is aggressive. With some types of loose players, especially in full-ring no-limit games, I think it is much better to sit to the player's right.

Let me explain what I mean. The logic behind the conventional wisdom goes like this: sitting to the left of a player allows you to see what he does before you have to make a decision, and this will give you an idea of what he might be holding. If that player is playing every hand, you maximize the number of times you can use this advantage. This logic breaks down, however, if the player is crazy or doesn't know what he's doing, because his actions are nearly random and will actually give you very little information about his cards. If this player often raises instead of merely calling, you are in even more trouble because you are now at a disadvantage against everyone else at the table; you have to respond to the maniac's raise before you get to see what everyone else does. By sitting to the maniac's right, you can observe how everyone responds to his raises before you decide what to do. This can save you a lot of money, and sometimes suck in a few extra bets when you have a big hand. In the Bike's $500NL game, the advantage of sitting to the right of a maniac is increased even further because you are allowed to straddle from any position. Maniacs tend to take "advantage" of this, so sitting to his right means you act after everyone else before every flop.

Jay fits this definition of a maniac far better than anyone else in this game. He goes through long stretches where he straddles and raises 90% of his hands, sometimes without even looking at his cards. Then he makes terrible decisions after the flop. For example, I once saw him in a three-way hand with one player all-in. The flop came 567, and the pot was about $500. Jay checked, and the other player still in thought for a few second. Jay showed the 2c. The other player went all-in for $500, and Jay called. What could the other card be? A 7 or an 8 maybe? Nope, he had a J2.

Needless to say, I like to sit to Jay's right and just let him do the betting for me. Admittedly, betting into him will also work just fine most of the time, but why bother when he will bet it himself and I can watch how the rest of the players react? When he is in one of these moods (which is at least half the time), I will limp with a wide range of hands and fold the rest. I simply will not raise before the flop. Let me give you four examples from Thursday and Friday (incidentally, I lost all four). To be fair, I want to point out that these are picked from several hours of play, but Jay had plenty of other similar hands that I was not involved in.

Hand 1: Jay straddles for $20 in late position. I am to his right and limp with AKs after several limpers. Jay raises to about $100 and gets two callers. I raise to $500. Jay raises all-in to about $600. Everyone folds. I call. Jay shows 76o.

Hand 2: Jay straddles. A few limpers. I limp with A5s. The player to my left limps. Jay recklessly tosses in about $100 of yellow $5 chips. All fold. I raise all-in to about $600. The player to my left folds. Jay calls and shows T3o.

Hand 3: Jay straddles, I limp with A4s after a couple of limpers, Jay raises to $200. All fold to me, I raise all-in to $800. Jay calls and shows ATo. (Whoops!)

Hand 4: Jay straddles. A couple of limpers. I limp with ATo. Jay raises, all fold to me, I go all-in for about $500. Jay calls with AQo. (Oops again!)

Hmmm, looking at that progression it seems like Jay may have set me up a bit for those last two hands, but I still don't think I should play those hands any differently.

Raising as a Bluff

2010-03-22T14:40:00.000-07:00

I'm going back to work tomorrow. Since I haven't thought about poker for six weeks, I thought I'd get my mind back in shape by describing a play I made a few months ago. In this hand, I was playing against another prop: a good player who is very observant and has a very clear idea of how I play. He looks for opportunities to exploit my tendencies whenever possible. Knowing this, I make sure to stay on my toes against this player, and sometimes I'm able to catch him bluffing me. I think he is a winning player, but he sometimes succumbs to "Fancy Play Syndrome" (FPS). I don't think he'd ever seen me make a play like the one I made on the river in the following hand, wherein I raise the river as a bluff after my opponent had shown strength. In fact, I'm not sure I'd ever made such a play before this.

I'm starting to worry that people at the casino may have discovered my blog, or will soon, so I am going to refrain from naming the other prop. Let's just call him "X".

This hand is from mid-November. I made some notes after the hand, and I'm going to try to reconstruct my thought process. I don't remember how many players there were, but my opponent was in the big blind, and I was two to his left.

I limp in with AhJd and $1260 behind. One other player and the small blind limp. X checks (he has me covered.

Flop ($35): Ac 5s 3s. X checks, and I value-bet $25. Everyone folds to X, who check-raises to $75. I call. X knows I continuation-bet a lot, but this is not a c-betting situation because I didn't raise preflop, and I had a player behind me. Still, X knows I will bet and fold with plenty of hands here, so he could have just about anything. I can't fold because even though I am now on the defensive, the chances are just too good that X is bluffing or semi-bluffing.

Turn ($185): Jh. X bets $150. I call. The Jack puts me ahead of any flopped two-pair, which are unlikely but plausible holdings. I like my call here (as opposed to a raise) for a few reasons:
1. If X has nothing, this play is best because he might try to bluff again on the river.
2. If I have X beat, he will probably fold to my raise, but I will be able to get another bet from him on the river if the river card isn't too scary.
3. It's becoming more likely that X has a real hand or a strong draw. If X has a draw or a strong hand, he might re-raise. If I then fold (which I might), I will have lost my raise plus the chance to see the river card (on which I could make a full house). I could call, but that might be even worse.
4. If the spade flush hits, I can probably win the hand with a raise on the river. My line to this point looks to X like I have either a moderate made hand (which I do) or a nut draw. Unless he has the nut draw himself, he will probably have to fold to such a raise.

River ($485): Qs. X bets $225. I raise all-in for $1025 total. X folds. As you can see, #4 above came into play, but it still took some nerve to pull it off, if I do say so myself. I would've felt better if I had the As rather than Ah, because then I could be sure I wasn't up against the nut flush. Also, I could have just called to catch X's bluffs, but this is a marginal play at best. In retrospect, I still this raise-bluff was the best play. I think X would even fold a straight or a baby flush in this situation, because he felt he had such a good read on me. That is, he felt he knew I had a nut flush or a made hand, and he has to figure I would never try to bluff with a made hand. After all, consider Concept No. 47: "If it's clear your opponent has a hand at least worth a call, but he raises instead, it's almost never a bluff." This may have been the thought that went through his head after I raised. However, my hand was right at the bottom edge of my calling range on the river here, which means it is close to the optimal type of hand to raise-bluff with.

Hiatus Update

2010-03-14T00:29:00.000-08:00

As expected, I have played no poker during my break so far. On my list of projects is: "study poker/game theory," but it's in the middle of a list of similarly ambitious projects. Indeed, I've barely given a moment's thought to poker since Calvin was born, and I also have to do my taxes. (I'm joint-filing this year, but I don't think I can claim Calvin as a dependent until next year!) However, since I don't want to be completely rusty when I go back to work March 23, I'll try to write an analysis-type post before then.

Baby Time!

2010-02-17T11:00:00.000-08:00

My wife Brigid and I had a baby boy on Wednesday, February 10, at 7:02 pm. We named him Calvin Brett Wilson, he was 9lbs, 4oz, and after a rough couple nights, he's been letting us sleep pretty well at night.

I'm taking six weeks off from work, and I will probably play almost no poker until then. If I have time before then, I'll post some thoughts and stories from the past few months at the Bike.

"Santa Claus" Steve, Running the Board Twice, and a Bad Beat

2010-01-27T23:30:00.000-08:00

On Friday, I suffered what I think was probably my worst beat ever. I consider it bad form to tell bad-beat stories (nobody really wants to hear them anyway), but there is a ridiculous story around this that makes it rather interesting, and I wanted to use this opportunity to describe the practice of "running the board" twice or three times.

A regular player in my game is an elderly man named Steve. Steve is a losing player, but supposedly a few years ago he played far worse, virtually giving his money away whenever he came to the table.This along with his white beard earned him the nickname "Santa Claus" Steve. Despite being extremely animated and friendly, Steve often seems on the brink of death. He is diabetic, has heart disease, and his fingernails are falling off. He is sometimes medicated with Valium and probably other drugs, and he aggravates his condition by regularly playing 24-hour sessions regularly, including drunken ones at the Korean home game that I've been invited to. Anyway, on Friday he arrived at the Bike while I was playing in a $300-500 buyin NL game. He walked right up behind me and began telling me a bad beat story from 4 am that morning at the Korean club. I said "Hi, Steve," and turned back to my game. This didn't deter him from continuing on with his stories, as he proceeded to tell me a second and a third story from the previous night without any response from me. This was unusual behavior even for Steve.

Later, Steve told me he had been up for about 40 hours at this point. There was nothing I could do to get him to shut up. I knew I was going to be playing with him all day, so I went to the gift shop and bought some headphones for my iPod. I generally do not listen to my iPod while I play because I find it too distracting, but I clearly needed to be able to tune out Steve.

Without exaggeration, I would estimate that Steve talked for 45-60 seconds out of every minute for the next 7 hours. I was glad for my iPod, but he was still really getting on my nerves. Two of the bigger losers in the game left early because they could not put up with Steve's incessant ramblings. At one point I refused to rabbit-hunt for him after I won a hand from him before the flop. This upset him greatly and he told me he was making a target of me and would be putting me all-in before long.

The "bad beat" hand in question happened about 5 hours into the session. Before I describe the hand, I need to explain a type of deal that is sanctioned at the $500+ buyin NL game at the Bike, and possibly at other casinos.

If there are only two or three players left in a hand and everyone is all-in with more cards to come, those players still in the hand can agree to deal out the rest of the cards either two or three times. Then the pot is split into two or three pieces, and each player gets as many pieces as number of times he his hand won. For example, if I go all-in with AK and get called by QQ, my opponent and I can agree to run the entire 5-card board twice. If I win both times, I get the whole pot. If I win one of the two times I get half the pot. If I lose both I lose the pot. Deals can also be made after the flop or turn.

On the hand in question I was in the big blind with 86 of diamonds, I had about $3000, Steve had $1380, and the small blind had about $1300. One person limped for $10. Steve raised to $50 on the button, the small blind (a weak player) called, I called, and the limper called.

The flop was 9c7c5d, giving me a straight for the nuts and also a backdoor flush draw. When the small blind checked, Steve was rambling on and said something about needing to make a continuation bet. I decided to check, too, figuring Steve would probably follow through and make the promised c-bet. The third player checked and Steve made a huge bet of $500 (the pot was only about $200). Surprisingly, the small blind pushed all-in. I also pushed all-in, and Steve called for his last $830.

This was a big pot, and I figured I was up against a club flush draw, so I asked my opponents if they wanted to make a deal. Steve said, "well, let's see what you have," so I showed my 8d6d. The small blind showed Ac6c, for the nut flush draw and a straight draw. Steve had QcTc, for a flush draw.

"No way, I don't want to make a deal," said Steve, continuing to shout more inane comments. My supervisor, who was also in the game, yelled at Steve to be quiet and reminded me and the third player that we could still make a deal without Steve. So we agreed that, assuming Steve lost on the first run, we would run the turn and river two extra times and split the pot accordingly. I expected to win two thirds of the pot, or maybe only one third if I was a little unlucky.

Notice that Steve's only chances of winning are for the turn and river to come KJ or J8 with either no clubs or both clubs (for a straight flush). Also, even if neither card was a club, if both cards were diamonds, I would make a flush to win. Surprisingly, this means he has a 2.21% chance of winning, or about 1/45. I would win 61.24% and tie with the third player 6.53%. The third player would win the remaining 30.01%.

Needless to say, Steve won the $4000 pot as the turn and river came Jh Ks. I counted out $1330, gave it to Steve, put back on my headphones, and played the next hand.

Baduci

2010-01-17T19:19:00.000-08:00

There's a new poker game being played at the Bike called Baduci. Supposedly, it's being played at Commerce and the Bellagio, as well, but at the Bike it is usually played at $30-60 limit stakes.

Baduci is a split-pot combination of badugi and deuce-to-seven triple draw. In both badugi and 2-7, players have three draws and try for the low hand. In badugi, you need four different suits, so the best hand is A234 of different suits. In baduci, though, A is always high (at least, the way it is played at the Bike), so the best hand is 2345. In baduci, half the pot goes to the best four-card "badugi" hand, and the other half to the best five-card 2-7 hand.

I like playing new poker games. It forces me to concentrate intently and work out strategies, which is my favorite part of poker in general. However, 30-60 is way too expensive for me to try an entirely new game, even if there are known fish at the table. So, some other props and I have started playing 5-10 baduci until customers show up to play the $500 NL game. This past week I played a total of 4 hours and lost about $50. Sometimes other people will join us for our baduci game - on Friday, I was the only prop playing, but I played heads up for over an hour and won $39.

My Job As a $500+ NL Prop So Far

2010-01-04T10:06:00.000-08:00

It's been a little over three months since my "promotion," and I think taking the position was a good decision. One of the main things I was worried about was the massive egos I would have to deal with. Indeed, this has been a bit of a problem at times. The most ridiculous example is "Corporation" Mike (who supposedly owns the corporation that acts as the "house" in the table games, because it is illegal for the casino to do this on its own in Los Angeles), but there are several other examples. Sometimes they manage to get to me, but I just say very little to them and eventually they stop bothering me. Another thing about I was worried about, of course, was how well I would do in the game financially. As it turns out, I've done very well (perhaps my NLHE:TAP analyses have helped a bit), but my volatility has gotten a little out of control.

For various reasons, I've resisted revealing most of my poker results here in the blog. However, I want to make an exception because the increase in both my win rate and (especially) my volatility is quite remarkable. The sample size is not particularly large considering the huge variance inherent in poker results, but you can make of it what you will.

From my promotion through December 31, I played about 450 hours of poker, including 357 at the $500+ NL holdem game. My win rate and my variance in this NL game are both approximately twice what they were previously. Specifically, in those 357 hours I have won about $60/hour, but my hourly standard deviation is about $630/hour. For a whole day of playing for eight hours, this works out to $480 +/- $1780. This means that it's not at all unusual for me to lose over $1500 in a day or win over $2500. When I took the job, I was expecting something more in the range of $20/hour and $300/hour ($160+/- $850). In all, the experience has been quite a lot more stressful (between the egos and the swings), but I can't complain given my results and the pay bump.

Another interesting statistical question is: what is a 95% confidence interval of my "true" win rate? Yes, I have a win rate calculated from my results, but what can I expect my win rate to be in the future? This is complicated by the fact that I also don't know what my variance will be in the future, but let's just assume my variance stays at $630/hour. Then, if I am doing this correctly, I can say with 95% confidence that my true win rate is $60 +/- $65 per hour. This is a very big range, so I shouldn't get too excited! My guess is that my "true" win rate is somewhere around $30/hour.

Analyzing NLHE: TAP Concept 60

2009-12-31T10:09:00.000-08:00

This is the final installment of my series looking at the sixty concepts at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller. Soon I can get back to telling stories from the felt, but I also want to revisit some of these concepts, as well as the project as a whole, in future posts.

Concept No. 60: If someone bets into several players, and you have a hand that is somewhat likely to be best, but unlikely to improve, you often have to fold.

Yes. Similar ideas have been discussed in topics a few times before (particularly concepts 18 and 32, and to some extent concept 50, while concept 6 sort of argues the other way). I agree with the author's closing statement that this may be the single most profitable concept in the book for many readers. The reason is that our human nature (mostly due to the regret aversion and confirmation biases) begs us to call in this situation. For example, if we call with top pair and a good kicker and someone raises behind us, or if we have to fold on the turn or the river, this is easily written off as bad luck because we couldn't have anticipated those things, and we don't regret our call; hence, we will probably call again next time. Of course, the fact that there were so many possibilities we could not anticipate is what should have made us decide to fold. On the other hand, if we were to fold and it turns out we would have won the hand, it is psychologically devastating, and we are likely to call in such a situation next time.

With several players yet to act, two cards yet to come, and very little chance to improve our hand, we lack all sorts of crucial information that we would need in order to continue the hand profitably. Certainly, it depends on the situation (perhaps your hand is a big favorite, or your opponents are very passive), but many players call far too liberally in such situations.

Analyzing NLHE: TAP Concept 59

2009-12-30T09:46:00.000-08:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 59: Don't help your opponents play correctly.

I agree with this one, and it seems incontrovertible, but there is at least one example of advice that suggests you should help your opponents to play correctly. I think it is worth considering.

Barry Greenstein has a total of eight "play lessons" in his book Ace on the River. Lesson 5 says the following: "If your bets define the strength of your hand, it may make decisions easier for you on later streets." The idea is that if you confuse your opponents too much, you will have trouble interpreting their plays later in the hand, and you won't know how to react. I think Dan Harrington may have similar advice in his book, but I can't quite remember. Anyway, I think Sklansky and Miller's concept holds up despite Greenstein's lesson. You can use Greenstein's advice for your made hands but still make it difficult for your opponents to play correctly if you play bluffs in the same way. However, bluffing actually seems to go against Greenstein's Lesson 5. He suggests you let "your bets define the strength of your hand." This implies that you should not let your bets "equivocate" (my word, not his), which is what happens if your bets could mean either a bluff or a made hand. Bluffing occasionally seems to go against Greenstein's Lesson 5, and so it should not be taken too seriously. I have to take Team Sklansky's side on this one.

Okay, just one more concept to go. Hopefully, I'll finish this year after all!

Analyzing NLHE: TAP Concept 58

2009-12-27T16:38:00.001-08:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 58: Any strategy relatively close to a game theoretical strategy is at least almost as good as the optimal strategy, and sometimes it's better.

Sklansky and Miller are a little messy with their terminology here, but I think they get their point across. The way I interpret this concept, I agree with the authors. Here's my interpretation: even if you don't know precisely what the optimal play is (and you probably don't), it's still worth trying to approximate it. Playing a strategy that is close to "optimal" (that is, unexploitable) is almost always better than playing a strategy that is not close to optimal. Furthermore, if you have identified exploitable weaknesses in your opponents, it can, in fact, be better (in terms of EV) to deviate from the optimal strategy. One problem I have with this idea is that there probably is no mathematically "optimal" strategy in games with more than two players... but I think the main idea still holds up.

I disagree with the last two sentences of the books discussion. It says: "If you plan to make a play that will give away your hand, choose a different play occasionally and make the same play sometimes with a different holding. If you do this consistently as you play, you'll usually do even better than the game theoretical strategy."

First, I don't agree that you should necessarily change anything just because you plan to make a play that will give your hand away. Hopefully, you've chosen this particular play because it maximizes your EV, so changing it can only reduce your EV. S+M suggest either choosing a different play occasionally (but assuming that you've chosen the play that maximizes EV, changing will lose you money), or making the play sometimes with a different holding (I suggest you only do this if you can do so without losing any EV with this other holding). I've discussed before why I don't like the idea of making certain plays "occasionally."

Second, S+M suggest that as long as you think about what your range and your opponent's range is, and you mix up your play, you can do better than the game theoretically optimal strategy. I doubt that this is true unless your opponents are tremendously weak. The problem is that it's impossible to avoid making mistakes, so very few people would ever be able to do better than if they could consistently play an "optimal" strategy. However, if your competetion is weak enough, you can probably find enough opportunities to exploit them to make up for all of your mistakes.

Analyzing NLHE:TAP Concept 57

2009-12-26T22:42:00.000-08:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 57: Don't be fooled by players who have giant amounts of cash in front of them.

Sklansky and Miller suggest in their discussion that players who buy in for exorbitant amounts often do so in order to trick other players into thinking that they will be willing to lose their entire stacks, thus enticing these other players to play too loosely. This doesn't fit my experience at all. In my experience, players who buy in deep do so either for mundane strategic reasons (they feel they can outplay the other players at the table with deep stacks) or in order to gain a psychological advantage (either they want to intimidate the shorter stacks, or they want to avoid feeling intimidated). I don't think anyone buys in deep in order to trick players into gambling with them more.

The issue of whether it really is strategically advantageous to buy in deep is something I've addressed in posts a few times before. While many people are intimidated by playing against bigger stacks and believe they are at a disadvantage, I believe it is actually an advantage to have a smaller stack at a full table. It's possible that in certain games you will have higher expectation if you have a big stack, but this is only if you are far superior to your opponents. If everyone plays about the same, players with smaller stacks should be expected to do better.

Analyzing NLHE: TAP Concepts 55-56

2009-12-23T23:40:00.000-08:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 55: Unlike limit, limping first in on the button is frequently correct.

In a pure NL holdem game, I think this is probably right, mostly for the reasons given by the authors. Specifically, I agree that making the blinds fold is not as profitable in NL, because the blinds are much smaller compared to the normal raise size and final pot size. This probably makes some hands worth limping with, but only against certain opponents.

In practice, however, I practically never limp first on the button. This is largely because of the way pots are raked in my normal game (and most other games in Los Angeles). The casino will take out $1 if there is no flop, but they take $6 if there is a flop ($1 of which is for the jackpot drop). Winning the pot after the flop therefore costs me $5, which is a significant amount when we're looking at a profit of only $10 or $20.

Concept No. 56: Pot odds (as opposed to implied odds) matter a lot less in deep stack no limit than in limit.

Yes. This is central to the difference in the strategy for the two games. Bet sizes in no-limit tend to be much larger in proportion to the pot than in limit, so future bets will have a much larger impact. Since pot odds do not take future betting into account, they aren't as relevant in no limit poker. In no-limit, it's important to try to estimate implied odds rather than relying on pot odds to help make your decisions.

Analyzing NLHE:TAP Concept 54

2009-12-20T14:23:00.000-08:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 54: Checking to induce a bluff is a significantly stronger play in no limit than it is in limit.

Instead of taking this concept's wording completely literally (it's ambiguous how we should define the "strength" of a play), let me rephrase it in a way that I think reflects the authors' point more accurately: "Checking to induce a bluff is the best play much more frequently in no limit than it is in limit." I think this is right.

I should point out that Sklansky and Miller are double-dipping here: we've already discussed this idea in Concept 33. As I implied in that post, I personally don't usually think of checking on the turn with a moderate hand as "inducing a bluff." Rather, I think of checking as moving my hand range toward the weaker end, which then forces me to call on the river if my hand is on the stronger end of my range. I will admit that "induce a bluff" is a simpler way to get this idea across.

Analyzing NLHE:TAP Concept 53

2009-12-19T15:38:00.000-08:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 53: In heads-up pots, whether you are first or second to act is more likely to affect your decision in no limit than it is in limit.

I think Sklansky and Miller are having another issue with semantics (or perhaps it's my fault for taking them too literally), but any way I look at it, I can't see the use of this concept. It's also quite awkward trying to judge whether it's true. I happen to think it is true as stated, but not for the reasons the authors were probably thinking of. This post is an almost purely academic analysis of this concept's claim, without much poker insight, so let me apologize. I personally think it's rather interesting, though. First, let's look at the example Sklansky and Miller give.

Their example is that if you have the nut flush draw in limit holdem, you will probably want to bet regardless of whether you are in position. In no-limit, though, you should be much more willing to bet if you are first to act. If you check, they say, you are likely to have to face a bet anyway, so by betting out, you can set the bet-size yourself. If you are second to act, you might want to check to give yourself a free card and a chance to win a big pot.

Well, that is only a specific example. Let's take a step back and try to answer the question: Should your position be more likely to affect your decision in limit or in no limit? Of course, your position is only one of many factors affecting the decision of whether to check or bet. Your hand range, your opponent's range, and your opponent's tendencies are usually the most relevant. Let's imagine holding all of these other factors constant, and distill your "position" down to the following. If you are "first to act" and you check, your opponent has the opportunity to bet. If you are "second to act" and you check, the betting round ends. In either case, if you bet, your opponent has the opportunity to raise. So, in this formulation, you should always (whether you are playing limit or no limit) be more inclined to check if you are second to act, because you gain the added benefit of denying your opponent the opportunity to bet. So, the question simply becomes: Is this added benefit more valuable in no limit or in limit? I think the answer must be "no limit." Giving your opponent the opportunity to bet tends to be much riskier in no limit than in limit, because a bet can be much larger in proportion to the pot. So, denying your opponent this opportunity has greater value in no limit. Thus, I would have to agree with this concept's claim that, in no limit, your position is somewhat more likely to affect your decision than in limit.

In practice, though, we are more likely to bet when we are second to act than when we are first to act. When we are second to act, this means our opponent has checked, which means his range is weaker. When our opponent's range is weaker, we should be more inclined to bet. In my analysis in the previous paragraph, however, we held these hand ranges constant, which led us to the awkward and counter-intuitive conclusion that you would rather check if you are second to act than if you are first to act. This conclusion led me to agree with this concept's claim. However, this is, of course, not the point the authors were trying to make with the concept. This is made abundantly clear from their example about how you would play a nut flush draw, which incorporates plenty of good ideas about poker, but nothing that really addresses the concept's claim. It attempts only to show one specific case where the concept holds, and it fails even that because it does not hold the opponent's ranges constant (the opponent's range weakens after he checks).

I won't address the ideas that Sklansky and Miller were trying to get across in this concept, which they revealed in their example, except to say that I essentially agree with them.

Analyzing NLHE:TAP Concept 52

2009-12-17T21:05:00.000-08:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 52: The play of check-raising to knock people out, an important tool in limit, should rarely be used in no limit.

I think this is true. Sometimes when I check-raise on the flop in no limit, I do so with the intention of knocking out some middle-position players, but this is almost never the primary objective of my check-raise. I will either have a very strong hand or a semi-bluff.

In limit, it's sometimes better to check with a low or medium pair, and then raise if a late position player bets. This play is very likely to force players who have overcards to your pair to fold, even if they may have called had you bet out instead of check-raising. If the late position player was betting without a pair, getting these players out substantially improves your chances of winning the pot. In limit poker, as we discussed in Concept 9, winning the pot is the main focus.

In no limit holdem, this play makes far less sense. Here, you don't need to count on someone to bet so that you can check-raise in order to confront them with two bets at once. If you want to deny a middle-position opponent the right odds to call, you can just bet more yourself right out of the gate. Also, in no limit, a check-raise tends to be much more expensive in relation to the pot. Defending a relatively small pot with a large bet should not generally be your main objective (concept 9 again). When you do want to knock out middle position players with your check raise, it's either because you are semi-bluffing with a small flush draw and you want possible bigger draws to fold, or you have a made hand and you want strong draws to fold. It's not like in limit where you are hoping to make players with overcards fold. In no limit, these players will already be folding to the original bet (unless the bet is unusually small), and you won't need to raise it.

Analyzing NLHE:TAP Concept 51

2009-12-16T20:53:00.001-08:00

If I'm going to get through these by the end of the year, I'd better try to get a few done during the week. So, here is my analysis of the next concept from the end of No Limit Hold 'em: Theory and Practice. Sorry to those of you who are more interested in my narratives from the poker tables! I'll try to get one of those out in the next week.

Concept No. 51: In tournaments, other things being relatively equal, prefer small river value bets that will often be called to large river value bets that will seldom be called. Put another way, if a smaller bet has a bit less EV, it is still right to make it in most tournament situations.

I haven't played tournaments in years, so I'm no expert, but this concept is seems obviously correct. It's a specific example of a more general tournament concept: it can be worth giving up a little bit of EV in exchange for less volatility. The reasoning behind this idea is that since you can get paid in a tournament even if you do not come in first, it's worthwhile to hold on longer than other players even if your chances of coming in first are diminished slightly. This more general idea would have made for a much better concept idea (ie, more insightful, useful, and generalizable), except perhaps that most tournament poker players already understand this idea.

I'm not sure why, but in these concepts, Sklansky and Miller often forgo more general concepts like this in favor of specific examples that the reader might have difficulty generalizing and incorporating into his game. Maybe using specific examples is more effective in marketing poker books; Sklansky is certainly experienced at writing poker books that are popular.

Also, does anyone else find it strange that the authors are bringing up tournaments in this one concept for this rather obscure point? I guess tournaments are fair game since they are a common form of "No Limit Hold 'em," but I had thought they were focusing on cash games.

Analyzing NLHE:TAP Concept 50

2009-12-14T23:18:00.000-08:00

In which I analyze the fiftieth concept at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 50: If someone bets the flop and gets two or more calls, anyone who bets a significant amount on the turn should get respect.

This seems to be happening a lot, but once again, I don't like this concept even though I do agree with it. A big bet into a multiway pot after significant action on the flop is a very strong play, and the bettor should have a very strong hand if he expects to make a profit.

I have two main gripes with the way this concept is presented. First, the concept is a very specific example of a more general idea, which is that when someone bets with the expectation of being raised or called, his hand range must be very strong. I think the book's "concepts" are more useful when they are more general, because they can be applied to various situations.

Second, the example in the discussion is very unconvincing, a sort of "straw man" argument. If the authors felt confident in the generality of their concept, they would set up an example where all factors would suggest that you should not respect the bettor's bet, except for the reason given in the concept. On the contrary, in the example in the book there are many reasons why you should respect the bettor's bet. Sklansky and Miller try to use this to their advantage, saying, "you are out of position with a hand that is unlikely to improve..." However, this just muddles their argument. Thus, their conclusion that "you ... should frequently fold" to the bet on the turn is true, but it doesn't bolster their main argument in the least. They have completely failed to make a logical argument in support of their concept.

Recently, I haven't been doing EV evaluations like I did at the beginning of this project, and that is partly do to my own laziness. However, I think Sklansky and Miller also were lazy in formulating these concepts and discussions. It's frustrating, but enough of them are thought-provoking that I think this is still a worthwhile project. Only ten more to go!

Analyzing NLHE:TAP Concept 49

2009-12-13T23:33:00.000-08:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 49: If someone makes a big bet into multiple players, typically he will have a good, but not great, hand.

This is very similar to concept 35, and once again, I don't have anything very insightful to say. I think the claim made by this concept is usually true, but it's not very reliable. Different people play differently at different times.

Analyzing NLHE:TAP Concept 48

2009-12-12T20:44:00.000-08:00

From No Limit Hold 'Em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 48: Often make small bluffs (about one-third the size of the pot) in multiway pots when it appears no one has hit the flop. Balance those bluffs by also sometimes making small bets with good hands.

This is too general. It's also rather vague as to how it can "appear" that no one has hit the flop, but I'll take this to mean that most players have checked (as in the discussion in the book).

Yes, there are situations where a small bluff into a multiway pot can be profitable, but you will probably lose money if you apply this advice indiscriminately. Whether such bluffs are profitable depends on your opponents and on the flop texture. There are lots of players who will call small bets with weak hands or will check-call with relatively strong hands when they are out of position. Also, bluffing small on flops with straight draws usually won't work, because people can call a small bet with a gutshot. In general, your best chance will be on boards with the fewest draws, such as paired boards or A- or K-high boards. Boards with these textures are also the best for making small bets with your good hands, so it will be difficult for observant players to exploit you.

You also might want to use your hand as a guide to when you should bluff. If you have a backdoor draw or overcards, your bluff will have some of the benefits of a semi-bluff, since you will have at least a slim chance to outdraw your opponent if you get called.

Analyzing NLHE:TAP Concepts 46-47

2009-12-07T10:24:00.000-08:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 46: Don't just think about what you put your opponents on. Think about what they put you on also.

Yeah, this is what I'm always talking about. You need to think about what your range is and what your opponent's range is. That is the basis of game theory.

Concept No. 47: If it's clear your opponent has a hand at least worth a call, but he raises instead, it's almost never a bluff.

I think this is an overstatement to the extent that it is misleading. Also, it is very difficult to tell when your opponent has a hand "at least worth a call." However, this does occasionally arise if your opponent played in a way that was probably a made hand but if not, must have been a draw. If the draw comes in, you might want to bet to get value from his previously-made hands, but you'll have to fold if he raises. I would argue that your opponent could still be bluffing in this situation, but it's unlikely enough that you should usually still fold.

Suppose that you identified a situation where your opponent certainly had a hand that was at least worth a call, and he has raised you. Sklansky and Miller say it is almost never a bluff. However, it could still be a bluff if your opponent is overly aggressive. He would likely be making a mistake, but mistakes like this are not that rare. Moreover, if he knows you will fold to this bluff (which S+M are recommending to you), it means his bluff was actually the correct play after all.

This last idea is a bit convoluted, but I have used this against my more astute opponents. For example, I played a hand that went something like this: suppose you have AsJh and the board comes Jd 5s 4s. There is a lot of action on the flop. The turn is the Ace of clubs and you get check-raised. I think you are probably behind here, but you might still want to call because you might be ahead, and you do have four outs against a small set. If the river is a spade and your opponent bets, you can raise as a bluff. Your opponent will figure you would only do this with a flush, and fold his set. He might even fold a small flush or straight.

Analyzing NLHE:TAP Concept 45

2009-12-04T10:28:00.000-08:00

After this post, I'll be three-quarters of the way through the concepts at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 45: Know when a hand (even a good one) has more value as a bluff catcher.

This is good advice (after all, it's always good to know things), but the Sklansky and Miller don't give a good explanation of how to identify this type of situation.

The authors merely point out that sometimes you should check with your good hands, especially if you think it's likely that your opponent has a hand that's too weak to call with. This is true, but it's a meager assessment of the circumstances that make it profitable to check-call with good hands rather than to value bet with them. It would be helpful to discuss these circumstances.

For one thing, we need to consider our opponent's style. As I summed up in my analysis of Concept 10, if you've identified any weakness in your opponent's play, try to put him in situations that will allow you to exploit this. There are two types of mistakes your opponents might make that would turn some of your strong hand into bluff-catchers.

The most common weakness that you will be able to exploit is if your opponent bluffs too often. Against such opponents, you should be much more willing to check with your strong hands and use them as bluff-catchers. Another type of opponent is so tight that he will not pay you off if you bet. These players are great to bluff against, but if you hold a strong hand, you want to get him to put more money in the pot. So, it may be better to just check and call against extremely tight players. Often very tight players will be very passive, though, so this opportunity seldom arises.

There are also circumstances that have nothing to do with your opponents weaknesses that can make many of your hands bluff-catchers. Generally, this will occur if your opponent likely knows whether he has your hand beaten. This can happen if your hand-range is extremely narrow (usually because of the type of board and the betting to this point, or maybe you accidentally exposed your cards), or if your opponent's range is polarized (that is, he probably holds either a very strong hand or a very weak one). In such a situation, your only viable options are to check or to put in a small blocking bet. Let's look at some situations where your opponents range might be polarized.

In my discussion of Concept 44, I noted that when your opponent's hand range becomes polarized when he bets on the river: either he has a reasonably strong hand or he is bluffing. If you hold a hand in between these ranges, it doesn't matter much exactly what you hold; all that matters is your opponent's bluffing frequency. If he bluffs too much, all of your hands in this middle range are good to call with. If he bluffs too little, they should all be folded (or, possibly, raised as a bluff).

Another common situation where your opponent's range is polarized is if he is very likely to have had a drawing hand, but you're not sure if he has hit his draw on the river. Your opponent knows if he has you beaten because his hand is polarized. Either he hit his draw or he didn't. Unless you can beat your opponent even if he hit his draw, your hands now turn into bluff-catchers.

There are other probably other situations where your hands might be best used as "bluff-catchers," but these are the most common ones I can think of.

Diane's Final Hand at the Bike?

2009-12-03T08:52:00.000-08:00

There have been some complaints that I have been focusing too much on my poker analyses recently and have neglected telling stories about my experiences at the poker tables. So, here's something that happened last night.

In the 5-10 blind $500+ buyin NL game, I was on the button and somebody straddled for $20 (he gets last action, like another big blind). One player limped, and Diane, to my right, raised to $85. Diane is an attractive Asian woman who prides herself on her ability to loosen up a table, encouraging people to gamble with weak hands. Just a few hands earlier, she had executed a successful bluff with a $250 flop bet followed by a $800 turn bet with ten-high, no draw. She had about $5000 in play.

I had about $900 and looked down at AKo, much better than what Diane was likely playing with. I raised to $275.

To my left (in the small blind) was one of the tightest NL players I've played with. He had about $2700 and called my $275 raise. Everyone folded to Diane, who raised to $1000, putting me all-in. I have to call about $625 more. I need about 30% equity to make the call correct. I call. Even against KK I have enough equity here. I'm hoping the tight player to my left will fold, or that he'll push all-in and make Diane fold (in which case there will be more money for me to win, and I'll only need to win 23% of the time).

While the player to my left was deciding what to do, Diane asked me if she could look at my cards. I smiled at her incredulously and shook my head no. She hadn't bothered to wait for my reply, though, and looked at my cards.

The player who had been in the big blind was quite upset by this, and the floorman was called over. It's rather unusual for a player who isn't directly involved in a situation to call the floorman, and some of the other players (most notably Diane and "Corporation" Mike) were quite upset with this guy. However, as the guy said, "I'm not going to just sit here if I see something fishy going on at the table! I'm supposed to just sit back and watch cheating going on?" I'm sure Diane didn't mean to cheat, but I still think it was right for this guy to call the floorman.

Anyway, I think you can see where this is going. The floorman misunderstood the first explanation and said "well, I can't kill her hand just because someone showed his hand to her!" Of course, she had taken it upon herself to look at my hand. Diane started shouting about how this wasn't fair and if they decided to kill her hand, she would never come back to the Bike. The floorman called over the floor supervisor, who, amidst a growing crowd of onlookers, took about two minutes to finally call Diane's hand dead. Her $1000 stayed in the pot. On the verge of tears, Diane left, loudly cursing the floormen and explaining that this is why nobody comes to the Bike anymore.

In my opinion, this was a relatively clear decision for the floormen. Although Diane was not trying to cheat, she did break the rules and give herself an unfair advantage. Technically, her hand would be dead even if she were also all-in already (even though looking at my cards would give her no advantage because she would have had no more decisions to make). However, it's unfortunate to lose a friendly player who was generally very good for the game.

With Diane's hand out of the way and her money in the pot, the tight player made an easy call with QQ and won the whole pot.

Analyzing NLHE:TAP Concepts 42-44

2009-11-29T15:57:00.000-08:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 42: If you check the river, most players will bet only with very good hands and with bluffs. They'll check down hands that could win a showdown, but that are unlikely to be called by worse hands.

Yup. This is the correct way for your opponents to play the river, and since it's rather basic and intuitive, most players have mastered this strategy. You will see players deviate from this, but it is quite rare. However, I think it is worth noting because you don't want to fall into a pattern where you pay off your opponents if they make huge bets with hands that are only moderately strong.

As Sklansky and Malmuth point out in their discussion, this fact means that a lot of your medium-strength hands become "bluff-catchers." That is, they can only win if your opponent is bluffing. For example, it doesn't matter whether you hold top pair or bottom pair if your opponent will only value bet with two pair or better. Both hands can beat only bluffs. As S+M point out in Concept 44 (which I analyze below), the bigger your opponent's river bet, the less your hand matters; for example, if your opponent is rational and makes a bet of ten times the size of the pot, a wide range of your hands become "bluff-catchers," since your opponent will probably either have the nuts or nothing. On the other hand, if your opponent bets only one-tenth of the pot, the strength of your hand is very relevant.

Concept No. 43: Big bets mean big hands. Don't make or call big bets very often with weak hands.

As uncontroversial as this concept seems, I don't think it's precisely right. Big bets can mean not only big hands; they can also mean big draws or hands worried about draws. When your opponent makes a big bet (or when you make a big bet and get called), his hand range becomes much stronger. Thus, you should only call or make big bets with hands that have the potential to beat your opponent's strong range. This means you should be calling or making big bets only with big hands or big draws.

We can look back at some earlier concepts that touched on this topic to find some more exceptions and possibly gain some interesting insights.

Concept 35 seems to contradict this concept: "Unusually small bets tend to be made either with a big hand ... or with a bluff... With one pair your opponents will usually either check or bet a larger amount." So Concept 35 suggests: Big bets mean one pair.

Concept 40 also somewhat contradicts our current concept. This one suggests: Big bets mean the board has lots of likely draws.

Concept 1: "When in doubt, bet more" suggests: Big bets imply more doubt. Or something. This concept was pretty dumb.

To be fair, several concepts do support our current concept. For example, Concept 11 said "A big bet is the most relevant and accurate information available."

Concept 39 also supports our current concept. This was the one suggesting that you respect bigger bets more than smaller ones.

Concept No. 44: The bigger a bet your opponent makes, the more of your hands that turn into bluff catchers.

As I said above in my Concept 42 analysis, I agree with this one. At least in my games, my opponents are usually smart enough not to bet a huge amount with a hand that is only moderately strong, because they know I will probably only call them with hands that are even stronger.

It occurs to me that if my opponent is especially talented, he might be able to trick me into calling with a weaker hand trying to catch his bluff, but this is a very high-risk maneuver for him if his hand is only moderately strong.

I like to think about these concepts in terms of hand ranges, when possible. When my opponent makes a big bet, his hand range is polarized: usually he'll have near the nuts, sometimes he'll have nothing. My range falls almost entirely between these two poles, so my hands are mostly bluff-catchers. When my opponent makes a small bet, it's usually with a hand that is only somewhat strong, or it could be a bluff. Many of the hands in my range will fall on either side of his value-betting range, so my hand strength is the main factor determining how I react to his bet.

Analyzing NLHE:TAP Concept 41

2009-11-24T22:33:00.001-08:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 41: When holding a mediocre hand, usually bet enough (but not more) so that a raise means you are almost certainly beaten.

I don't like this one. It falls into the category of advice that stems from the idea that you should avoid putting yourself in a position of having to make a difficult decision. As I've already discussed twice before in this series of concept analyses, I don't buy into this idea. I don't think that you can generally improve your EV by maneuvering like this. However, I have heard that Chris Ferguson espouses this idea in The Full Tilt Poker Strategy Guide, which makes me worry that I might be wrong. A project I'd like to take on when I'm done with these concept analyses is to try to disprove this idea in general (or prove it, as the case may be). I'll have to take a look at what "Jesus" has to say, since he really knows what he's talking about when it comes to game theory.

Analyzing NLHE:TAP Concept 40

2009-11-22T18:26:00.000-08:00

After this post, I'll be two-thirds of the way through my analysis of the sixty concepts at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 40: Certain flops require certain-size bets. No matter what hand you hold, your flop bets, on average, should be smaller on flops like AhKdKs than they are on flops like Jh9s7h.

I think the authors have overstated the idea here, but I still like this concept. Most players underestimate the importance of flop texture in sizing their bets, but the authors go too far when they imply that flop texture is the only factor worth considering. Also important are position, stack-sizes, number of opponents, your hand, your table image, and your opponents' tendencies. On the AKK flop, for example, the bet should usually be around 1/4 to 1/2 of the pot. Bets outside this range might sometimes be better if stack sizes are quite small or if your opponents are maniacs, but these are unusual circumstances. On the J97 flop, you should almost never bet less than 3/4 of the pot, and sometimes it will be correct to bet 3/2 of the pot.

The reasons for the different bet sizes on different flops are basically those described in the book's discussion. If you are ahead on a AKK flop, your opponents have little chance to outdraw you, and even if they do, they usually won't be able to make much more from you. They have very little implied odds and very little incentive to call a bet of over 1/4 of the pot unless they have you beat. Similarly, your bluffs should be small on this flop to cover your small value bets. On the J97 flop, however, there are all sorts of draws, meaning that your opponent could easily draw to beat your hand, and if he does, he might be able to win quite a bit more from you. Your opponents are likely to have good implied odds in this situation, and so you must bet more to discourage them from calling. Your bluffs must follow suit.

Another way to look at this is that if you have a made hand on the J97 flop, you can make large value bets without worrying about making your opponents fold, but on the AKK flop, the most you can hope to win is a small bet or two.

Analyzing NLHE:TAP Concept 39

2009-11-22T15:37:00.000-08:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 39: You must adapt your play to different-sized bets. If you will call a twice-pot bet as often as you call a half-pot bet, you're in trouble.

This is correct both in terms of game theory and in practice. There are probably some players against whom you should not take this advice, but they are rare.

Game theory assumes that your opponents play optimally against your strategy. If you call just as often whether the bet is big or small, your opponents can easily exploit this by making their bluff bets small and their value bets big.

In both theory and practice, I think it's true that big bets are more likely to be bluffs than small bets, and this is why some people are inclined to call big bets liberally. The big bets look suspicious. However, this does not mean you can call these big bets more often, because you need to win a higher percentage of the time for you to come out ahead. The fact is that you have to let yourself be bluffed once in a while, especially when your opponent makes a big bet.

As I said, there are probably some players against whom you should call big bets even more liberally than small bets. This situation can arise if you notice that your opponent always makes small value bets but his big bets tend to be bluffs. You still need to be wary, though, because players are liable to change their strategy at any time!

Analyzing NLHE:TAP Concept 38

2009-11-21T18:23:00.000-08:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 38: Be more apt to semi-bluff when your draw isn't to the nuts than when it is.

Yes. This was discussed indirectly in my analysis of Concept 34. The key point there was "the higher implied odds your draw has, the less attractive semibluffing with it becomes."A draw to the nuts has much better implied odds when it hits than does a non-nut draw, which makes checking or calling with it a more attractive option relative to semibluffing.

Put another way, semibluffing will often win the hand immediately when your opponent folds. This is the ideal result regardless of whether your draw is to the nuts, but it's more beneficial if your draw has meager implied odds. Nut draws usually have strong implied odds, so they are commonly worth just calling with.

As an aside, when semibluffing with a non-nut draw, I try to bet enough to make better draws consider folding. For example, if I have 8h7h and the flop is Ah6h5c, I will make sure to offer my opponent significantly worse than 2-to-1 odds. This way, someone with a better flush draw will have to consider folding, because if I have a pair of aces or better, calling would be incorrect for him.

Analyzing NLHE:TAP Concept 37

2009-11-17T23:24:00.000-08:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 37: Bets on the turn should, on average, constitute a smaller percentage of the pot than flop bets.

This is probably true for the reason given by the authors in their discussion, but they neglect an opposing factor that could conceivably refute this concept's claim.

There are some obvious differences between the flop and the turn. After the turn betting round, there is only one more card to come and one more betting round. After the flop, there are two more cards and two more betting rounds. As Sklansky and Miller discuss, both of these factors favor the EV of draws on the flop over the turn. It follows that, in order to make it unprofitable for a drawing hand to call, a made hand would need to bet more on the flop than on the turn.

However, there is another obvious difference between the flop and the turn that can have an effect of the EV of draws, and this one favors the EV of the draw on the turn. I am referring to the fact that while there are only three cards on the board after the flop, there are four after the turn. This extra card means that the board has much more potential to threaten multiple draws, which means that it will be less obvious which draw your opponent has. This, in turn, means that each draw has higher implied odds, because (as Sklansky and Miller pointed out in Concept 31) if your opponent hits his draw, it will be very difficult for you to figure it out. To combat this, you will often have to bet extra on the turn if you have a made hand. This factor is completely ignored by S+M.

So, on the flop, draws have the benefit of an extra round of betting to extract value if they hit on the turn, plus the a possibility of getting two tries to hit the card (although they may have to call another bet on the turn in order to see the river). These factors increase the EV of draws on the flop, and thus demand bigger bets from made hands.

On the turn, draws have the benefit of some extra "cover" because there will often be more draws on the board than on the flop. These factors increase the EV of draws on the turn, and thus demand bigger bets from made hands.

Although I suspect the former factor is more significant, which would make this concept's claim correct, it's not entirely clear. What is clear is that the latter factor was ignored by the authors in the book's discussion.

Analyzing NLHE:TAP Concept 36

2009-11-15T17:02:00.000-08:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 36: Be more apt to slowplay very good hands that aren't quite the nuts than the nuts itself.

This concept seemed wrong to me from the first time I read it, but the authors bring up an interesting point in the discussion. After considering it, I still think the advice is generally wrong.

The point that Sklansky and Miller make is that one of the benefits of slowplaying a hand that is not quite the nuts is that you will potentially save a lot of money if you happen to be up against the nut hand. The example they use is a J66 flop. Here they say you'd rather slowplay with K6 than with JJ, because with K6 you might save money if you are up against JJ, J6, or A6.

Well, this is true, but it's a minor concern because your opponent will so rarely hold one of these hands. In the extremely likely event that your opponent does not hold one of these hands, you should be more apt to slowplay with the nuts (well, JJ is not the nuts, but we can imagine we hold 66). It's possible that there may be some situations where you would save so much money by slowplaying with K6 when you are behind that it actually is correct to slowplay it in a situation where slowplaying with JJ is not correct. However, I think this would be extremely unlikely in practice.

Sklansky and Miller neglect to mention the bad things that can happen when you slowplay. By slowplaying:

1. You don't get as much money in the pot when your opponent would call you.
2. Your opponent might outdraw you with a hand he would have folded.
3. Your opponent might have called on the flop but be scared off by a turn or river card.
4. A turn or river card might scare you enough that you have to stop betting or raising.

Factors 2 and 4 are a much bigger concern if you hold the near-nuts than if you hold the nuts. These problems are relatively common, at least when compared to the likelihood of finding that you're up against JJ when you hold K6 on a J66 flop.

Analyzing NLHE:TAP Concept 35

2009-11-14T15:20:00.000-08:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 35: Unusually small bets tend to be made either with a big hand (a suck-in bet) or with a bluff (a cheap stab at the pot). With one pair, your opponents will usually either check or bet a larger amount.

This is a strange concept because it contains no advice. I think the information is correct, but, to me, it seems only slightly useful.

In my experience, I think it's true that when someone makes a small bet it means it's slightly more likely that he has a big hand, and slightly less likely that he has one pair, but it's not a very significant difference. Depending on the game you are playing in, this concept could be off the mark for a stereotypical player; different types of plays are more or less popular in different venues, and this can also change over time. Also, once you have figured out what a particular opponent likes to do, the generalization made by this concept will be obsolete for that opponent; this concept applies only to players you do not know much about, and for them, bet-size is only a weak indication of hand-type.

Supposing that your opponent's bet-size really were a strong indicator of the type of hand he held, this information would be quite useful, but not devastatingly so. On the one hand, if you knew your opponent either had a big hand or a bluff, you could decide whether to fold right away or just call; raising would never be a good play in this situation. If, on the other hand, you knew your opponent held a pair, it could be a good play for you to raise either for value or as a bluff, but it would still be unclear how your opponent would react to this raise or if he would continue to bet his pair on future streets.

With this concept, Sklansky and Miller are pointing out a very marginal interpretation of how to read an opponent's action, and it's dependent (as they admit in their discussion) on who your opponent is. They offer no insight into how to use this information, although I can accept that they probably consider it outside the scope of this concept (or maybe they just think the answer is obvious).

Analyzing NLHE:TAP Concept 34

2009-11-09T10:32:00.000-08:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 34: If you have a close decision between semibluffing with a draw and checking it, be more inclined to check if you could make your draw with an overcard to the board.

Sklansky and Miller explain that if you make your draw with an overcard to the board, you might be able to win a big pot if your opponent happens to hit this card, too. I agree, but I don't like how this concept is presented. The discussion begins with the observation that "the higher implied odds your draw has, the less attractive semibluffing with it becomes." This is an important idea, and it would have made for a better "concept" than the one the authors chose. By semibluffing, you often eliminate your implied odds by ending the betting right away.

As it stands, Concept 34 describes a specific case of this idea. The authors not only missed this opportunity to put a particularly useful idea in their concepts, but they also failed to emphasize that the reader needs to be careful not to overgeneralize the advice given, which I think only holds in the specific case where you are deciding between semibluffing and checking. If you are deciding between semibluffing and betting, the opposite advice seems to hold: be more inclined to semibluff if you could make your draw with an overcard to the board.

The reason for this subtle distinction is that your implied odds only improve if an overcard is likely to help your opponent. This is generally only the case if your opponent has two overcards, which is unikely if you are thinking about calling (meaning your opponent has bet), because your opponent probably already has a pair. In this case, you would rather your draw be to undercards, because your opponent might be scared away by an overcard, thereby reducing your implied odds. In the case described by S+M, you are considering checking with your draw, meaning your opponent has not bet. So, it's a lot more likely that he his holding two overcards, and indeed it might help your implied odds if your draw included overcards to the board.

This is a little confusing, but I think the important insight is rather clear: "the higher implied odds your draw has, the less attractive semibluffing with it becomes."

Analyzing NLHE:TAP Concepts 32-33

2009-11-08T01:21:00.000-08:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 32: It can be correct to fold a hand before the river that has a better than 50 percent chance of being the best hand.

This is certainly true, but there are two reasons that each would be sufficient even in the absence of the other. Sklansky and Miller ignore the first of these reasons in their discussion, and only touch on part of the second.

1. It matters how far behind you are when behind, and how far ahead when ahead. For example, TT is ahead 4/7 of the time against a range of AA,KK, or AK, but it only wins about 40% of the time. This is because it is way behind 3/7 of the time and only a little bit ahead 4/7 of the time.

2. With more cards and more betting still to come, other factors come into play when it comes to EV. Your pot equity can take a back seat to the power of having more information about your opponent's hand than he has about yours. The obvious example is that if you are out of position, you will have to act first in later rounds, and thus you will give your opponent information about your hand before each of his actions. Also, if you are a tight player, your opponent will have a better idea of what sort of hand you are likely to be holding. Furthermore, drawing hands have an information advantage on later streets; whether the draw is hit or missed, the player who was drawing can be fairly certain of whether he has the best hand or the worst hand. All of these factors are more important in NL holdem than in Limit, because players can make larger bets after accumulating the new information.

Sklansky and Malmuth are right about this concept, but their analysis neglects all these factors except that position becomes more important in NL, and that "vulnerable" hands (ie, moderately strong hands that can lose to many draws) lose some value in NL.

Concept No. 33: Be willing to risk free cards to manage the pot size and induce bluffs.

This is good advice. With certain types of hands (in particular, "vulnerable" hands), you would prefer to play a small pot. I've never had much use for the concept of "pot control" or "managing pot size," but it's not really such a bad way to conceptualize why it's best not to bet with certain moderately strong hands. I'm not in the habit of using these ideas; I always just think about it in terms of managing my range and trying to maximize my EV. If I bet with a medium-strength hand on a drawish flop, I will tend to be called mostly by better hands than mine or draws; I will lose a lot against the stronger hands, but gain only a little against the draws. Making matters worse, players holding draws will sometimes raise as a bluff, forcing me to fold. If I do decide to bet the flop despite all these dangers, I will probably check on the turn, regardless of whether the draw comes in. If I bet, I will have problems similar to those I had on the flop, only worse. I will have shown strength by betting, but my hand will be among the weakest in my betting range, and I will have to consider folding if there is a substantial bet on the river. If instead I check and show weakness, my hand will be among the strongest in my checking range, and I can pick off lots of bluffs on the next street.

There is way too much information to process exhaustively at a poker table. Even when I sit at home and analyze hands, I often have to generalize and guess at EV in certain situations, because it's just too complicated to approach it more thoroughly. So, it's necessary to conceptualize poker and use principles or heuristics to simplify decisions. The way I think about the game lends itself much better to the EV and hand ranges conceptualization, but there is value in using a higher-level conceptualization such as pot control and bluff-inducing, as Sklansky and Miller recommend. In future analyses, I might try occasionally to approach problems with both conceptualizations if I think there is a chance they will be at odds.

Poker Riddle

2009-11-07T10:26:00.000-08:00

Yesterday, a guy named Jesse, his friend (can't remember his name), and the actor Michael Muhney were in the 500 NL game discussing probabilities and IQs and other nerdy things. I learned that Michael is in MENSA (actually I knew this from his IMDb page), Jesse has a 168 IQ, and his friend went to a school that required an IQ of at least 150. They had a discussion of how many times you'd need to double up to get $1 million if you started with $3. Jesse concluded that the probability was 1-(1/2)^18. He was emphatic on this point for a while even after it was suggested to him that the real answer was more likely (1/2)^18.

Anyway, Jesse had a riddle that he was sure nobody could figure out: you are heads-up in a holdem game, and you're ahead preflop, on the flop, and on the turn, but you have no chance to win on the river (only fold or chop). Jesse offered Michael 3-1 odds on a bet that he couldn't figure it out in 15 minutes, but Michael refused because, as Jesse put it, he is a "life nit," meaning that he is unwilling to gamble on things outside of poker. (A "nit" in poker is someone who is unwilling to gamble much, mostly only playing the nuts.) Michael confirmed that yes, he is a "life nit," if, by that, Jesse meant "a responsible person with two kids who doesn't want to have to explain to his wife in 15 years that he can't pay for their kids to go to college because he gambled all his money away to some guy at the casino with a 168 IQ who can't even do simple algebra."

I asked Jesse's friend, who had heard the riddle and was sitting next to me, how they define "being ahead on the turn." My definition would be that "being ahead" means you have the best chance to win the pot. Clearly, they had a different definition, since the problem is set up such that the hand that is "ahead" supposedly has no chance to win the pot. Jesse's friend said that a hand was defined as being "ahead" if it would win without any more cards coming. Jesse offered me the deal as well ($25 to $75), but, being a life nit myself, I turned him down.

I thought about the problem for a minute but did not figure it out. I eliminated the possibility that the answer involved flushes, and decided that it probably involved low cards. With low cards, it's much easier for kickers to get counterfeited on the river. Anyway, after playing for another half hour, I asked Jesse's friend what the answer was.

"You have to figure it out for yourself, man. Jesse! He wants us to just tell him the answer!"
"Okay, let me think about it," I said.

I thought about 32 against 42, but it didn't quite work. I thought about 43 against 42, with a flop of QQ4. Then a 2 on the turn. So far, so good. 43 is ahead preflop, on the flop, and on the turn, but I can't think of any river card that would result in a win for 43. If the river is a 2, then 42 wins with a full house. Any X higher than 2, and both players have QQ44 with a X kicker. Any Q or 4 and both players have the same full house. After about 1 minute, I told Jesse's friend I thought I figured it out.

"Did you think through all the possibilities? Just think about it." Jesse told me he still wanted to bet me 3-1, and he would give me twelve minutes and let me discuss it with anyone in the casino except his friend, who knew the answer. I hesitated, partly due to his confidence (although he had been similarly confident about the 1-(1/2)^18 formulation), but mostly just because I do not like making proposition bets, especially at poker tables. After a minute, I took the bet anyway. I asked Tony, another prop at the 500NL table, to confirm my answer. We discussed it for about five minutes, and he thought it looked good. Meanwhile, Jesse, having heard my discussion with Tony, proclaimed that I was "a million miles off" and wanted to double the stakes and give me a hint and let me call someone on the phone. I didn't want to escalate the situation any further, so I declined. I gave him my answer. After studying it incredulously for ten or fifteen minutes (and briefly trying to argue that 43 was not "ahead" on the turn), he conceded that it looked right and gave me my $75. I gave $15 to Tony for helping. Jesse said he had seen this question in a magazine and thought there was only one answer, which he told me. He said he had been asking that question at poker tables for five years and nobody had figured it out. I suspect he left something important out of the question, but I can't think what it would be. Anyway, Tony now thinks I'm a genius.

My answer can actually be generalized quite a bit. Instead of 43 and 42, I think any X3 and X2 will work, except X=2 or 3. Similarly, in addition to QQ on the flop, any YYX flop will work, unless it gives X3 a backdoor straight draw. So, X=Ace and Y=4 does not work, but X=7 and Y=4 does. The key is that a 2 has to come on the turn in all cases.

Jesse's answer does not fall into this category. Can you think of it? I'll give clues in the comments if anyone asks. I haven't thought of any solutions besides Jesse's answer and mine.

Analyzing NLHE:TAP Concepts 30-31

2009-11-06T10:15:00.000-08:00

After this post, I'll be more than half-way through my analysis of the sixty concepts at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 30: Implied odds are a critically important decision-making tool, but always be aware that different opponents offer different odds.

I like this one. Players often overestimate their implied odds by assuming they will win their opponent's entire stack if they make their hand. In reality, of course, sometimes the other player will fold. Other times, you will make your hand only to see it lose to a better one. The probability of either of these two things happening can be approximated without any knowledge of your opponent. However, as Sklansky and Miller point out, if you do have any prior knowledge about your opponent, you'd better take it into account. It can make the difference when deciding whether to call with a drawing hand.

I also like the authors' observation (in their discussion) that the players who offer the least implied odds (because they will fold if you hit your draw) will also be the easiest to bluff. This slightly increases the EV of calling a player who offers low implied odds, but it also influences how you should play your draws and the types of draws you should be calling with. First of all, against such players you should be much more inclined to raise as a semi-bluff. Not only are they more likely to fold, but you're also giving up less in the way of implied odds had you just called. Second of all, you'll want to look for opportunities disguise one draw as another. For example, if you're heads-up against such a player on a board of Ad Th 8d, it's probably better to have the 97 straight draw than the diamond flush draw. You have fewer "outs," but with the straight draw, you not only have decent implied odds for the times you hit your straight, but you'll also probably win the pot by bluffing if another diamond comes. On the other hand, if you have the flush draw, your only chance to win is probably to make your flush, and if you do, your draw is so obvious that you have little chance of getting paid off. This leads directly to the next concept, so let's move right along...

Concept No. 31: Your implied odds with any draw will be better the less obvious the draw is.

Since you just read my analysis of Concept 30, you can guess that I agree with this one. If your opponents are worried about a particular draw and it comes in, they are not likely to pay you off if you hit it. Against some players, you'll probably want to make only a tiny bet if you hit such a draw, because that is your only hope to get paid. In other words, if your draw is obvious, you have very little implied odds. S+M use the example of the nut flush draw on a flop of three diamonds. Everyone is worried about the flush. On the other hand, if you decided to play 53 and the flop comes K42 rainbow, you will have very good implied odds for drawing to your straight.

Analyzing NLHE:TAP Concept 29

2009-11-05T16:58:00.000-08:00

I'm working my way through the sixty concepts at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller. Almost halfway done!

Concept No. 29: It's okay to make small raises (2-3x the big blind) to build the pot or to set up a future play.

My standard raises are already rather small, about 3-4x the big blind, so I have to agree that there's probably nothing wrong with raising only 2-3x the big blind instead. In fact, I will sometimes raise as little as 2x the blind, but this is almost always in order to deal with awkward stack-sizes. For example, if the effective stack sizes are around 8-12 times the big blind, I think 3-4x raises will commit me to the pot, but going all-in is too much to risk for just the blinds. In this scenario, I might make a tiny raise pre-flop. Another conceivable reason for a minimum-raise would be to manipulate your opponents to either reraise you or just call you (as S+M suggest in Concept 24), but unless you are extremely attuned to your opponents, it will be hard to convince them to react exactly how you intended. I don't think I personallyhave the talent to make this play work. In any case, Sklansky and Miller have an entirely different reason for making these small raises, and I am not impressed with it.

The authors say, "often you should make this sort of raise with 'brave' hands - pocket pairs, suited connectors, and suited aces - hands that play well after the flop." While I do like calling such hands "brave," I think it's because they are capable of going up against bigger hands and beating them for a big pot. You can be "brave" and call a raise with 98s because you have a chance of winning a big pot with a small investment. However, intentionally increasing the size of this initial investment defeats the whole purpose! By doubling the bet, you are essentially cutting your implied odds in half. If the effective stack size was 100 times the big blind, a 2x raise means you can now only win 50 times your investment if you get lucky and hit your straight. Usually all that will happen is you will fold on the flop and lose two blinds instead of one.

Note that I'm not suggesting that you should never raise with "brave" hands. In fact, I think raising with them is an important part of a balanced strategy. However, that doesn't work if you raise an abnormally small amount with them. You need to raise your normal 3-4x amount in order to disguise your hand.

Analyzing NLHE:TAP Concept 28

2009-11-04T20:15:00.000-08:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 28: With strong hands, generally raise either a small, pot-building amount or a large, hand-defining amount. Don't raise an amount in the middle that both tells your opponents that you have a good hand and offers them the right implied odds to try to beat you.

I think it's better to just always bet a normal amount. I don't think you should you ever raise a "hand-defining amount." This will enable good players to play correctly against you, which means they will probably just fold unless they have you beat. This is clearly a terrible scenario for your strong hands. Bad players might call you with worse hands, but they even bad players are usually more likely to call a smaller bet. Then you can outplay them post-flop.

I'm also not a fan of "pot-building" bets, but these could conceivably work. Personally, I'd rather bet a little more and risk making a few players fold. Usually the result will be a pot of around the same size with fewer opponents, meaning you have a better chance to win.

Analyzing NLHE:TAP Concepts 26-27

2009-11-02T19:43:00.000-08:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 26: When there's an ante, your opening raises should be larger than if there were no ante. But they shouldn't be larger in the same proportion that the size of the initial pot increases; they should be somewhat smaller than that.

I don't know of any NL Holdem cash games that actually use an ante, but in theory I think Sklansky and Miller are right that this would be the correct way to adjust. With more money in the pot, it becomes more profitable to "steal"pots, and it becomes correct for you and your opponents to play looser because you have better pot odds. This involves not only raising more, but also widening your raising and calling ranges.

Concept No. 27: When semi-bluffing before the flop, usually do it those times you have one of the best hands that you'd otherwise fold. However, when you are in the blinds in an unraised pot, you should usually do it when you have one of your worst hands.

This one is complicated. I used to like this strategy, but now I think it's probably wrong. I now think the best hands to "semi-bluff" with are the hands that play the best against your opponent's likely calling hands. These include primarily suited aces, but also pocket pairs and suited connectors. Note that I don't think it is relevant whether you would "otherwise fold" with these hands, as Sklansky and Miller suggest. Many of these "semi-bluffing" hands are hands that you would likely have otherwise called with.

Sklansky and Miller's advice seems to be based on game-theoretically optimal river strategy, when there are no cards left to come. On the river, your bluff bets should indeed be with your worst possible hands, and your bluff raises should be with the best of the hands you would otherwise fold. This mirrors S+M's advice that you should bluff when "you have one of your worst hands" from the blinds, and that if you are not in the blinds you should bluff when "you have one of the best hands that you would otherwise fold."

The problem is that this optimal river bluffing strategy does not apply preflop. Preflop, the logic is much different because there are such things as drawing hands and semibluffs. Preflop, you do not need to bluff with terrible hands in order to induce your opponents to play hands weaker than your range; they will already be calling with some hands that they know are behind your range because they are "drawing hands." Instead, you should be bluffing with moderately strong hands as "semibluffs." The best hands to semibluff with preflop have two qualities. 1. They contain an ace, thereby reducing the chances you are up against AA. 2. They have a decent chance of making a big hand like a flush or a set. If your opponent is very tight, or if there have already been a couple of raises, point 1 is reasonably important. Otherwise, point 2 is much more important, because your opponent is unlikely to have AA anyway. In any case, this is why I suggested that the best hands to semibluff with preflop are suited aces, suited connectors, and pocket pairs.

Besides these types of hands, if you want to add some "bluffs" to your range, I think the best approach is to add some more hands that you would otherwise have called with. For example, try reraising with AJ or 77 on the button if you feel the need to bluff. Although these hands do have a lot of equity in just calling, they will also fare okay when your bluff is called. In the end, it's just my opinion, but I think this is a better approach than taking S+M's advice and raising with hands you would otherwise with fold, such as K7s. Although you are not losing any "calling equity" with K7s (since you would be folding otherwise), against normal opponents, these hands are just too unlikely to win if you are called preflop.

Analyzing NLHE:TAP Concept 25

2009-10-31T16:00:00.000-07:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 25: The button is the true bread and butter position in no limit. In many games you can play an extremely wide range of hands from the button, even for a raise.

Sklansky and Miller say that if effective stack sizes are at least 200 times the big blind, then, as long as you have at least one opponent who plays too loose after the flop, it is correct to limp on the button with over 50% of hands ("probably any two suited cards, any big offsuit cards, any ace, and any offsuit connector down to at least five-four"), and possibly with 100%. They also suggest that you call with over 30% of hands "if the raise represents only a few percent of the stacks (e.g., no more than maybe $50 with $1000 stacks)."

This is another one that is tough to analyze precisely, but in general, I think this advice is encouraging the reader to play too loosely. Unless you are much, much better than your opponents, this advice is probably -EV. I would be especially wary of the advice to call a raise to $50 with KTo in a $2-5 blind game, even if the stacks are over $1000. First of all, this advice completely neglects to consider whether the raise is coming from early or late position, which can have a drastic effect on your opponent's range. Even if the player is in late position and is rather aggressive, though, I would not be happy calling with KTo in this spot. You need to flop a straight or have the flop to contain KT or TT in order to be confident with your hand in there is a lot of action. Otherwise, a hand like this is going to have no implied odds, or worse, negative implied odds.

I do think the general idea that the button is a powerful position is correct, and indeed there are a lot more hands that can be played profitably from here than any other position (except the BB with no raise). However, in my humble opinion, S+M take the idea a bit to far here. If I were an online player, or if I took careful track of my results during poker sessions, such data might be helpful in coming to a well-informed conclusion. As it stands, all I (and also S+M, I suspect) can really do is guess.

Analyzing NLHE:TAP Concept 24

2009-10-30T02:26:00.000-07:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 24: If you have a hand that you would limp with in a passive game, consider making a small raise (two to three times the big blind) in an aggressive game instead of limping.

The idea here is that by raising, you reduce the chances an aggressive player will put in a big raise because he will be afraid of you. As long as your raise is rather small, this should allow you to see a flop more cheaply than if you just limp.

In my experience, this doesn't really work. After I first read this concept, I tried this strategy a few times with no success. I found that if I was in a game that was so aggressive that I felt like trying this strategy, I very often found myself facing a large reraise. Players who are hyper-aggressive preflop tend to be interested in gambling, and they will not be satisfied with your 2-3x raise. They will reraise you. Some players will even (correctly) see your abnormally small raise as a sign of weakness and raise with hands with which they may otherwise have limped or folded. In fact, in such situations you might want to consider making these small raises when you have strong preflop hand in order to trap your aggressive opponents when they reraise you.

If you are in a game where the aggressive players are not maniacs, this "blocking raise" strategy could conceivably work, but this is rarely the case. As I said, I personally have never utilized the strategy successfully, but I've only tried it a few times. If you do find yourself in this situation and want to try this "blocking raise" strategy, it's probably a good idea to also make small raises with big hands like JJ+ in order to balance your range, as S+M suggest in the discussion of this concept. Without at least some balance, a strong, aggressive opponent won't take long to figure out that your small raises indicate weakness.

Analyzing NLHE:TAP Concept 23

2009-10-27T22:51:00.000-07:00

From No Limit Hold 'Em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 23: It's ok to limp in, planning to fold to a raise. It's sometimes ok even when you think a raise is likely.

This piece of advice is meant for limit players, who are used to automatically calling a raise after they limp in. I certainly agree with this advice; the only thing possibly controversial is that some would argue that you should never limp in, you should always open with a raise. I think limping is fine, though, and I do it often.

Sklansky and Miller give a good, simple example to support their stronger claim that limp-folding is "sometimes ok even when you think a raise is likely." Basically, the example says that if you think your limp for $2 will return $6 on average when nobody raises, then even if there is a 60% chance someone will make a raise and you fold, it's still profitable to limp. EV= (.6)*(-$2) + (.4)*($4) = $0.40. Although this ignores the possibility that raising could be even more profitable than limping, it proves their point that limping can be better than just folding even if you are likely going to fold anyway.

Analyzing NLHE:TAP Concept 22

2009-10-26T23:46:00.000-07:00

Another installment in my analysis of the concepts at the end of No Limit Hold 'Em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 22: Ace-king is a powerful "move-in" hand and frequently moving in preflop is by far the best play with it.

I think this is a powerful idea that is underutilized by many of the good players I play with. Sklansky won me over to this idea when he introduced it in Tournament Poker for Advanced Players.

AK has a negative reputation as being kind of a "sucker" hand, since it is rarely the favorite if another player puts lots of chips in before the flop, because the other player usually has a pair or another AK. I think this reputation is undeserved. While it's true that AK has less than 50% chance against many other strong hands, it is only a big underdog against AA (6.5%-12%) and, to a lesser extent, KK (~30%). Against other pairs, AK has 43%-50%. There are three points that I think are misunderstood by players who think it's a sucker play to move all-in with AK preflop.

1. Players put way too much emphasis on having 50% equity when all-in. Whether a play is "correct" is determined by calculating (or guessing at) the play's expected value (EV). Actually heads-up winning percentage is only one factor in an EV calculation. When you are raising all-in, your EV depends only on the size of your raise, your pot equity (the amount in the pot after your raise is called times the probability you will win), and your fold equity (the amount in the pot before your raise times the probability your opponents will fold). Because fold equity is always positive, the required equity (when you are called) to make raising better than folding is always less than 50%. Having a higher probability of winning when you are all-in is nice, but it is only one factor to consider, and the difference between 50% equity and 43% equity is pretty small. Using the criterion of having a 50% or better chance against a certain hand or range of hands is wrong. It misleads people into thinking AK is worse than it really is because AK often falls just below this threshhold.

2. If you hold AK, this reduces the likelihood an opponent could hold AA or KK, which are really the only two hands you need to worry about. Players do understand this, but I think the effect is underrated. There are only half as many ways to make AA or KK when only three of each are left in the deck. If you hold AK and your opponent's range is AA-JJ, there is only a 1/3 chance he holds AA or KK, and your equity is about 35% (38% with AK suited). Note that when your opponent's range is this small, your fold equity is likely quite large.

3. Many players tend to view a big preflop raise by a good player as AA. They will often fold JJ or QQ, and some will even fold KK in certain situations. Although this means you are usually way behind when you are called, your fold equity is enormous.

Good players tend to play very tight ranges when there is a lot of action preflop and not much money left to play with after the flop. Players often fall into the habit of playing only AA or KK in these situations, sometimes QQ. AK is the perfect hand with which to balance your big-pot play before the flop. In some situations where your opponent's range is especially strong, it can certainly be correct to fold AK before the flop, but I think this is done way too often. Players are missing out on lots of situations where moving all-in with AK (and especially AK suited) is a +EV play.

Standard Work Week

2009-10-24T22:56:00.000-07:00

Starting this coming week, I'll be working Monday-Friday for the first time since I started playing poker professionally. This isn't much of a shift; I was already working 11AM-7pm Tuesday-Friday and noon-8pm on Saturday. It used to be the case that poker games were juicier on the weekends, but for some reason, things have been slower recently on Saturdays than the rest of the week. Today, the $500+ NL game never even got started. This is not uncommon, which is the reason my supervisor decided to change my schedule.

I noticed last week that a local bar has poker every Saturday. I might check it out, but I doubt it will be worth my time. They have some sort of point system and at the end of the year someone gets a prize. I was also invited to a house game supposedly run by Koreans in downtown LA. I'm told it runs 8pm-4am on Tuesdays and Thursdays and that there are incredible amounts of money to be won. I don't think I'll go. Even if it felt safe to me, I have to work both those days, and I would find it difficult to play for 8 hours at the Bike and then head off to another game.

I've been seeing and meeting some actors and other entertainment industry types recently at the Bike. One of the producers of Zombieland plays the $500NL sometimes. Teri Hatcher came and played the $300-$500 NL game at least twice this month. Michael Muhney, who was in Veronica Mars and now stars in The Young and the Restless played $500NL with us for a few hours yesterday. There was a guy who claimed to have been a drummer for Parliament Funkadelic, but I forgot his name. He bragged of a patent he has for some denim jeans design. Bo Koster of the band My Morning Jacket plays quite often. He's a good guy and a good player. I've chatted with him quite a bit, but I haven't seen him at the Bike for the past couple weeks.

Analyzing NLHE:TAP Concept 21

2009-10-22T09:42:00.000-07:00

Here's my analysis of the next concept from No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 21: Sometimes you can try for a deep check-raise with the nuts (or close to it).

By "deep" the authors mean that you are in middle-late position in a large field. I have seen it recommended that you not try a check-raise in such a situation, because some of the reasons for a check-raise are diminished in a large field, while the risk of being outdrawn is greatly increased. Still, I think Sklansky and Miller are right about this, and I would actually say you often should try for a deep check-raise with the nuts. It's very difficult to do a proper EV analysis of this situation, but here's my subjective opinion, for what it's worth.

In a small field, check-raising with a strong hand is standard (although there are situations where you would want to bet out even with the nuts). One reason for this is that a late position player is more likely to bet behind you if he is facing a small field. It's very common for the player in last position to bet if the first player or two check, because he will often be able to take the pot with a bet in this situation. A second reason is that the downside risk of checking is not as great when there is a small field; even if nobody bets on the flop, it's very unlikely that anyone will outdraw you, because you only have one or two opponents. A third reason to check-raise with strong hands when there is a small field is that it disguises your checks when you miss a flop. If your opponent knows you might check-raise, he'll be slightly more likely to check the flop and let you see the turn for free.

These reasons for check-raising do not hold up as well when you are in middle-late position in a large field. You need a stronger hand to check-raise in this situation. Still, with hands that are nearly the nuts, I think it's often correct to try it. A flopped set or straight is only a little vulnerable to being outdrawn, and the reward for a successful check-raise can be quite huge if there are multiple callers. If nobody bets, often another player will make two pair or three of a kind on the turn, which is likely to result in a very big win.

Analyzing NLHE:TAP Concept 20

2009-10-17T22:52:00.000-07:00

After this post, I'll be one third of the way through the concepts at the end of No Limit Hold 'Em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 20: Sometimes you should limp behind limpers with pocket aces.

I agree with this. It does sound a little like it's recommending that you "randomize" your play, which I've argued against previously. However, this one is a little different for two reasons.

First, Sklansky and Miller are not actually recommending that you apply this advice in a random manner. Instead, they say, "you'd do this if you have opponents yet to act who like to raise a series of limpers with weak hands." I agree, but I think there are also other situations where you may want to limp behind limpers with AA. Basically, any situation where you think it likely that someone behind you will raise is a good time to limp with AA. In fact, sometimes you should be limping with weaker hands, as well. This week I was sitting to the right of a maniac, and I literally stopped raising preflop with any hands because it was so likely that the maniac would reopen the betting for me if I just limped. This was a great situation because I got the best relative position before the flop, meaning I got to see how everyone else reacted to the maniac's raises before I had to decide how to proceed. This is an extreme situation, but even if the player to your left is only somewhat maniacal, limp-raising with JJ+ (or even weaker) may be correct.

Second, although randomizing your play is not usually a good idea, it can be theoretically correct to randomize your play in certain situations with the best possible hand. Before the flop, AA is the best possible hand, and it can be useful to include it in your limp-raising range. Even if you are never in a game with a maniac or with players that like to try to steal before the flop after several limpers, it still might be a good idea to limp randomly sometimes with AA behind other limpers. This play is probably only worthwhile if your opponents do not expect you would try such a thing. If they already do expect you'd try this play, it's probably not worth actually doing; its value is in its deceptiveness.

Analyzing NLHE:TAP Concept 19

2009-10-16T00:18:00.000-07:00

Here is another in my series analyzing the concepts at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 19: Don't call in protected pots without a very good hand.

By "protected pot," Sklansky and Miller mean a pot where bluffing will obviously not work. The most common example is when one player is all-in. Then, there is no point in bluffing because the all-in player will probably win the pot even if you get the other player to fold.

I think this should be good advice in theory, but in practice, it is astonishing how often players will bluff into protected pots. I generally follow S+M's advice and fold my moderate hands in such situations, but, in so doing, I've been bluffed out of many pots. In fact, I've recently decided to relax my calling standards slightly except against thoughtful opponents.

Sklansky and Miller extend this advice to pots that are "protected" by a loose player in the field or by a player who is nearly all-in. Unless you know your opponent is an alert and logical player, I would not suggest taking this advice very seriously. Players still sometimes bluff in these situations. Many will fail to notice that these factors are in play, and many who do notice it will still fail to realize that this means the pot is protected and that they should not try bluffing. This is my personal experience, so take it with a grain of salt.

Surprisingly, the seemingly obvious idea that you should not bluff when a player is all-in (and there is no side-pot) is not supported by game theory. Bill Chen and Jerrod Ankenman show in Chapter 29 of The Mathematics of Poker that it actually can be theoretically advantageous to bluff into protected pots. This is basically because it forces your opponent to play much more loosely. In "theory," all players always know the strategy of their opponents. In practice, of course, this is not the case, and your opponent probably will not expect you to bluff into a protected pot. So, bluffing in these situations is probably never a good idea after all. Actually, if you can get your opponent to suspect that you might bluff into a protected pot, you can forgo ever actually making such bluffs and still gain the benefit of making your opponent play too loosely. I'm not sure how you convince your opponents of this. Maybe pretend to be very drunk?

Analyzing NLHE:TAP Concept 18

2009-10-15T23:26:00.000-07:00

Continuing my project of analyzing each of the sixty concepts at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 18: Don't get trapped with a fourth street top pair in multiway checked pots.

Wow, Sklansky and Miller are really going out on a limb with this one! "Don't get trapped" is pretty hard to argue with. The question is whether this advice is likely to help anyone.

Actually, I think this is marginally good advice, but it's too specific. There are plenty of circumstances where you can get trapped by underestimating the chance that someone in a large field of opponents is lurking with a big hand. For example, top pair is also a treacherous hand to call with in multiways pots on the flop. Still, this doesn't invalidate the more specific point made in this concept.

It's true that you need a much stronger hand to call a bet when there are several players behind you than when you are heads-up, especially if there are various draws on the board. A top pair hand with a decent kicker is much weaker than it looks if you're used to having only one or two opponents on a flop, and thus it's pretty common for players to get trapped with such hands. In their discussion, Sklansky and Miller say "there's a decent chance you have the best hand, yet this isn't reason enough to call." This is a good point. This idea seems paradoxical at first, and it would make for a more interesting Concept topic, in my opinion.

Analyzing NLHE:TAP Concept 17

2009-10-12T18:01:00.000-07:00

From No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 17: If your preflop raise is called behind you, check a lot of flops.

The standard play is to continuation-bet in these situations, in order to maintain the initiative and keep the pressure on your opponent(s). I think this standard c-bet is probably overused, so in this sense Sklansky and Miller's advice to check a lot of flops is good. Still, I disagree with the reasoning they offer in their discussion of this concept. They focus too much on your hand and on randomizing your play, and not enough on the texture of the flop. I think better advice would be, "... often check on certain types of flops." This is mostly based on my intuition, and I don't won't be presenting any quantitative evidence.

I often do like to continuation bet even if I miss a flop because many players like to call preflop raises with small pocket pairs or suited connectors, hoping to catch a set, two pair, or a big draw and win a big pot against the preflop raiser. Usually, these hands will miss the flop, and they will fold to a continuation bet. For example, if I have AT and the flop comes Q43, I have a decent chance to win with a continuation bet even though my opponents often have a small pair or a healthy six outs. On this flop it's also a good idea to bet with many of your other likely preflop raising hands for similar reasons. With a good hand like KK, you can bet for value to balance all your weaker hands. However, there are certain types of flops where the continuation bet seems counter-productive. Generally, the flops where you don't want to bet are ones where there's a good chance you have the best hand and not too much risk of being outdrawn. For example, I think KK on a board of A92 rainbow is often better off just checking. On this flop, you're probably okay checking lots of your other likely hands, too. This includes strong hands such as AT. By waiting until the turn to bet with these hands, you are probably more likely to get called by a small pocket pair.

There are also more extreme examples of flops that don't have many draws, such as AA6 rainbow, or, to a lesser extent, 66T. On paired flop such as these I will often make a small bet. If my opponent has something, they'll call or raise, and I can react according to the strength of my hand. Often, my opponents will have completely missed these flops and just fold.

This seems like it could make for a bigger project if I want to come back to it later and do more quantitative analysis. For example, I'd like to test whether it's better to just alter my bet-sizes based on the texture of a flop rather than changing my betting frequency.

Analyzing NLHE:TAP Concept 16

2009-10-11T13:55:00.000-07:00

Okay, let's keep the ball rolling. Here's the next installment in my analysis of the concepts at the end of No Limit Hold 'Em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 16: Occasionally overbet with moderate hands to disguise your overbets with excellent hands.

No; this seems like terrible advice. By "occasionally," I think Sklansky and Miller mean something like "randomly," and I've already discussed in my Concept 3 analysis why I think this idea is vastly overrated. In their discussion, S+M say "as long as you don't do it too often, these overbets won't cost you too much, and they will support you those times you make big bets with excellent hands." I think this is wrong. If a play costs you anything in the long run, it should be considered "too much," because you can just fold and lose nothing more. If you determine that a certain play is +EV, you should do it every time, not just occasionally. If it's -EV, never do it (except maybe in some extremely rare instances if you really know what you're doing). Something I forgot to mention about randomizing your play in my Concept 3 analysis is that if you ever make mistakes when you play poker (ie, make a play that is -EV), you are already randomizing your play. Don't make matters worse by adding extra mistakes to your game! Of course, I assume everyone makes mistakes, so this advice should apply to everyone; to some extent, human error automatically disguises your hands.

There's another, more obvious, explanation for why this concept's advice is bad. If you want to "disguise your overbets with excellent hands," the best way to do this is by overbetting with draws as semibluffs. The example in the book suggests occasionally overbetting with KQ on a board of Ks9s7c. This is going to force your opponent to fold most of the hands you can beat. When you are behind, you will be called or raised and have only about three outs. I would suggest simply value-betting KQ while overbetting with hands like T8 or flush draws as well as with your monster hands. Semibluffs are great because your opponents are likely to fold better hands than yours, but you have lots of outs if you get called. Neither of these advantages exist when you overbet with mediocre hand like KQ on this flop. Moreover, semibluffs actually do a better job of "supporting" your overbets with excellent hands, because if your opponent has KJ or KT, he might think about calling if he suspects you are on a draw. If he thinks you have at worst KQ, he will fold right away.

Analyzing NLHE:TAP Concept 15

2009-10-10T10:30:00.000-07:00

After this post, I'll be one quarter of the way through the sixty concepts at the end of No Limit Hold 'em: Theory and Practice by Sklansky and Miller.

Concept No. 15: Bet more than usual when your opponent likely has a hand that he thinks might be good.

Taken literally, it seems to me that Concept 15 is useless. A recurring problem I'm having with these analyses is that the concepts are worded so vaguely or figuratively as to lose any clear meaning. In these cases, in order to do my analysis, I feel obliged to parse the concepts into something that both makes some sense and could plausibly be what Sklansky and Miller were trying to say.

Let's look closely at concept 15 to see if we can glean something from it. It starts out "Bet more than usual when..." Okay, so this suggests that in "usual" cases, Sklansky and Miller assume that we will bet within a certain range of amounts, but that in some unusual cases (to be revealed at the end of the concept's sentence) we should be betting more. So far, so good. Let's look at the end of the sentence to find out what these unusual cases are: "... when your opponent likely has a hand that he thinks might be good." Hmm. This doesn't seem like an unusual circumstance. In fact, since we almost never know what our opponent is holding or thinking, it seems to me that it's almost always the case that it's at least somewhat likely that he thinks his hand might be good. Sklansky and Miller's unusual circumstance is actually the norm.

As worded, I don't think the concept makes enough sense to be analyzed. Let's try to salvage it by giving it some plausible interpretation that can be analyzed. Using clues from S+M's analysis of this concept, I think they are trying to say something like: "If you hold the nuts and you somehow know your opponent has a made hand (as opposed to a drawing hand), bet more than you would if you knew he was on a draw." I think this must be what S+M are trying to say; I'm looking back at the book at the chapter on "bet sizing" (p54), and this is essentially the advice given.

The standard here is still too vague because not all draws are alike. If I know my opponent has 21 outs going to the river, he has a 21/44 chance of winning. Then, ignoring implied odds, the correct play is to bet over 10.5 times the size of the pot and hope he makes a bad call (if you don't have this much, just go all-in). On the other end of the spectrum, my opponent might have only 1 out. Here (again ignoring implied odds), you need only bet over 1/43 of the pot. Suppose the pot is $430. In the first case you should be betting over $4515. In the second case you should be betting over $10. So there isn't really a "usual" amount to bet if you somehow knew your opponent was on a draw unless you knew how many outs he had.

Let's refine the advice a little further and say, "If you hold the nuts and you somehow know your opponent has a made hand (as opposed to a drawing hand), make a big bet of around the size of the pot." In the book, one example of a "normal" bet against a draw is 1/3 of the pot, so a pot-sized bet seems like it should qualify as big.

I still don't think this advice is good in general. First of all, you almost never actually know what sort of hand your opponent is holding, so it makes the whole argument moot. Supposing you could know that your opponent didn't have a drawing hand hand, the correct bet size would still depend on your opponent's hand range and your opponent himself. Some players get very suspicious of very big bets because they suspect they are bluffs. Against such players, it really is a good idea to be big with the nuts, but not all players are like this. You also need to consider your opponent's hand range. The stronger his range, the more you should bet. In particular, if your opponent's range is very weak, you should usually be betting almost nothing. This invalidates the advice that you should generally be making a big bet. Sometimes yes, sometimes no.

Analyzing NLHE:TAP Concept 14

2009-10-05T22:16:00.000-07:00

I'm offering analysis of each of the concepts at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 14: Raise less often than you would in limit, because raising reopens the betting, and that's riskier to do in no limit.

I think this is good advice, but not entirely for the reason given. The advice actually holds even if you know your opponent will not re-raise you, such as when you are raising all-in. This is because in no limit your raise is almost certainly going to be larger (in proportion to the pot size) than in a limit game, which means your opponent will need a stronger hand in order to call you. If your opponent is only calling with stronger hands, then you can only profitably bet with even stronger hands. Thus, you need to be raising less often. (You may protest that since your opponent is folding more often, you should be bluffing more often. In fact, you do need to be bluffing more often, but only as a proportion of your raises. Since you are value-raising less often, your bluffing proportion automatically increases. In order to achieve a reasonable bluffing rate when making big bets, it's probably not actually necessary to bluff more often.)

The reason Sklansky and Miller give, namely that it's riskier to reopen the betting in no-limit than in limit, is also true. If you hold a hand that has some outs against possible raising hands in your opponent's range, it's sometimes best to just call in no-limit even if it would be better to raise in a limit game. This is partly because it's simply more expensive to be caught raising with a second best hand in a no-limit game, but another reason is that if you are raised, you can often call a small bet (such as in a limit game) with a drawing hand for +EV, but if you're forced to fold to a larger raise (such as in a no-limit game), this is necessarily 0 EV (actually -EV if you count the loss of the amount you just raised). Even if you can profitably call a large raise, it will not be as profitable as it would be if you only had to call a smaller amount.

Analyzing NLHE:TAP Concept 13

2009-10-04T18:42:00.000-07:00

Okay, time to get back in the saddle and analyze another one of the concepts at the end of No Limit Hold 'em: Theory and Practice by Sklansky and Miller.

Concept No. 13: If you're thinking about raising, but you wouldn't know how to respond to an all-in reraise, usually you should either move in yourself or raise a smaller amount (that would allow you to fold easily to a reraise).

Here in Concept 13, Sklansky and Miller advise that we should try to avoid situations where we would not know how to respond to a reraise. This is essentially the same as saying that we should avoid a situation if it forces us into a difficult decision. As I said at the end of my analysis of Concept 7, "I think conventional Sklansky-wisdom is overly concerned with playing hands in a way that avoids difficult decisions." I've often heard the advice on TV, in writing, and from other players that it's good to put the other player "to the test" by betting in such a way that you expect they have a difficult situation. I consider this advice to be pretty dubious (players will often pass this test!), and I think that Sklansky is applying a corollary: if it's good to force your opponent into a difficult decision, it must be bad to force yourself into one.

As poker players, our primary job is to make decisions that maximize our Expected Value at every point. Thus, we can define a "difficult decision" as one where we have two or more options (eg calling or folding) that have approximately equal EV, thus making it hard to choose which is best. Since folding always has EV=0, any difficult decision that includes folding as a candidate will have EV of approximately 0. We cannot make money in situations where we have EV=0, and I suppose this is why Sklansky advises to avoid them. However, I disagree with the notion that these situations should be avoided. We have to make our decisions with incomplete information, and when we initially bet, we do not know that we are going to be raised. When the raise comes, we must re-assess the situation, accounting for the fact that our opponent's range is now stronger than it was a moment ago, before we knew he would raise. Sure, it's unfortunate your opponent has a stronger hand than you realized, but that does not invalidate the decision to bet (except in hindsight).

To take an example from limit poker, if you bet and are raised and aren't sure how to respond, this implies that your hand fell solidly into your range of "betting hands." You should certainly not be checking with such hands just to avoid a difficult situation.

The situation described here in Concept 13 is a bit different. It may even be technically true. Sklansky and Miller use the term "usually," so it's hard to disprove unless I can show that it is never correct. In fact, S+M contrive a situation in the book in which the advice does indeed hold; my question is whether their example is representative of the "usual" situation. This involves making arguments about how our opponents are most likely to respond to different sized raises with particular hands, and so, really, it's just a matter of opinion. It is probably possible to find the game-theory answer (where we assume our opponent plays optimally). Even this will not give a definitive answer as to what is the best play against actual human opponents, but I might come back to this later if I feel like doing some more hard-core game theory.

Propping the $500 Minimum Buy-In 5-10 NL

2009-10-03T09:42:00.000-07:00

I'm back from my honeymoon, and I started my new job propping the $500 NL game at the Bike. When I left three weeks ago, the game was seldom being played, so I had the impression that I wouldn't really have much to do. To the contrary, I've played almost 30 hours already in four days. The game is pretty good - most players are too loose preflop, as usual, but other than that they play mostly okay. Of course, there are also some very good players and one or two terrible ones.

I'm a little unused to playing deep-stack no-limit. My job for the past year and a half had me playing mostly limit games. When I did play no-limit, it was always at a small buy-in for short periods of time, meaning I rarely had time to build up a deep stack to play with. So, for this week at least, I've been buying in for less than $1000 every day. There are some built-in strategic advantages to having a short stack, and I think it's necessary to be much better than your opponents in order to overcome that. Plus, I think having a short stack significantly reduces volatility. (I recently read an article in a magazine suggesting that having a short stack actually increases volatility! The claim was unsubstantiated, and I don't see how it could be right.)

I've lost three out of the four days so far, but the losses were minimal. Overall, I'm up about $600, plus my table hit a jackpot on Thursday and I won a $950 table share. (Yes, even the $500+ buy-in game has a jackpot now, to my chagrin. This has been the case for at least six months now.) I think once I get over my jet lag and become more comfortable with the game, I will have a big enough advantage on most of my opponents that I can start buying in for $1000, maybe more. On the other hand, I sometimes have issues with concentration, and that is likely to get worse as I get more comfortable with a game. I also think I may get sloppy about giving off tells if I get too comfortable. I'll have to keep an eye on this.

I hope to write my analysis of Concept 13 tomorrow. I basically disagree with it, but the analysis is complicated.

Analyzing NLHE:TAP Concept 12

2009-09-10T22:16:00.000-07:00

This will be my last post until at least September 28. I'm heading to Paris for my honeymoon.

Concept No. 12: Be wary of overcallers.

Yes! Good idea. Overcallers are often on a draw, but they are also often slowplaying a big hand. This is especially true if there are no draws on the board, such as the JJ4 rainbow flop in the example in the book.

That's all I have to say for this one. See you in a few weeks!

Analyzing NLHE:TAP Concept 11

2009-09-07T15:56:00.000-07:00

I'm commenting on the sixty concepts at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller. Let me apologize in advance: this one is a little more mathematical and a little less conclusive than most.

Concept No. 11: A big bet is the most relevant and accurate information at the table.

Once again, I think Sklansky and Miller's advice here is probably bad, but this one is particularly difficult to analyze because it's unclear what is meant by "relevant and accurate information." In any case, this concept's claim is far too broadly stated, and only holds in some circumstances.

If we take the claim in the most literal sense, this concept is not always true. Infinite counterexamples exist. Perhaps you know that your opponent always makes big bets; in such a case, the big bet provides essentially no information at all. Or, sometimes you may have the nuts, which is probably the most "relevant" factor if you're trying to figure out how to proceed with the hand. As far as "accurate" information goes, usually preflop play is most accurate, since you will have observed your opponent in many more preflop situations than postflop situations. Of course, all of this varies from player to player. It seems overly bold for S+M to make a claim that a big bet is (presumably, always) the most relevant and accurate.

If we're not to take this concept literally, let's consider whether it is at least good advice in a figurative sense. This concept seems suggest that players should respect the big bet more than they do, and thus fold to it more. Do players tend to underestimate the importance of a big bet when trying to determine their opponent's possible hand? Human nature actually suggests the exact opposite; there is a phenomenon called the "base rate fallacy" that seems like it could apply here. It has been established that people tend to discount base rates (which could correspond to your read of your opponent before the big bet), and focus only on the most immediate and salient information (such as the big bet) when estimating likelihoods. Are poker players similarly likely to focus to much on the most immediate information? I think sometimes yes, sometimes no. There are certainly a lot of players who are not sensitive enough to bet sizes, and for these players, taking this concept to heart is probably a good idea. I'm not sure that most players fall into this category, though.

In their explanation of this concept, Sklansky and Miller say "all information from the past takes a back seat to the fact that they've made a big bet." I think a fair way to interpret this is "the probability your opponent holds the nuts, or nearly the nuts, given that he just made a big bet, is greater than the likelihood that he did NOT hold the nuts before he made that big bet." Mathematically, we can write this as:

P(nuts|big bet) > p(nuts' before the big bet). That is: P(nuts|big bet) > p(nuts').
(Note that nuts' means "not the nuts.")

I'm fairly confident that this is not always true, although it is might be true if your opponent is a very good player. I think that Sklansky and Miller might have succumbed to the base rate fallacy and are underestimating the importance of their initial read of their opponent's preflop tendencies. Let's do some Bayesian analysis of the example they give in their explanation of this concept.

Suppose we are facing a big bet and we think our opponent is either bluffing or holding the nuts. Before he made the big bet, suppose we thought that the way he played the hand meant he had only a 0.05% chance of holding the nuts. This seems reasonable in S+M's example where your opponent is very tight, raised pre-flop, and the nuts is 74 (actually, .05% seems a bit too high, but let's give S+M the benefit of the doubt). Now let's say we think our opponent would make a big bet 80% of the time if he held 74. Otherwise, he would make the same big bet 2% of the time as a bluff. The base rate fallacy would be to think that your opponent would now be holding the nuts 80/82 times, or about 97.6% of the time. Of course, this is way too high because it ignores base rates. In this example, we can use Bayes' theorem to find the actual probability that you are up against the nuts. Bayes gives us the following equation:

P(nuts|big bet) = P(big bet|nuts)*P(nuts) / (P(big bet|nuts)*P(nuts)
+ P(big bet|nuts')*P(nuts'))

From our assumptions above, we have:

P(big bet|nuts) = .8
P(nuts) = .0005
P(big bet|nuts') = .02
P(nuts') = .9999

and so:

P(big bet|nuts)*P(nuts) = .0004
P(big bet|nuts')*P(nuts') = .019998

Then,

P(nuts|big bet) = .0004 / (.0004 + .019998) = .0004/.020398
= .0196

So, under these assumptions, our opponent holds the nuts less than 2% of the time when he makes a big bet! You may quibble with the rates I chose, but even if our calculations are off by a factor of 10, our opponent will still only be holding a winning hand 20% of the time, and bluffing 80%, making it correct to call any sized bet.

If you don't like the rates I chose, I guess it's most likely because you think that even very tight players tend to hold 74 on the river more than .05% of the time in this situation (the situation: he raised preflop, and 74 is the nuts on the river). I admit, this is a tricky one to estimate, but we can do another Bayesian inference to examine my .05% claim. That is, we want to know if .05% is a reasonable approximation for how often a tight, pre-flop raiser holds 74 on the river in this situation. That is, we want to find P(74|saw river).

First of all, let's assume our "tight" player raises preflop with 74 only 1% of the time when dealt to him. Also, assuming we don't have a 7 or a 4 in our hand, our opponent will have been dealt 74 only 1.3% of the time. So, P(74) = .013*.01 = .00013.

Second of all, we need to approximate how often 74 will see the river in this situation. Remember, the situation is: 74 has already raised preflop and seen a flop that gives him a draw to the nuts. IN order to be conservative and to simplify the math, let's assume he will never fold before the river in this situation. So, P(saw river|74) = 1.

Third of all, we need to approximate how often a player would have seen the river in this situation given that he raised preflop holding anything. This is another tough one. I think this is likely over 50%, but let's be conservative and choose 26%, which will also help out with the arithmetic. So, assume P(saw river) = .26. Bayes theorem then gives us:

P(74|saw river) = P(saw river|74)*P(74) / P(saw river)
= 1*.00013/.26 = .0005 = .05%

Well, this is precisely the number I used above, and I was using conservative numbers in this example. Of course, you could still contend that my numbers or other assumptions are unreasonable, but I have at least convinced myself that in Sklansky and Miller's example, our opponent's big bet usually will not indicate that he has the nuts.

Analyzing NLHE:TAP Concept 10

2009-09-03T23:55:00.000-07:00

I'm working through all 60 concepts at the end of Sklansky and Miller's No Limit Hold 'em: Theory and Practice.

Concept No. 10: Sometimes you should go for a check-raise bluff on the river when a bluff bet would be unprofitable.

Sklansky and Miller are technically correct that you should sometimes check-raise as a bluff, but the advice is still bad. It's confusing for them to state this advice without noting the unusual circumstances under which it holds. They say, "sometimes you should..." Well, yes, but rarely. Readers who take Concept 10 at face value are in danger of trying check-raise bluffs indiscriminately, which would probably be a big mistake. My problem with this advice is actually very similar to Concept No. 4: "Sometimes you should bluff to stop a bluff." In both cases, Sklansky and Miller are missing the main point, an idea that I've attributed to Mike Caro (though I can't find it anywhere - maybe I thought of it myself!): If your opponent bluffs either way too much or way too little, be more willing to check to him. Or, more generally: If you've identified any weakness in your opponent's play (such as bluffing too much), try to put him in situations that will allow you to exploit this (for example, by checking and letting him bluff).

In Concept 4, Sklansky and Miller refer to an opponent who folds way too often to a small bet. You should bluff often against this opponent. Here in Concept 10, they use an example where your opponent bets 5/9 of the pot and is bluffing "the majority of the time." This is too often. (When betting 5/9 of the pot, game theory suggests you should be bluffing only 5/14 = 35.7% of the time.) Against an opponent who bluffs too much, checking is commonly the best play. This is the real lesson of the example they give: If you know your opponent bluffs too much, exploit it!

I know Sklansky and Miller are not talking about game theory here, but I just want to acknowledge that theoretically, it is indeed sometimes profitable to check-raise bluff even if your opponent is playing perfectly. For an optimal strategy, these bluffs are needed to balance the times you check-raise with a strong hand. In this theoretical case, the hands that are best to check-raise bluff with are actually not the very worst hands in your range (which are the best hands to try regular bluff bets with). Instead, the best hands to check-raise bluff with are the very best of the hands that you would otherwise fold. For example, if 66 is the worst hand you would call with in a given situation, 55 is actually the best hand to try a check-raise bluff with. In practice, if you want to try a check-raise bluff, the decision should depend a lot more on your read of your opponent than on your own hand, but I always think it's worth considering what game theory has to say about a situation.

Analyzing NLHE:TAP Concepts 8-9

2009-08-31T23:28:00.000-07:00

Discussing the concepts at the end of Sklansky and Miller's No Limit Hold 'em: Theory and Practice.

Concept No. 8: Other things being equal, when you're in one of the blinds your preflop raises should generally be a little larger than normal.

I often follow this advice in my own play, but I'm not convinced that it is generally correct. Maybe it is, but I'm not sure. This is rather difficult to analyze objectively, and I think it will be a subject of discussion among poker theorists and enthusiasts for a long time. Anyway, Sklansky and Malmuth list three reasons why they think this advice is correct. Let's look briefly at each.

1. S+M say:
You'll be out of position, and raising bigger increases the chances you'll win right away.
Me: Yes, but you could also argue that you'd rather play a small pot if you're out of position, and so you should either raise smaller or only with very strong hands like JJ+.

2. S+M say: Cuts down your opponents' implied odds.
Me: Well, yes, but it also costs you more. Is it worth it?

3. S+M say: In early position, it's more important that you narrow down your opponents' possible hands, which you can do by raising more.
Me: Good point. Again, I wonder: is it worth the extra investment?

Finding the right strategy for raising in the blinds is something I'm still working on. It probably deserves a lot more consideration than I'm giving it in this post, but I don't feel that I have anything insightful to say about it beyond what I'm writing here. My current strategy is this: In the blinds, I like to raise only with a small number of strong hands. The actual range will depend on who has limped into the pot so far, but sometimes I will check with a hand as strong as pocket tens (although I will usually raise this hand). Occasionally, I will bluff with weaker hands (sometimes even extremely weak hands such as 72o if I think my image is very tight and I will likely make everyone fold). Since I seldom bluff from the blinds, I don't usually feel the need to make my raises particularly large. If my opponents know me well, they should fold to a normal-sized raise of about 2 BB larger than the current pot size, which is about what I consider normal-sized from other positions, as well. However, I will often raise larger than this if my opponents don't know me or if they seem to play too loosely. Since this is often the case, I actually do raise larger than normal from the blinds pretty often.

A related question is how much to raise in early position versus late position. I've seen all three alternatives argued: larger raises in early position; larger raises in late position; keep raises about the same size. The argument that you should raise bigger from early position is the most popular: you don't want to get called and then have to play the pot out of position, which is the same as S+M's 1st point above. I've also seen it argued that you should raise the same amount from each position. One argument for this is that it will always give the blinds the same pot odds if nobody else joins the pot. I've rarely seen it argued that you should raise bigger from late position than from early position, but this is what Chen and Ankenman argue in The Mathematics of Poker. They say that since your raising range is much smaller from early position, it's not necessary to raise as much. Also, by raising small, you save money if one of your opponents reraises, which is much more likely if you are raising from early position with 7-9 players yet to act than if you raise from the button with just 2 players left after you. Personally, I've decided to take the middle road and raise about the same regardless of my position. For me, this philosophy extends to how I play from the blinds, where I raise about the same as from anywhere else.

I think this topic deserves a much more objective, EV-based analysis, but this seems like a big project. I'm not up to the challenge just yet. I hope to return to this question at some point after I'm done going through the rest of these concepts, but that will not be for quite a while.

Concept No. 9: Bets are usually more important than pots.

I'm tacking this one on the end here because I don't have much to say about it. The concept's claim is not literally true because even in no-limit holdem, bets are usually smaller than the pot, but S+M's point is well-taken: in contrast to limit poker, winning or saving extra bets is extremely important in no-limit poker.

No-limit players should be much more willing to give up a pot in order to save a bet. In limit poker, on the other hand, the pots tend to be big compared to the bets, and so calling is much more commonly the right decision.

For limit players, it can be difficult to adjust to this difference. I had the opposite problem when I started playing more limit holdem last year: I was folding way too often for a limit game. My experience with no-limit poker had gotten me used to the idea that saving bets was important, and giving up pots was okay. In limit, the exact opposite is true!

Analyzing NLHE:TAP Concept 7

2009-08-30T11:56:00.000-07:00

It's my weekend again, so it's time to get back to analyzing Sklansky and Miller's No Limit Hold 'em: Theory and Practice concepts. I'll try to do one or two during the week, as well.

Concept No. 7: Don't telegraph that you have one pair unless you can profitably call big bets.

Sklansky and Miller say, "One pair can be a very tricky hand to play in deep stack no limit." I agree with this statement, but I do not agree with Concept 7 as stated. It suggests that except under certain circumstances, you need to play your pairs abnormally in order to throw off your opponents. This is terrible advice. You want your "normal" game to maximize EV. Thus, any advice to deviate from this is, by definition, going to lose some expected value. Losing EV=bad.

Certainly, we do not generally want our opponents to know what we are holding. So, the advice that we not telegraph that we have one pair seems sound. The problem with this advice is the implication that by playing a hand in our normal way, we "telegraph" our hand to our opponent. If this were the case, our entire poker strategy would need a complete overhaul. If we are playing a well-rounded game, we will never be telegraphing our hands (or if we do, it's not in a way that our opponents can exploit). Even if our strategy is not so well-rounded, it takes an extremely perceptive opponent to discern our hand precisely.

Let's consider for a moment S+M's suggestion that it's okay to let your opponents know what you have under certain circumstances. Specifically, they say, "If you welcome a big bet with one pair because you expect that bet to be a bluff, then it's ok to telegraph your hand by playing in a way that makes it obvious what you hold."

I don't really know what to make of this. If it's okay to "telegraph" my hand, should I just reveal my hand to my opponent in such a case? Surely not, although by the logic included in this concept it would seem that S+M would expect that this would accomplish the desired goal of inducing a bluff. This is plausible, but it still doesn't seem like the best way to play the hand.

Obviously, S+M are not advising that we telegraph our hands by simply revealing them to our opponent. What they mean by "telegraphing" is playing the hand in a normal, straightforward manner. However, as I said before, your normal strategy should not be telegraphing your hand, anyway.

I think Sklansky and Miller's advice is designed to protect the reader from developing a strategy that is too predictable. It's true that a NL player needs to disguise his paired hands, but it should not be done by playing them abnormally. Instead, just make sure that you play some drawing hands in the same way, as well as some stronger hands. I think conventional Sklansky-wisdom is overly concerned with playing hands in a way that avoids difficult decisions. It's good to avoid difficult decisions, but not if it means playing abnormally and thus losing EV.

Promotion!

2009-08-26T23:20:00.000-07:00

Yesterday, I was offered a new position and a $10/hr pay raise. My new responsibilities would be to help the $500+ buyin NL holdem game. That's about it. The floormen would no longer be able to move me from one game to another, and I would have some more flexibility about whether to stay in a game or get up for a player who is waiting. If no $500 NL game is running, I can play whatever game I want, but I would be required to help start new $500 NL games. My hours would be pushed back two hours from 9am-5pm to 11-7, which I think is somewhat better because the traffic should be lighter.

I told my supervisor I would have to think about it. Before I was hired by the Bike, I used to routinely play the $500 NL game at Hollywood Park, so working the $500 NL at the Bike might seem like an ideal situation for me. However, I've come to prefer the limit game over the past year. My results are better, and I feel more comfortable in limit. Also, the $500 NL players have extra intense egos, and I like to try to avoid getting too involved with such people. Since there are pretty much the same people at the $500 NL game every day, it will be difficult for me to escape their bullshit.

After thinking it over last night, though, I decided to take the job. I don't think it will take long for me to become comfortable with it. Hopefully only a day, and no more than a few weeks, I'd guess. As for dealing with the out-sized personalities in that game, I'm hoping it won't be too much of a problem. I already have to deal with plenty of BS in the holdem and hi-lo stud games I play every day, but somehow it seems that the variety of different people it comes from makes it more tolerable. Having to deal with the same people every day is going to be at least a little grating. I decided I could put up with it for the extra $10/hr.

Since I'm taking time off from Sept 11-27 for my honeymoon to Paris, my supervisor decided I should wait until October 1 to start in my new position. Anyway, this means I'll be playing way more no-limit pretty soon, so it's quite appropriate that I've been analyzing No Limit Hold 'em: Theory and Practice this past week. I hope to continue that tomorrow night.

Analyzing NLHE:TAP Concept 6

2009-08-25T22:42:00.000-07:00

From No Limit Hold 'em: Theory and Practice by Sklansky and Miller.

Concept No. 6: It can be right to call with decent hands that have little chance of improving even if you plan to fold if there is a bet on the next round.

I like this one. It's not groundbreaking, and it should be pretty obvious, but it's common for experienced players to give the opposite advice: don't call a bet on the turn if you can't face another bet on the river.

Well, often enough, that river bet never materializes after you call on the turn. As S+M say, "there are plenty of reasons to bet the flop, but check the turn if called (or to bet the turn, but check the river if called). You'll do it, and so will your opponents." I agree.

Again, this seems pretty straightforward, but I'll go through the basic idea. Many players who bluff on the turn and get called will expect you to follow the conventional wisdom and call any river bet as well. Naturally, these players will often give up the bluff and just check on the river, since they figure any further bluffs will be called. This means that if they do bet again on the river, they will have a stronger range of hands. This necessitates a stronger calling range on your part. That is, you'll have to fold some of the decent hands that you called with on the turn.

Sometimes I find myself in a game where I get called a lot pre-flop, but then my opponents tend to give up easily on the flop. I think they often have decent hands on the flop, but they don't want to face another bet on the turn, so they figure they should fold right away. By folding too early, though, they make it far too easy for me to win these small pots.

Analyzing NLHE:TAP Concept 5

2009-08-24T17:01:00.000-07:00

One by one, I'm analyzing the concepts at the end of No Limit Hold 'em: Theory and Practice by David Sklansky and Ed Miller.

Concept No. 5: When you first sit down, evaluate your game and decide whether your profit should come more from big pots or small pots.

I don't have a whole lot to say about this one. It's certainly a good idea to consider your situation when you sit down at the table, so I guess the only question here is whether deciding between big pots and small pots is really a top priority. Frankly, I don't know how to analyze this concept. I'll try comparing it to what I do when I first sit at a table.

If you were to ask me what the first thing you should do when you sit down in a NL holdem game is, I would tell you to first note your opponents' stack sizes. Then, listen to any table banter. This might give you an idea of who is winning and losing, who is aggressive, and who is passive. You'll need to take these impressions with a grain of salt, but they can give you hints as to how your opponents might behave or how they think about the game. Then you should watch the action closely, noting who plays lots of hands and who plays few. Ask yourself "is this table generally loose/aggressive, or are they more tight/passive? Do they tend to call too much preflop and fold too much on the flop? Generally, how can I exploit my opponents at this table?" This is a lot to think about, so maybe there is some value in simplifying things a little and just asking myself whether I should be trying to win big pots or small pots, as suggested by this concept.

Evaluating this concept further doesn't really fit my brand of analysis. The best approach probably depends on your personality. In any case, I like this concept because it encourages the reader to focus on his opponents, to assess his situation, and to think about how to exploit it.

Analyzing NLHE:TAP Concept 4

2009-08-23T16:35:00.000-07:00

The third installment of my analysis of the Concepts in Sklansky and Miller's No Limit Hold 'em: Theory and Practice.

Concept No. 4: Sometimes you should bluff to stop a bluff.

This is a really interesting idea, but after giving it a lot of consideration, I'm confident that it is generally wrong.

There are, of course, plenty of situations where your hand has some showdown value but you'll fold if your opponent bets. Obviously, your opponent will gain a lot if he bluffs in these situations. What this concept says is that sometimes it's worth bluffing with these mediocre holdings yourself in order to avoid being put in a difficult situation. This is almost true in some extreme examples, but it's kind of a stupid way to think about it because the reason you bet isn't really that you want to stop a bluff. I remember a similar piece of advice, I think it is from Mike Caro, that is much more insightful: If your opponent bluffs either way too much or way too little, be more willing to check to him. This gives you a chance to exploit his extreme bluffing frequency. Call if he bluffs too much, fold if he never bluffs. Let me explain how Caro's advice is similar and superior to S+M's.

Against most opponents, it's not a bad idea to assume they play about as well after you bet as they do after you check. If you've noticed that a certain player does not fit this description, you can try to exploit it. As Caro points out, if they play terribly after you check (by not bluffing a reasonable amount), you should tend to check very often. This is especially true if your opponent plays reasonably well after you bet. On the the hand, if your opponent plays terribly after you bet (eg by folding way too much), you should tend to bet very often. This is especially true if your opponent plays reasonably well after you check.

In the example Sklansky and Miller use to illustrate their point, they describe an opponent who folds to a bet of 30% of the pot 50% of the time. This is way too much. (In this example, he should call/raise with over 75% of his hands.) Bluffing such an opponent is extremely lucrative, and should be done as often as possible. To make this point even stronger in the book's example, your opponent bluffs reasonably often if you check.

The thing is, Sklansky and Miller do not acknowledge that this opponent is folding way too much, which is the real lesson of their example. Instead, they frame the example around the fact that you are holding a hand that is difficult to play against a bluff. Thus, the reader is given the impression that players with mediocre hands should usually consider bluffing. This is only true against opponents who play terribly when facing a bet! Even in these cases, you are not really betting to avoid a bluff, as Sklansky and Miller put it; rather, you are betting to exploit a weakness in your opponent's play (ie, he folds way too much). Against most opponents, betting mediocre holdings is a big mistake! Note also that against the opponent in this example, you should be bluffing not only with mediocre holdings, but also with all weaker hands. The weaker the hand, the more profitable it is to bluff. This is a basic lesson from game theory. Assuming Sklansky and Miller know this, they obscure this point so badly that they make it seem like it is actually better to bluff with mediocre hands than with weaker ones.

Although I think this Concept's claim is sort of correct, it's very misleading and seems based on bad reasoning. I think that if readers were to take this concept's advice to heart, it would make them play worse! Instead, take Mike Caro's advice and try to exploit your opponents' weaknesses by putting them into situations where they don't play as well.

So far Sklansky and Miller are a surprisingly bad 1 for 4 in their Concept advice. Of course, you may think they are correct and I am the one who is a surprisingly bad 1 for 4 in my analysis! Anyway, I'm quite surprised to see how little I agree with them after only four concepts. When I started this project, I knew there were a few points I disagreed with, but I thought I was mostly going to be integrating their advice into my poker consciousness. I had no intention to be quite so contrarian. I am hoping things are less contentious from here on out, but I guess disagreement probably makes for more interesting blogging!

Back to Work

2009-08-23T09:21:00.000-07:00

I went back to work at the Bike this week. Yesterday was the first day of the main event of the Legends tournament, and there were quite a lot of people milling about. Men "The Master" and David Pham were the only TV stars I'm sure were there. I think I saw Amir Vehedi, too. Not the most impressive list. The Bike's new tournament room is quite nice, though. I took a peak yesterday after the tournament started. There weren't as many players as I expected, but then again, there are at least two start days. In the corner were a bunch of people on laptops set up in official-looking rows. I guess this was the "press box."

There is more action than usual at the Bike, but not like last August, when we had tons of games going round the clock. This week, we haven't had any big games going when I got to the casino at 9 am. Even on a normal day in June there were overnight 20-40 limit holdem games going at least twice a week. On the other hand, the place was pretty packed by about 2 pm.

I have the next two days off, so I'm hoping to be able to get through Concept 6 of my NLHE:TAP analysis by Tuesday.

Analyzing NLHE:TAP Concept 3

2009-08-20T18:47:00.000-07:00

This is the second installment of my analysis of Sklansky and Miller's No Limit Holdem: Theory and Practice.

Concept No. 3: Most of your actions should include an inherent randomness against perceptive opponents.

"Avoid making virtually any play 100 percent of the time against good players." A few years ago, I was a big believer in this one, but now I just don't buy it. The idea, of course, is that you want to be unpredictable and thus difficult to read. If you never play 62, you are vulnerable if the flop is 662 or 345. Also, if you always raise with AA, your opponent can be sure his QQ are best with a AQ7 flop after you limp in. So, according to this idea, you need to limp at least rarely with AA.

I disagree. As an extremely example, I'm quite confident you should never raise 62o against good opponents when you are five off the button in limit holdem. This holds true for just about any hand worse than about 97o, and sometimes even for hands as good as ATo if your opponents are very tough.

So, why don't you need to worry about flops like 662 or 345 if you never raise with 62o? Three reasons:

1. Even the most perceptive opponents won't be able to figure out exactly what you are raising with anyway. Even if you do raise with 62o sometimes, your opponents are still pretty safe assuming you don't have this hand when 662 flops.

2. There are other, stronger hands that you can play that will make your opponents think twice on flops like this. Instead of playing 62o, play 67s, A6s, and/or 66. These hands do well enough on 662 and 345 flops, and they connect with plenty of other flops as well.

3. Even if you never play 67s, A6s, 66 and always fold when the flop is 662 or 345, this is probably okay! You will still win plenty of other times because the overwhelming majority of flops a card higher than a 6. Even if your opponents know you will always fold when the flop is all under 7, they can't really capitalize on this because those flops rarely show up! This is a very interesting point that I can't remember seeing anywhere else: it's okay for your raising range to include NO hands that connect with certain flops, even if your opponents knew exactly what your range is (which they don't).
**EDIT** 4. This relates to point 2 below. There may be situations where you actually will raise 62o. Who knows, maybe you actually think you opponents are so bad that you think you have +EV in this situation. The point is that your situation encompasses more than just your cards and your position at the table. So, even if your opponents know you never play 62o in the situation they perceive you to be in, you still might have 62o, because you will have perceived the situation at least somewhat differently. Note that this does not mean you should randomize your play like Concept 3 suggests. If you were to play 62o, it would be because the situation seemed to be profitable (+EV).

Another thing Sklansky and Miller say in this concept is "You might sacrifice a little bit of profit in this hand, but by doing so you make all your future hands more profitable." According to game theory, as I understand it, this is just plain bad advice. While it can sometimes be optimal to mix up your game by occasionally playing some hands, these hands need to be profitable in and of themselves... or, at least, not unprofitable.

I also don't really think you need to worry much about randomizing your actions when you have a good hand like AA. If you think raising AA preflop is the best play in a given situation, then it's probably worth doing every time. If you raise with plenty of other hands in similar situations, it's impossible to tell you have AA. You may be worried that you then give up too much information when you limp, since you are essentially announcing "I don't have AA because I always raise AA in this situation!" I have two things to say to this:

1. As in point 3 above, this is probably okay! Just as there are not many flops with three cards under 7, there aren't that many situations where your opponents can exploit you here. For example, even if they know you will always fold to an all-in raise, your opponent cannot exploit this by raising you out, because there are usually several other players for your opponent to worry about.

2. Even if your opponents somehow knew exactly how you play AA in a given situation (and again, they don't), they can never know exactly how you have perceived the situation at hand. For example, I might have noticed a tell that the player to my left is planning to raise, so I might limp in with AA. The player to my right might not have noticed this, and thus he will perceive the situation differently. If he perceives the situation as one in which I would never limp with AA, he would be liable to make a big mistake if everyone folds to him and he tries to bluff me out of the pot. Even more simply, maybe I am in a situation where I always raise with AA, but I misread the situation and call instead. This sort of thing happens all the time.

Some of my conviction on these points comes from studying some game theoretic examples from The Mathematics of Poker by Chen and Ankenman. There actually are situations in poker where you need mix up you play in a given situation (in game theory this is called a "mixed strategy"), but this always happens at the margins of your decisions. For example, if you've somehow determined that you should always raise with K8o on the button but always fold with K6o on the button, there is probably some rate between 0% and 100% at which it is optimal to raise with K7o. Clearly, whether you choose 20% or 80% is not going to make much difference in your results, and you'll be fine at either 0% or 100% as well. Notice, however, that with all other hands, including K8o and K6o, you should not be randomizing your play whatsoever according to game theory. K8 is a raise, K6 is a fold, period. Admittedly, mixed strategies can also be optimal at the extremes, like with AA, but, as I said above, I think you can safely play a fixed strategy, since nobody else really knows what you are thinking, anyway!

This took longer than expected, so I'll save "Concept 4: Sometimes you should bluff to stop a bluff" for next time. Preview: I am not convinced!

Analyzing NLHE:TAP Concepts 1-2

2009-08-19T16:51:00.000-07:00

This is the first in what I'm hoping will be a series of discussions of the "Concepts" section of No Limit Holdem by Sklansky and Miller. There are 60 concepts total. Today I'll look at the first two.

Concept No. 1: When in doubt, bet more.

Right off the bat, I have to say I'm not a big fan of this one. My main problem is that it's not really clear what this means, although the discussion in the book gives some clues.

Taken literally, this concept suggests that it is always best to just push all-in: since there is doubt inherent in every poker situation (even with the nuts, it's not clear how much is best to bet), we should always be betting more than any given amount X, unless X is all-in. I know this is not what they are trying to say, so I guess we should not be taking this concept so literally.

Taken more figuratively, I can see two reasonable interpretations. One is that players are generally inclined to bet less than they should, especially when they are in a lot of doubt as to how much to bet. I think this is good advice, actually. Beginners, especially, tend to bet far too little (compared to what would maximize EV), and one reason for this is probably that they doubt themselves. However, in my experience, lots of intermediate players tend to bet too much when they are in doubt, trying to end the hand immediately. In any case, I don't think this is the interpretation that Sklansky and Miller were thinking of, either.

Judging by the discussion in the text, I think the authors are saying that the EV lost when betting too little is worse than the EV lost when betting too much. "Try to err on the big side," they say. "In general, you're better off betting a bit too much than you are betting a bit too little." These comments suggest that there is a bet size that maximizes EV, and I whole-heartedly agree with this. I also agree that it can be difficult to determine this bet size (usually, it's impossible). However, I do not agree that a player should stray from the bet size that he thinks will yield the greatest EV. They say: "try to err on the big side." I say: "try not err." If trying to decide between betting $X or $X+1, the authors suggest you bet $X+1. I suggest you choose whichever seems better!

There actually are situations where there rules might not allow you to bet the amount you think is optimal. For example, you might want to bet $17.50 in a game where you are required to bet in increments of $5. So what is better? Betting $15 or $20? Honestly, I don't know, but this concept suggests you should bet $20. Let's come up a sample situation. I doubt this will be very fruitful, but sometimes this can help to get a better idea of what's going on.

Suppose I'm bluffing into a $30 pot, and would like to bet $17.50 because I think I would win the pot 50% of the time with this bet (EV = $30*.5 - $17.50*.5 = $6.25). However, the rules require $5 increments, so I'll bet either $15 or $20.

Suppose betting $20 will win the pot 52% of the time. Then EV = $30*.52 - $20*.48 = $6.

Suppose betting $15 will win the pot 48% of the time. Then EV = $30*.48 - $15*.52 = $6.60.

Oops! my example broke because betting less than my supposed "optimal" amount was actually better than "optimal." Of course, these numbers are entirely dependent on my approximations of folding rates, but it doesn't look too good for the "bet more" philosophy!

Now let's try those same numbers again, except now I have a hand that I think beats my opponent 90% of the time.

My supposed "optimal" amount is still $17.50.

50%: my opponent folds and I win the $30 pot.

40%: my opponent calls and I win $47.50.

10%: I lose $17.50.

EV = $30*.5 + $47.50*.4 - $17.50*.1 = $32.25.

Betting $20: EV= $30*.52 + $50*.38 - $20*.1 = $34.60.

Betting $15: EV = $30*.48 + $45*.42 - $15*.1 = $31.80.

Once again, my example broke, but this time betting more had a higher EV than my supposed "optimal" bet size of $17.50. I have to admit that if these numbers were correct, I would do better betting $20 than $15 in general, but I think the real issue here is that I should have made my opponent more responsive to changes in bet sizes so that my examples actually made sense (maybe I should have used 55% and 45% instead of 52% and 48%). In any case, I think it's still an open question whether it's better to "err on the big side," but I still say it's better not to err at all if you don't need to!

Concept No. 2: Don't give action to tight and trapping players. Know who not to play big pots against.

I think we can all agree with this very straightforward advice. Tight players tend to have better cards, so you must be careful! I'm not sure why this was worthy of it's own "concept" on the list, but I suppose it is a common mistake people make.

Hitting the Books

2009-08-18T15:12:00.000-07:00

As I mentioned last time, I'm taking some time off from work, and I wanted to use some of my free time to analyze poker. As planned, I did absolutely nothing poker-related for my first week off, but now I've started to hit the books. I reread a few sections of The Mathematics of Poker (probably my favorite poker book despite typos and other flaws), and I'm almost done with Gus Hansen's book, Every Hand Revealed. The only thing really earth-shattering about Hansen's book is his humility, which is very uncharacteristic of poker players. He unabashedly admits that he often doesn't know what the best play is, but describes his thinking of the pros and cons of each option. It's a good book, as it gives the reader a taste for how to play a super-aggressive style and what it's like to play in one of these big televised poker tournaments, but I don't feel that I've taken much away from it strategically except that I may be playing too tight in the blinds and with suited connectors.

In addition to The Mathematics of Poker and Every Hand Revealed, I'm also revisiting No Limit Hold 'Em: Theory and Practice by David Sklansky and Ed Miller. I never got around to writing a review for this book, but I thought it was mostly quite good. There are already lots of reviews online. (The book is three years old now, but one extensive review was just published yesterday.) However, I remember thinking that there was a lot of questionable advice, and, as always with "2+2" publications, astonishingly feeble editing. Anyway, the last part of the book, called "Concepts and Weapons," is simply a list of 60 NLHE concepts, and I've always thought this would be fertile ground for some poker discussion. I think it might be interesting to go through them all and give my impression of them. No promises, but I think I'll start that tomorrow. I go back to work at the Bike the next day, but hopefully I'll eventually work my way through the whole list.

The other thing I thought I might do before I go back to work was play in the $1070 tournament in the Bike's Legends of Poker. However, my plans for being staked by other players fell through, and I opted not to pay for it myself.

Summer Vacation and Being Staked

2009-08-06T10:12:00.000-07:00

Starting last Saturday (Aug 1), I'm taking two and a half weeks off and going back to work on August 20. This should give me time to run errands, make appointments, do some reading, plan a honeymoon, think about my future, and maybe start an online course. (Did you know MIT puts all their courses online?) I'm also going to Cleveland for a few days (after Hawaii airfare almost doubled). All the props at the Bike were encouraged to take time off this month because the big Legends tournament attracts plenty of action to the Bike. Of course, the action would probably have been profitable for me if I stayed and played, but they offered unlimited time off in August without penalty- but without pay, either.

For the first week or so I'm not doing anything poker-related (other than this blog post). I think it may be beneficial for me to take a step back from poker for at least a few days. I've been having more difficulty concentrating at the table, and it's interfering with the quality of my play. Also, I've been doing almost no analysis of my game when I'm not at the casino. Analyzing poker theory, strategy, and tactics not only keeps my game sharp, it also is what keeps the game fun for me. When I don't study, I don't have as much fun playing, I don't concentrate as well, and I have almost no chance of getting any better. If I'm not getting better and I'm not having a lot of fun, what's the point of playing poker? Well, there's the money, of course, but I don't make enough for that alone to justify it. I haven't completely lost interest yet, but if I can't get myself to refocus on studying the game, I think I'd be making a mistake if I kept on playing just for the money and job benefits.

In the second week of my break, after my poker hiatus, I want to re-immerse myself in poker analysis. Discovering new theories and strategies has always been the driving force that has made poker fun for me and made me want to get back to the tables. I'm hoping this will reignite my excitement in playing poker. I think there's a good chance that it will. The real challenge will be to maintain this interest for more than a few months.

At the end of July, I had several people offer to put me into various tournaments during Legends. I haven't played any tournaments in quite a long time. There are lots of reasons. Essentially, I just think I can make more money in cash games, and for the past year I've been paid a salary by the Bike when I play in cash games. Tournaments have lots of hidden fees that make them tough to beat: they often take 20% up front, plus sometimes another 2% for "bonus chips", plus often 3% goes back to tournament staff and dealers, and then they will certainly ask for a tip at the end, expected to be another 2-5%. I don't like having to prepare myself to play for 14 hours when I might be done after 1 hour. I also don't like the culture of tournaments. For one thing, there is a lot of pressure to chop the winnings at the final table, and I find the negotiations for the chop to be an unwelcome distraction from the game. I could just refuse to chop, as I've done in the past, but this actually incentivizes the other players to try to knock me out as soon as possible. In a cash game it is profitable to have people gunning for me, but in tournaments it is very unprofitable. Another problem with tournaments is that people routinely work together. For example, players might sell 50% of their winnings to other players in the tournaments for 50% of the entry fee. The problem here is that these players have incentive to let each other stick around, which is unfair to all players who are not involved in such deals because it makes it more difficult to outlast those who have made deals. Of course, people push chips to each other and soft play in cash games a lot, too. I just don't think the effect is nearly as deleterious as in tournaments.

Anyway, I have had several people offer to stake me for the Legends of Poker tournaments. I have almost never made any deals in poker. The exceptions include a few intances involving close friends when I first started playing casino poker and one chop I agreed to at a final table in a tournament. My general philosophy regarding such things is that even if I were willing to trust other players, such deals often have insidious effects on the integrity of the game. However, as long as the person staking me has no other "horses" in the tournament and does not enter himself, I don't see how there could be any conflict of interest. I suppose I have to take my backer's word that he is not backing anyone else, but as long as I don't know of anyone else, there shouldn't be any problem (unless that person is aiding me unfairly without my knowledge, but this idea is pretty far-fetched). The deal, by the way, would be that my backer would pay my entire entry fee and we would split any winnings 50/50. According to one of my prospective backers, I can even ask the tournament director to cut me two checks, each with the taxes taken out, to make it a little more official. I've had one person offer to back me for as many of the tournaments as I am willing to play. Frankly, though, only the bigger ones are worth my time, even playing for free. Most of the tournaments are only $300, which is too small. I'm considering playing in the $1070 NL holdem tournament on Aug 17. As a rough guess, I'd say my EV for this tournament is around $1400. This means that buying myself into the tournament, I'd expect to net about $330, but by getting backed for it, it's worth about $700 to me. Also, my volatility is obviously much lower if I pay no entry fee and only get half the winnings.

Frankly, I think my backers are overly optimistic about my chances: my EV would have to be at least $2140 after taxes for them to make a profit on me. Then again, I may be shortchanging myself; I have very little idea of what the level of competition will be. Another reason it seems like a bad idea to stake someone to a tournament is that it would be so easy for the "horse" to screw you over. For instance, if I took five people up on their offer for one tournament, I could take the $5350 and then intentionally dump off my chips before reaching the money, ensuring that I wouldn't have to pay anyone off! Of course, this would require quite a bit of subterfuge on my part, which has never been my strong suit.

"Exterminator" Mike Defends his Honor

2009-07-22T20:58:00.000-07:00

On Saturday, there was a strange occurence at the 20-40 limit holdem game. As you might expect, players are not allowed to turn over the cards of another player under any circumstances, even if the hand is over and they are just curious about what the player had. This would be considered a form of cheating, and, ideally, the offending player would be thrown out of the casino indefinitely. In actuality, this happens every few weeks, and is usually taken as a joke and not such a big deal. The floorperson will, at worst, give the offending player a stern talking to. This seems way too lenient to me, but I can live with it. A much worse offense, of course, would be to turn over another player's hand while the hand is still being played out. A player who did this intentionally should probably never be allowed back into the casino. Until last week, I would have told you I would be unwilling to play with such a player ever again. However, this exact situation occurred on Saturday, it was done pointedly to screw over the other player, and, remarkably, I was quite willing to keep playing in the game with the offending player. Oddly enough, he revealed the hand of the player next to him on the river in order to defend his poker honor.

The player in question is a latino guy named Mike (AKA "Exterminator" Mike because he runs an exterminator business), who I have since learned was in the Marines. He's generally been pretty straight, only rarely getting in arguments, and always keeping his cool. He also happens to be one of the few other players who (like me) doesn't chop.

Here's what happened. An unfamiliar player saying he usually plays at Commerce was in seat 4. I was on the button in seat 7, a talkative Asian man was in seat 8, and Mike was in seat 9, next to the dealer. I wasn't paying very close attention to the hand until the end, but this is how I remember it. Seats 1-3 folded before the flop, seat 4 raised, and only seats 8 and 9 (the blinds) called.

The flop was something like 973 with two spades. The turn was the 7 of spades, and the river was the 6 of spades. So, there were 4 spades on the board. I'm not sure how big the pot was, but probably around $240.

On the river, seat 8 bet out, saying something along the lines of "I have the flush, save your money!" Of course, it's not acceptable to talk like this when there are still more than two players in the hand, but it happens a lot. Anyway, Mike asked, "what's that?" and seat 8 repeated, "save your money, throw it away!" At this point, seat 4 became upset, complaining about the chatter. "Are you guys working together? I'm still in the hand here!" Mike tried to explain to seat 4 that he didn't know the guy in seat 8, but the player in seat 4 pointed out that he had no way of knowing if Mike was telling the truth.

At the time, I didn't really understand what Mike was doing or why, but he suddenly threw his own hand in the muck and simultaneously flipped over seat 8's hand. It was J9, no spades. "There, see! He doesn't have a flush!" Seat 4 called, showing 44 with the 4 of spades for a small flush. A quite impressive scene ensued, wherein seat 8 became considerably animated and angry and called the floorman over. Mike immediately said, "it's my fault. I was out of line." The ruling was that seat 4 would be awarded the pot, and in my opinion this was a pretty easy decision. No "disciplinary" action was taken whatsoever except to tell everyone at the table that there would be no more talking during hands and no more turning over people's cards.

I thought about the situation after the hand and I can't think of any other way Mike could have convinced seat 4 that there was nothing fishy going on. Personally, I wouldn't have screwed over seat 8 like that in order to prove that I wasn't cheating, but that really was an incredibly effective way to prove it. Still, I can't understand why he wasn't at least forced to take a 20 minute "time-out."

Mike was back again today. He said "hi," and I joked "they let you back in here after what you did last week?" He laughed and said "Yeah, any other casino and I would have been 86ed for at least a month."

In other news, I wanted to mention that for the first time in my life I was dealt one of the two candidates for the best possible opening hand in Omaha Hi: AAKK double suited. The other candindate is AAJT double suited. I was playing $80NL Omaha (a new game at the Bike that I think has some hope of catching on... they have also spread it at $100NL), and I won about $50 in the hand by limp-raising and then betting on the flop with a set of kings (both players folded).

Jackpots, My Win Rate, and Volatility

2009-06-14T15:36:00.001-07:00

Shortly after winning over $20k in a jackpot and another $1500 table share, I won yet another table share of over $1000.

I make daily records of my results in an Excel spreadsheet. I have it set up to calculate my hourly win rate and hourly standard deviation. After I won the jackpots, I simply included them each in a row of my database, listing each as having taken one hour. Of course, each jackpot actually only required one hand, so the assignment of one-hour time period was completely arbitrary.

Needless to say, the jackpots have a had an effect on my win rate and standard deviation. My SD especially has gone haywire: it went from about $350/hr over the course of my entire career to about $600/hr. My SD for this year comes to $1218/hr after being only $338/hr last year. In other words, recording the jackpots in this way is screwing with my volatility metric. What can be done about this?

I could just leave it like it is. After all, it's true that the jackpots increase the volatility of my income. However, the arbitrary choice of 1 hour per jackpot has far too much influence on the SD for me to be comfortable. For example, if I change the entries to say that each jackpot took only 1/10th of an hour, my SD increases from $600 to $1564/hr, and my 2009 SD skyrockets to $3721/hr.

I think a better solution is to try to separate out my poker-playing results from the jackpot results. I'm reluctant to do this because, in reality, the two are entangled quite insidiously. For example, I am much more likely to call with QQ when there are three aces on the board if I know there's a good chance I'll win a $20kjackpot. Similarly, my opponents certainly play differently - a few will play anytime they have an Ace before the flop because these hands have the best chance at making a jackpot. Many players would not be willing to play the game in the first place if not for the jackpot, and most players won't play with fewer than 4 opponents (the minimum needed for the jackpot to go into effect). Also, my win rate in jackpot games has always been dampened by $2-$8/hr because $1 is taken out of each pot for the jackpot.

Still, what I'm going to try to do is separate out the jackpot results from the poker results. I'll ignore all the above complications except for the most straightforward: I'll subtract out my jackpot winnings and add back in the $4/hr that I approximate I pay into the jackpot drop.

One other thing: the Bicycle Casino is being sued by some poker players over the jackpot drop. The owner is quoted a few times in the LA Times article.

30-60 Holdem, Other Games Returning to the Bike?

2009-04-27T14:48:00.000-07:00

I played 30-60 limit holdem at the Bike this past week, and the game was also spread at least two other times since then. This is the first time in months that the Bike has had anything between 20-40 and 200-400. It's a welcome sight to me, because although I do not have to play in games bigger than 20-40 limit, I usually have the option to do so. If I were playing on my own (rather than propping for the Bike), I think I would be playing 40-80 limit mostly. The competition is actually often worse at 30-60 and 40-80 than at 20-40, because the worst players from the 20-40 game are actually the most likely to move up in stakes. In particular, these are often the extremely wealthy people who come to blow off steam but have no patience for trying to play well. I think they just like the comraderie of the game and the excitement of gambling.

Meanwhile, some other new games have been spread at the Bike the past couple of weeks. The most successful is a $100-$300 buyin NL game that has replaced the $100 fixed buyin NL game. It still uses 2-3 blinds, but now players can buyin up to $300. Obviously, this game overlaps with the $200 NL game, which has indeed suffered. Usually, in the afternoon there have been about four $100-$300 and one $200 NL game, although there have been as many as ten $100-$300 NL games at once.

Another thing I'm keeping my eye on is an effort to convert the 20-40 stud hi-lo game into a mixed game combining that and Omaha hi-lo. Hollywood Park has been spreading this exact mix game for years now, and supposedly they often have two games a day (as they did last time I was there). So far I haven't seen this mixed game get started, but other mixed games have occassionally been spread at the 15-30 limit level. For example, I played a badugi-razz mix for two hours two weeks ago, a badugi-razz-holdem-2/7 triple draw the next day, and a badugi-razz-stud hi/lo-2/7 triple draw this week (I won $580 total). I tend to do well in these mixed games. I like to think that it's because I have a good understand of genreal gambling/poker theory, but for the amount I've played, the results depend mostly on luck.

Jackpot(s)!

2009-04-17T11:04:00.000-07:00

I've mentioned my disdain for the jackpot promotions in poker rooms quite a few times in this blog. As I was complaining to my brother this weekend, nobody will be willing to listen to my complaints anymore, as I won a jackpot for over $20k on Friday (the 10th) around 3pm. Then, on Tuesday, the jackpot was hit again at my table, and I won an additional $1477 for the table share. I've calculated that I've contributed between $5k-$10k to the jackpot drop since I started, so I'm now up a considerable amount. I still think the jackpot is stupid. Anyway, here's how it happened:

I was in the big blind, playing 6 handed. The first player limped, the second player (Joel, a host for the $500 NL game), raised, and everyone folded to me. I reraised with QQ, the limper folded, and Joel called. The flop was A86, and I bet (not my standard play, but I think it was okay against Joel, who I think is more likely to call me with a pocket pair than to try to bluff my with one). Joel called. The turn was another A. I checked, Joel bet, and I called (I had the jackpot possibility in mind at this point, but I likely would have called anyway). The river was a third A. I sat straight up a bit in surprise. Again, I checked, Joel bet, and I called.

"I hope you have it," said Joel, but I wasn't sure if he meant he hoped I had the A (he could have been holding KK, QQ, JJ, or TT, and hoping that I had the A, but he probably would have expected I would keep raising in that case). He showed AJ. The bad beat jackpot require that both cards in both players' hands play. The losing hand must be aces full of tens or better, and the winning hand must be four of a kind or better. I've come close to winning before, but was thwarted by my opponent's small kicker not playing.

The jackpot was up over $46k (it starts at $40 and goes up by a few hundred a day until it is hit). I got 45% (20,911), Joel got 20%, the other four player in the hand got 5% each, and the players at the other 20-40 table shared the last 15%.

We had to wait two hours to get paid (the excuse was that another jackpot was hit in the casino just after ours, and we had to wait for all the paper work to be done). After finally getting my money (paid in chips), I opened a player's bank account so that I would not have to carry it all home with me. So now I have money at the casino that I can withdraw whenever I want, which is nice because I don't have to carry much cash to the casino with me anymore.

New Schedule,Again

2009-03-23T09:51:00.000-07:00

This past week I've been working on a new schedule. It's not all that different: I now go in at 9am instead of 7am. I'm not thrilled about the change, since it means I have to drive through traffic before 9 and then again at 5pm when I go home. The traffic isn't so bad, though (about 15 minutes extra in both directions), and it's nice being able to get up later than 6am. Also, I was ready for a change of pace after listening to NPR's Marketplace at 3pm every day for the past several months.

It seems like the 2-11 game has died out. I don't think the Bike ever spread it above 4-8.

I'm getting married this Saturday, so I'm taking most of the week off from work.

Soft Play and A Gift Pot

2009-02-23T12:54:00.000-08:00

I've come to view my no-chopping policy as part of a larger campaign against "soft play." I would define soft play as any behavior that is intended to benefit another player or players at the table. Since this behavior is usually intended only to be nice, it can be awkward to protest it. However, when players are being selectively "nice" only to certain other players at the table, it becomes unfair. As a professional gambler who is wary of gambling in general, I am not comfortable when I'm in a game that I consider "unfair," even when it is relatively benign.

A few common examples of soft-play: two players may agree to always check on the river if it's heads-up, or they may agree to chop the pot in half, or a player may say "take two chips back" after raising. Sometimes, a player with just give $10 or $20 back to a losing player after the hand is finished. In my mind, the main problem with soft play is that it is akin to collusion and undermines the basic integrity of the game. In order to make good decisions in a poker game, I need to try to figure out my opponents' most likely actions, which depends upon having an understanding of their motivations.

In a poker game devoid of emotions and personal interactions, each player would be concerned only with maximizing his own EV, and the best players would simply be those who were best able to figure out how to accomplish that. In real life, of course, players have all sorts of motivating factors beyond. For example most players are at least a little concerned about their reputations as decent poker players, so they may be less likely to call with a long-shot draw (which other players will identify as a "lucky" play if the draw is hit) or might be inclined to show their hands at the end if they feel they made a great play. Or maybe two players don't like each other, so they try to give each other bad-beats. These and all sorts of other deviations from "pure" poker play are commonplace at poker tables, and, in fact, this is one of the reasons I can make money playing poker.

This is all fine and good. I'm not arguing that players cannot or should not consider factors beyond EV. (In fact, if they did that, over 90% of players would be correct not to show up at the casino at all!) In my mind, all motivating factors are fair game unless it can be construed as collusion.

I have more to say about this, but I feel I'm starting to ramble, so I'll leave it for a later time.

In addition to chopping, there are certain situations where "soft play" are so commonplace that I think people view me as cold-hearted. Here's an example that I felt a little bad about.

Last week I lucked into over $280 when my opponent mucked his winning hand after calling my bluff on the river. I've seen this happen before, and the winning player will sometimes give the other player his last bet back, or even give half the pot back, so I couldn't look him in the eye when he got up and left afterwards. Here's how it went down, as best I can remember:

In a 20-40 limit holdem game, I had 44 in the big blind. Everyone folded to the button (a supposedly talented omaha hi-low player) raised. The small blind folded, and I re-raised. The button called. $6 is taken out for the house and the jackpot, so the pot was $124.

Flop($124) 998. I bet $20, button raised, I called.

Turn($204) 7. I checked. Button checked.

River($204) 8. Now I play the board. My hand was so weak that I decided to bluff. My opponent called the $40. I quickly turned over my 44. My opponent started to muck his hand, then stopped to think, and then turned his cards over (but he did not lay them on the table). I saw AK, which beat me. Then he mucked his cards. The surprised dealer pushed me the pot.

While I was stacking my chips, other players at the table pointed out my opponent's mistake. He took it pretty well, said something like "well, I'd better go home if I can't even read the board anymore," and left.

Introduction of 2-11 Poker at the Bike

2009-02-02T15:27:00.000-08:00

A week from today, on 2/11, the Bike is going to start spreading a game that they are calling "two-one-one" poker (even though the inventor of the game says it should be called "two eleven" in this youtube interview). The name is a reference to the fact that, while there are many similarities to other holdem games like Omaha and Texas holdem, 2-11 has only two cards on the flop. Like Omaha, each player gets four cards, but unlike Omaha, players can use either two or three cards from their hands. Half the pot goes to the low hand, but there is a 7-qualifier (ie, you must have five cards 7 or lower, the best low hand being A2345). It seems that the Bike has exclusive rights to the game. At least, the Bike is hosting its "Grand Premier."

Actually, the game is already being spread at the Bike, but only for practice for the dealers. I played for a couple of hours one morning with the fake chips that were available. I thought it was fun, but that should be no surprise because I always like trying new games. Frankly, I would be a little surprised if 2-11 becomes a popular casino game. Most casino poker players these days are really stuck in their ways. It's not like a few years ago when there were lots of new players who were up for anything. Nowadays, players won't tolerate it if anything changes about the game they want to play. They won't play short-handed, they want a particular seat at the table, and sometimes they get angry at me for not chopping with them. I hope I'm wrong, but I just don't see poker players getting excited about a new game right now. The best case scenario is that the game attracts a different sort of poker player who is willing to play for the fun of it rather than trying to grind out a few dollars an hour by playing by the book. After all, there is no book on 2-11 strategy, as far as I know.

Since I'll probably be playing this game in the near future (the Bike plans to spread 4-8 and 15-30 limit), I'd like to consider some strategy this week. If I have any insights, it may make for an interesting post.

I'm Getting Married!

2009-01-26T21:02:00.000-08:00

Let's see... what have I been up to since I last posted three months ago? Most significantly, Brigid and I have decided to get married; the wedding will be March 28 in Cleveland. I'm still working at the Bike, where things have slowed down a bit. I went home to Massachusetts for Thanksgiving, but I stayed in LA for Christmas. I was recognized at the casino by a reader of this blog (a first for me - see the comments in the previous post). One of my friends who shared my schedule has taken the past two weeks off due a death in his family; I'm not sure when he'll be back. Poker's still going well for me: I made more this year than the past two, but mostly because I played more hours (last year I had a much better win rate). I played a very small tournament in Vegas and came in 5th out of 40 players.

Possible topics of future posts:

A new game coming to the Bike called "2-1-1," a variation on Omaha high-low
The strange conventional wisdom among poker players pertaining to being "stuck," playing short-handed, and other things
Good things about playing at the Bike
My future in poker
Interesting or amusing poker hands (these still come up almost every day)

Chopping the Blinds

2008-10-29T18:37:00.000-07:00

If everyone folds around to the blinds in holdem, it's common for the two players in the blinds to "chop," meaning they take their blind bets back and move on to the next hand. In Los Angeles, $1 is taken for the house from the person in the small-blind. In Las Vegas, the house takes nothing. On the other hand, if there is a flop, usually there is a lot more taken (eg $5 more is taken in 20-40 limit holdem at the Bike if there are at least 7 players). There is an unwritten rule (it is rather strongly enforced socially at the poker tables) that you should either always or never agree to chop when given the opportunity. This means that you shouldn't be looking at your cards, seeing AA, and deciding not to chop if you have established yourself as someone who does not chop. I'd say that at least 90% of players agree to chop, but if either player refuses, then the two players play the hand out heads-up.

I recently stopped agreeing to chop. Although I don't like having to pay the extra $5 to the house for what is often a small pot, I think it's worth it because I have a big edge against most players, and lots of players play even more poorly heads-up. One issue for me is that there is social pressure to chop. Some people take offense if I refuse to chop, and in fact, this was the main reason I ever agreed to chopp in the first place. It didn't seem worth making enemies. Since I had been chopping with people for the past several months, I was in particular danger of angering people by not chopping with them all of a sudden. On the advice of another prop player (Johnny), I made myself a little sign on a sticky-note saying "no chop." After a day or so it was defaced with "Please Raise Me!" Now I use a slightly larger sign that a player made for me. It's pink and says "please Raise me! NO CHOP" It's ridiculous enough that it seems to defuse any animosity towards me.

Re: The Pinky Nail

2008-10-20T14:19:00.000-07:00

In a previous post I brought up the odd trend of men keeping a long pinky nail. Reader comments informed me that the purpose was to snort coke. Since then, I've actually seen a lot of women with the extra long pinky nail, as well.

This past week, for the first time, the topic was brought up at a poker table. A middle-aged middle-eastern man at my 20-40 limit table sported the long pinky nail, and a 40-something Asian woman asked him, "what's with the long finger-nail? Is that supposed to be a sex symbol or something?"

Rather bashfully, the man answered, "no, it's just a habit of mine. No reason."

I still find it remarkable that so many people have made cocaine such an integral part of their lives that they are willing to make a public statement about it by keeping their pinky nails long. My view of the average cocaine user has certainly been altered; while the pinky nail is still most common in middle-aged asian and middle-eastern men, these men have a fully diverse range of occupations and personalities.

YTD Results: High-Low Stud 8

2008-10-13T11:15:00.001-07:00

When I get home from work each day, one of the first things I do is go to the computer and record my results in as much detail as possible. This can include specific start and end times for each game I played, as well as notes and of course win or loss amounts. I try to keep track in my head each time I move from one game to another, but sometimes I move so many times that I can't remember, and instead of particular games, my record for that day will just be under "various" (I've done this 8 times for a total of 58 hours). I do have accurate records of my total win or loss each day, which is important for tax reasons; this is easier to keep track of because I can just subtract how much I started with from how much I have at the end of the day.

Fifty-eight hours of play in "various" games notwithstanding (and also a few hours in mixed games), here are my results this year in Stud High-Low Eight or Better:

month profit hours rate

Jan: 472 15 31.47

Feb: -48 35 -1.37

Mar: 2145 25 85.80

Apr: 172 23 7.40

May: 3793 34 112.39

June: 2041 24 85.94

July: -1392 23 -61.87

Aug: -562 9 -66.12

Sept: -566 13 -44.39

Oct: 1966 19 102.13

2008: 8021 219 36.67

If these results look erratic, I think it's only because that's the nature of poker and the fact that I didn't play very many hours of stud8 in some of these months. I think this chart may give you a better idea of how difficult it is for a lot of poker players to stay emotionally detached from their winnings and losses. Three straight losing months can instill a lot of doubt. Overall, I've made over $35 an hour, but I've had four losing months out of nine and a half. My hourly standard deviation is $300, about 8 times my win rate.

I think this is the first time I've listed any summary statistics here in my blog. I haven't felt comfortable giving detailed information about my income, but I think this cross-section is a good compromise between my own privacy and giving my readers an idea of what results can look like. Personally, I'm very happy with my result in this game this year- I had almost never played stud High-Low before.

$40 NL at the Bike

2008-10-05T13:35:00.000-07:00

Sorry for another long delay - I went on vacation for about ten days, during which I served as Best Man at my brother's wedding on Long Island. Congratulations, Max and Marie!

On Friday after work, my friend Alex and his friend Brian came to the Bike. They sat down in a $40 NL game, with $1 and $2 blinds. I moved from my $20-40 limit game to their game once I was off the clock. I had heard this game described as "the biggest little game in town" because there was supposedly so much action that it's possible to really make a lot of money despite the low stakes, but I had never ventured to sit in the game before. Although I had a lot of fun playing, I didn't really see the potential for big winnings. There was one guy who consistently pushed all-in with nothing, but he only lasted about an hour before finally giving up. A few of the other players were pretty bad, too, but they were losing their chips rather slowly. I think the rake was $4 - it may have even been $5 after the jackpot fee, I don't remember exactly. In any case, when pots generally range from $6 to $50 or $100, it's pretty significant to have $4 taken out of each pot. Unless there are usually two or three maniacs per table rather than just the one that was in our game in Friday, I think it would be very tough to average more than $5-$10 per hour at this game, and that's assuming it's possible to keep focused. Me, I was chatting with my friends and watching baseball on TV.