Thursday, December 20, 2012

Tournament deal analysis

Although it's not officially condoned by the casino, deal-making is pervasive in tournaments, and when I decided to start playing tournaments I knew that I would need to improve my understanding of this aspect of the game. As I've mentioned before, I think optimal deal-making is best viewed as an extension of sound poker strategy, even though I was originally reluctant to consider making deals. For this post, I'll quickly discuss the three deals that were under consideration in the tournament last week when I came in second place.

The Bubble Offer: The first deal offered came when we got down to eight players. The seventh place player would win nearly $1000, but eighth place gets nothing, so this is a rather severe bubble. It was suggested that we should all give $30 to whomever was knocked out next, essentially giving eighth place have a payout of $210.

A severe bubble like this creates a strategic advantage for the players with the biggest stacks. If the smaller stacks are playing optimally and mostly folding and waiting until one more player gets knocked out, the chip leaders can win all the blinds and antes hand after hand by simply putting everyone else's tournament lives at risk. As I said in my last post, the other players were playing far too recklessly, and so this effect was greatly diminished. However, the larger stacks still have some advantage to the extent that the other players realize they should be playing extra tight.

When the deal was offered, I was at or near the chip lead, and I refused the $30 bubble idea. My explanation to the other players was that, as the chip leader, I was clearly not going to be the next one knocked out, so it would make no sense for me to donate $30. I knew this made me look cheap and unsporting, but I didn't want to explain to my opponents the more subtle reason for my refusal: I didn't want to give up my strategic advantage against everyone as the table's chip leader. If the bubble gets $210 instead of $0, it's psychologically much easier to deal with, and so my opponents would not be as desperate to hang on to get into the money. In other words, I would not be able to steal the blinds and antes as easily. The other players, muttering about how cheap I was, agreed to make the deal without me. This didn't help my situation much (the bubble player would still be getting $180), so I objected that this was collusion against me. The floorman agreed. The players pointed out that there was nothing I could do to stop them. Indeed, I knocked out the next player before long and everyone gave the guy some money (I think one guy gave him $60 to cover my part). This is exactly the sort of awkward situation that made me dislike tournaments in the first place, as I mentioned in an earlier post about why I didn't play tournaments.

According to the other players, this $30 bubble deal is commonplace. I think I will continue to refuse it if I'm near the chip lead, but accept it otherwise. I wonder how long the other players will tolerate that!

Another option is to try to influence tournament policy to make something like this deal "official." If the eighth place player had been officially lined up to receive $400 of something, I could avoid the unpleasantness of needing to discuss under-the-table deals with poker players. Considering the strategy of trying to make more final tables but with smaller chip stacks that I discussed in my previous post, this extra payout place would also be advantageous to my EV if it were officially adopted. I think if I discussed the situation I experienced where the players all colluded against me (as the floorman agreed), the tournament administrators would consider making this change.

The proportional chop offer: The first deal of the traditional "chop" variety (where the rest of the money is split and the tournament is over) that was suggested was a proportional chop. This means that each player would get a proportion of the pot equal to the proportion of the remaining chips. I was well aware that this clearly favored the bigger stacks. In fact, it's easy to imagine the smallest stack(s) getting paid less than last place money and the biggest stack(s) getting paid more than first place money. It was not clear to me how exactly this would play out, but I was not about to be the lone holdout on this deal. At this point I had about 400K of the 1M chips in play, and there was about $14,000 left in the pot. This deal would have paid me about $5600, not far from the $6300 or so that was awarded to first place. I wasn't sure what my EV would be if I kept playing, but it seemed like it must be less than that. I simply started counting my chips and hoping everyone would go through with it. After about two minutes, one of the short stacks decided to back out, so the deal was off. (The defector happened to be one of the two people most upset with me for refusing to take the earlier Bubble Deal.) We continued playing.

I used an online calculator (which I don't trust because I found a logical inconsistency that suggested an EV of greater than first place money for someone holding 90% of the chips) that suggested my actual EV was $4340 at this point, assuming all players are equally skilled. If this were accurate, I guess my EV was closer to $4600 because I was almost certainly better than the average player at the table.

As I said before, the casino does not officially condone deals, although they do look the other way. This means that in order to end the tournament and make a deal, the players would have all had to go all-in blindly and have the dealer deal out hands until just one person was left. The casino would then hand out the official winnings to everyone based on where we were each knocked out, and it would be up to us to dole out the agreed-upon amounts. This requires a level of trust in other players that I'm not completely comfortable with. I do think it's pretty unlikely someone would have the guts to back out on a deal like this, but something similar did happen at the Bicycle Casino once (although not in a tournament*). In this case, whoever came in first would also have to fill out a tax form because it is IRS policy that anyone who wins over $5k needs to do that. I pay my taxes anyway, but this is still another unwanted complication. I'm also not entirely sure who would be doing the calculations. Together, these factors diminish the value of the chop somewhat - perhaps as much as 20% should be discounted from the EV of a chop to account for these concerns, but 10% seems more reasonable. Still, 80% of $5600 is still $4480, which is probably greater than the EV I would have by playing the tournament out. (I'm assuming the poker calculator was overestimating my EV as the chip leader. Perhaps my EV was actually around $4000)

Making the deal also has the added benefit of greatly lowering the volatility of our winnings. If we discount by 10% instead of 20%, it comes to $5040, so I do think the deal would have been well worth it considering all the above factors. As I will discuss below, however, there are still other factors yet to be considered. All told, I think the deal was worth it for me, but the fact that someone backed out was not the disaster for me that it seemed like at the time.

The First Place offer: After we had been playing with three players for about ten minutes, I had around 60% of the chips, and my younger opponent suggested a chop wherein I would take first place money (around $6300), and he and my older opponent would share second and third place (around $2400 each). I could hardly believe this offer - I couldn't lose! - but the older player did not seem at all interested, barely acknowledging that an offer had been made. We continued playing.

In retrospect, I think this older player, who later informed me he had trouble hearing, probably did not even realize a deal had been offered. The lesson I learned here is to be a little more assertive and persistent in pursuing lucrative deals. If this third player had still demurred after the offer was explained to him, as I expect he would have, I should have offered him $100 to take the deal, and been willing to go up to $500. I probably lost quite a bit of value with my passivity.


I mentioned that there were some factors worth considering that I skipped over in the above analysis. As a poker player, I have many objectives beyond just trying to make optimal strategic decisions by maximizing EV. When it comes to making deals to split the winnings at the end of tournaments, one objective in particular competes with my primary goal of maximizing profit: I would also really like to play the tournament out to the end because that would allow me to improve through experience. I learned quite a bit about my competitors at the Charles Town casino by playing out the three player and two player scenarios in the hour or two after The First Place Offer was passed over. In order to effectively balance these two considerations (immediate EV versus gaining valuable experience that will help my EV in the future), it would be helpful to put a monetary value on the otherwise qualitative value of this experience. I will explore the question of how to do this in a future post. I expect it will involve discounting the value of my future income, which is a standard practice in economic theory.

* One Bicycle Casino promotion was to give away about twelve keys to a car over the course of a day, eleven of which were fake. At the end of the day, all the keys would be tried and one of them would work and that person would win the car. The twelve people agreed that whoever won the car would give the others some amount of money, maybe $1000 each. The lady who won the car backed out.

Sunday, December 09, 2012

Comeback Update: First Tournament Cash

In my sixth tournament since deciding in October to return to poker on a part-time basis, I finally made my first cash (aside from $225 in bounties from a couple of bounty tournaments).

Yesterday, I came in second in a $250 re-entry tournament at Hollywood Casino in Charles Town. There were seventy entries. I made only a single entry (I doubled up early) and was paid about $3150, for a net of about $2900. First place paid about twice that, and I very nearly won. We played for quite a while with three players and then also heads-up. At one point I had about 80% of the total chips. At two points, we nearly made deals that would have been extremely advantageous to me, but both times we had one holdout. The winner was a large older guy with a pretty thick accent originating, I guess, from West Virginia. The tournament lasted from noon to 8:15; after the tournament was over, the winner made a late entry into the 7:00 tournament, and was just sitting down as I was heading for the parking garage!

This was my third time playing this tournament. It starts with blinds of 25-50 and each player gets 15,000 in chips, which is a good amount (the more chips, the more chance for "poker skill" to come into play - although I think my clearest advantage over my competition is due to their poor short-stack strategy). Like most tournaments, the blinds go up quite quickly, though, so it's not long before the skill factor starts to diminish.

Very early in the tournament, I had top pair and called a skilled player's multi-street bluff to go up to about 20K. A little later I made a silly mistake that ended up confusing my opponent and earning me a big pot. With pocket tens, I flopped a set on a board of KJT. My opponent bet small and I tried to raise to 1600. but I accidentally put in a 5K chip instead of the 1K chip, so my bet was 5600 (into a pot of around 2000). I knew I couldn't take it back, so the best thing to do was play it off as if I meant to do that. This way, I get the benefit of giving my opponent a wrong impression of my hand, plus (perhaps more importantly), a big bet like that is likely to be noticed by the rest of the table, giving them all a false impression of my playing style. The enormous bet was a mistake, but it has lots of pleasant side effects if I don't let on that I didn't do it on purpose. My opponent had about 12,500 left and called the bet.

A small card came on the turn. We both checked. If my opponent had a straight draw, I wanted to give him a chance to bluff me on the river after he missed his straight. The river was another King. My opponent checked and I put him all in for his last 7500. He made what I think was a very bad call with Kx and I was suddently up to about 35K in chips. Another call of a multi-round bluff (this time I had AK high) put me up over 40K. I had quite a few lucky hands (eg someone called a big semibluff and I made my straight) after that and cruised into the final table with about 180,000 in chips. There were 1,050,000 total chips in play, so I had about 17% of the chips at that point. I shared the chip lead with one other player.

Third place paid around $1700 and seventh place paid almost $1000. This means that the correct strategy for a short-stacked player at the final table is to try to hang on for dear life in order to get at least that $1000 prize for seventh place. Players certainly adjusted their style for this consideration, but in my opinion they did not adjust it nearly enough. Players were still far too reluctant to fold hands that they knew were strong pre-flop, even though "strong" can just mean "60% chance of winning." It's not worth a 40% chance of getting knocked out just for a 60% chance of doubling your stack at that point in the tournament. That the players almost all made this mistake is important information to keep in mind for the next tournament, because it has significant strategic implications: getting to the final table with a short stack has a higher than normal EV, because they players in this tournament will make it unusually easy for me to simply fold all my hands and get into the money. Had I known my opponents would have this bias against folding on the bubble, my strategy yesterday would have been quite different when I had about 150K chips with twenty players left. At that point, the correct strategy would have been to start playing extremely conservatively and cruised into the money. I was fortunate to build up my chips a little bit more before the final table by playing a few more hands, but in retrospect it was not worth the risk of getting knocked out when I had such an easy $1k win waiting for me.

The first deal offered was a "proportional" payout deal that was offered when I was up to about 400k in chips and there were six players left. I asked what this meant and was told that whatever proportion of the total chips we had in our stack would be the proportion of payout pool we would each get. This meant I would get about 40% of $14,000, or $5600, which is almost first place money. I didn't bother to calculate this at the table, but I already knew from some casual analysis that such a deal would greatly favor those who had the most chips, so I quickly agreed, as did everyone else. We had stopped playing and were all counting our chips before someone finally backed out and we continued playing.

The mistake I noticed players making of being too reluctant to fold their strong hands in order to move up in payment was even more acute when it got down to three players. The difference between second and third place was $1400. The older guy who eventually won the tournament had complete disregard for the strategic implications of this and played as if second and third place were equivalent and all that mattered was coming in first. Seeing this, the younger third player should not have played any hands until I had knocked out the older guy. Instead, the third place player only tightened up slightly and I eventually knocked him out. At one point, the older guy caught up to me in chips after I made a call getting 3 to 1 odds on what I thought was about a 50% shot. I should probably have folded, but I made the mistake in failing to tighten up my game enough. I should have just waited until the younger guy was knocked out before playing any more hands. To be fair to myself, I had a lot of things to keep track of after making it so deep into a tournament for the first time in a few years. Fortunately, it worked out okay, and now I know one extra thing I can focus on improving.

When we got down to three players was also when the second deal was offered. I had a big chip lead (I was at about 600k I think), and the younger player offered to give me first place money and split the second and third place money with the other guy. Obviously, this would have been a fabulous deal for me, but the older guy didn't seem interested. I probably should have tried negotiating around that incredible offer, but the older guy was a bit hard to communicate with and seemed entirely uninterested in what we were talking about. In retrospect, I think he might literally not have heard that there was an offer being made at all, and I may have cost myself quite a bit of money by not making certain that he understood the offer. One reason was that the casino did not officially sanction the deals, and the dealer would not stop dealing to allow us to discuss it. When the earlier offer had been made, we had all stopped playing, but this time the older player immediately kept playing and I took that as a cue to drop the subject.

By the time the tournament ended, the older guy and I had been playing heads up for almost an hour and the blinds were 25k and 50k with 5k antes. His style was pretty conservative pre-flop, rarely raising and sometimes even folding on the small blind. He would bet most flops, however. I was up about 800k to 200k at one point and had him all-in, but I lost on a 60% shot. On the hand that crippled me (bringing me down to 35k), I had 66 and my opponent raised to 150. He had been betting most flops, so I figured I would just call him pre-flop and let him bluff the flop. The flop came QQ4 and my opponent checked out of turn. (He often acted out of turn, blaming his hearing. He never took back an action that was made out-of-turn, so I'm inclined to believe he was not being manipulative.) This is an excellent flop for 66, and I did not want to give him a chance to hit a pair on one of what were likely 6 outs for him on the turn, so I bet out 140. He pushed all-in for his last 200 or so. I think his most likely hand here is Ace-high, but it was suspicious that he was planning to check the flop but then decided to raise when I bet. In any case I was getting about 4-1 odds and called. He had Q8 suited; I guess he had been planning either to check-raise (if he thought he was first to act) or slow play until the turn. Anyway, no 6 came. I got may stack back up to 140K, but then lost with K5 when he paired his 4 with a K4.

Certainly, this is a nice and encouraging result for me, but I am also very disappointed not to have won. Also, I got very lucky to get to the final table. However, I am happy to be solidly in the black for my new tournament career. Most importantly, I learned quite a bit about my weaknesses, and I'm eager to return to the felt to try to exploit the weaknesses I saw in many of my opponents. These are exactly the sort of motivations and progressions that inspired my professional poker career when I started seven and a half years ago. I don't have as much time to pursue that passion as a did back then, but it's an exciting development. I now think that playing in the 2013 WSOP is a real possibility.


I got a remarkable comment to my recent post about Poker Strategy by Nesmith Ankeny. The comment was really quite stunning to me because I had never heard of this book before I got it from the library and I certainly had no inkling that anyone would feel passionately about it. My impression was that this was an entirely overlooked book in the poker world, but then someone showed up out of the blue on my little-known blog just to defend the book's honor. Just now I looked at the book review section of Gambling Theory and Other Topics by Mason Malmuth, and indeed Malmuth reviewed the book briefly and gave it a 9/10. I did not remember it among the 124 he reviews there. Here is the entirety of Malmuth's review (p 348):
90. Poker Strategy, Winning With Game Theory (9) by Nesmith Ankeny.  This is an excellent book on draw poker based on a game-theory approach. Many strategic concepts are discussed, and I think this book is must reading for serious players.
I wish I had taken this seriously back in 2005 when I got Malmuth's book. Ankeny's book is now a little redundant if you read The Mathematics of Poker by Chen and Ankenman, but back in 2005 I think the concepts in Ankeny's book could have given me a head start of a few years in terms of how I now think about poker. I think I will search Malmuth's reviews for more books that he deems "must reading for serious players." Come to think of it, I think Malmuth was still doing reviews on the 2+2 website as of a few years ago, so I should check over there, too. I'll let you know what I find.

Wednesday, December 05, 2012

"Poker Strategy" by Nesmith C. Ankeny and Transferring Poker Skills Across Varieties

There is a wide range of skills that are useful regardless of what variety of poker you want to play, but for any particular game certain skills could be much more relevant than others. A classic example is the ability to successfully determine when a player is bluffing, which is useful in limit holdem but much more important in no-limit holdem. Employing squeeze plays, estimating implied odds, raising effectively for secondary reasons (and recognizing when you opponents might be doing this), and semi-bluffing are a just a few of the many other skills that differ in importance from one poker variety to another.

Sometimes, if I only play one type of poker for any stretch of time, I will completely neglect the skills that are less important for that game. By playing or studying other varieties of poker (or toy games), I often manage to remind myself of some of these other considerations. Not only does this provide an opportunity to make subtle improvements in my primary poker variety, but, for me, it's also a good way to rekindle some excitement about the game by opening up a new direction to explore. This was the main benefit I found to reading a book analyzing Jacks-or-Better poker. A side benefit was that I gained some historical perspective on the history of analyzing poker using game theory.

The book I finished reading was Poker Strategy by Nesmith C. Ankeny. Well, I skimmed it, anyway. That is, I skimmed the parts I didn't skip over. In some ways, the book is horribly dated - imagine if someone today tried giving an unspecific title like "Poker Strategy" to a book theoretically analyzing Jacks-or-better draw poker, which nobody even plays anymore - but much of it was timeless. The game theory analysis looked accurate and went deep enough to provide specific results related to draw poker that I imagine would be extremely useful if anyone still played it.

As I alluded to, there was one skill in particular that was clearly of utmost importance in Jacks-or-Better that is not as central to no-limit holdem: the ability to pin down exactly what sort of hand your opponents are looking for. Given a player's bets before the draw and the number of cards he draws, it is possible to significantly narrow down his range of hands with a high degree of confidence. In particular, you can usually tell if he has a flush draw as opposed to a made hand (or at least a bluff of a made hand). In holdem, it is much easier to disguise flush draws as made hands, and so figuring the probability your opponent holds one type of hand or the other is not nearly as determinative to holdem strategy. (It is relatively useful in stud games, however, and this was my most glaring weakness when I played that form of poker.) As a result, I have not spent much time thinking through the intricate tactics of playing when you have various opponents whose hand types are reasonably well known.

Let me give you an example. In any form of poker, if you strongly suspect your opponent either has a very strong hand or nothing (a drawing hand), it is usually correct to check to him, assuming your hand strength falls in between those extremes. Now suppose you have two opponents, the first of whom likely has a moderately strong hand and the second of whom has one of these drawing hands. This is an interesting situation that I hadn't considered carefully before because it simply doesn't conform to the way I usually think about no-limit holdem, my preferred form of poker. However, Ankeny has a nice, thorough analysis of this situation in his book. It turns out that this situation presents a strong bluffing opportunity if you are betting first, because the player with the moderately strong hand will find it very difficult to call, while the player drawing to the flush or straight will usually miss. I don't know if this situation will come up in any future game I play, but I might find myself in a similar situation, and at the very least it got me to think about the game in a way I might not have otherwise.

Much in the same way the Chen and Ankenman's Mathematics of Poker was useful to me even though it mostly analyzed toy games, the fact that Ankeny's analysis in Poker Strategy was sound and thorough made it somewhat worthwhile even though it did not cover any of the specific games I play.

Monday, November 12, 2012

Part-Time Poker Comeback

After a long hiatus from poker and a brief foray into academia, I've decided to return to playing poker part-time. (Most of the rest of my time will be spent watching my two year old and three month old sons, and I'm also doing some politics/skeptic blogging, not to mention my return to this blog.) For the next two months, I'll be playing one to two tournaments a week in Charles Town West Virginia and putting another three to five hours a week into poker research and blogging. That's not a whole lot of time, but my no-limit holdem game was very strong as of 2011, so I'm hoping it won't be too hard for me to translate that into tournament poker once I get the rust off.

One tentative goal I have is to be ready to play in the WSOP in 2013. I will probably only do this if I think I have positive winning expectation. I'm not sure how to determine that.

Live poker was legalized in Maryland casinos on Tuesday via a referendum. So, poker will be spread here quite soon, pending the result of a comically silly lawsuit in which the law's opponents are claiming that it required a majority of "qualified voters"as opposed to a majority of those who actually voted. (I guess if this gets overturned, then so will the gay marriage, gerrymander, and DREAM acts that also passed by referendum on Tuesday here in Maryland. Not to mention the electoral votes given to Obama!) The new law didn't figure much into my decision, though. Indeed, none of the Maryland casinos seem to be much closer to me than Charles Town WV anyway, and, besides, I made the decision to return to poker before the law was even passed.

The two tournaments I will be trying to play each week are at noon on Fridays and Saturdays. The Friday tournament is $100 plus a $25 bounty. I have begun doing some analysis of Bounty tournament strategy, and I hope to have a post up about that next week. The Saturday tournament is a $250 tournament. So far I have played four times and won $225 in bounties (in a single tournament). No cashes.

On my poker reading list:
Poker Strategy by Nesmith C. Ankeny. This is a book written by a mathematician in the early 1980's focusing on draw poker. I had not heard of this book before I found it in my local library system last month, and I'm very interested to see what the state of the art in poker game theory was thirty years ago. I've started it, and so far the author is on target with his poker philosophy, but he hasn't gotten into any real analysis. He has an unusual writing style that can interferes with getting to the point, but it can be amusing. For example (p 5):
A poker player considering luck in planning his moves at the poker table is like the Pope contemplating marriage. The thought is heresy and can only lead to trouble.
Poker Face: Mastering Body Language to Bluff, Read Tells, and Win. Also from the library, I thought this might be a more analytical version of Mike Caro's classic Book of Poker Tells, but after flipping through it, this one looks very fluffy and has no pictures. I'll take another brief look to see if there's anything worthwhile.

Kill Everyone. This book's peculiar name stems from its predecessor, Kill Phil, referring to Phil Hellmuth. One of the three authors is a professor at UMD College Park, and it looks reasonably analytical, so I think it will be worthwhile.

The Full Tilt Poker Strategy Guide: Tournament Edition. This is a book I bought a while back because I was interested in a few sections in particular. I really liked the analysis so far, and since it focuses on tournaments, I think it will be very worthwhile for me to read. (Full Tilt's legal issues notwithstanding.)

Tuesday, July 31, 2012

The Bike contests a prop's unemployment claim

Back on December 1, 2010, I was informed by the Bicycle Casino that they were eliminating my position as a host/prop for the $500 NL games. They told me I could choose either to become a prop in the $2 green chip section (where they play games like 8-16 limit and $80 buyin NL holdem) or be laid off. They gave me a sheet to sign that looked something like the following, except instead of the second option being "I choose to be laid off," it said something like "I prefer to quit," which might have imade it difficult for me to collect unemployment insurance payments. When I decided to "choose to be laid off," I was a little worried that I wouldn't get my benefits, but everything worked out fine.
I signed this form after HR agreed to rephrase the "laid off" option. (I removed my ID#.)

I'm bringing this up now because recently one of my former fellow props asked me if I still had this document. Back in December 2010, he and another prop opted to take the pay cut rather than be laid off. He was assured, as I was, that if he took this option he could continue to play the $5 yellow chip games in the Plaza section, even though his position would officially be as a prop for the smaller games in the Royal Section. Unlike me, he trusted them to honor this promise. I thought they would allow it for only a month or two, but as it happens, they actually honored it for over a year. Then they told him and the other prop that they had to start working in the Royal Section after all. He refused this role change and quit. The Bike then contested his application for unemployment insurance payments, claiming that he had quit and was not laid off. According to him, the Bike also claimed that the above document had never been offered. That's why he asked me if I had it.

As you can see, I did have a photo of the memo. It seemed prudent to have a copy for myself in case I had any trouble getting my unemployment benefits. I had several reasons not to consider the casino particularly trustworthy. These include several minor broken promises, rumors of illicit business dealings such as accepting kick-backs on overpriced renovation projects, and a clear disrespect for the props by some of the middle managers. Also, they routinely changed the expectations of our roles in minor ways without consulting us and sometimes without even informing us. In any case, if I was to be leaving, they wouldn't have any particular interest in doing me any favors. I had a chat with an employment lawyer who said it was best for me not to sign anything but that the above document sounded okay. I signed it and had no problem getting my benefits.

In the end, the prop won the case against the Bike, and he will be getting his unemployment benefits. I don't know what the ruling hinged upon exactly, but I guess it was that his agreed-upon role at the casino had been altered significantly enough to be considered an elimination of the position on the part of the casino.


The big news today is that PokerStars has acquired Full Tilt as part of a settlement with the Department of Justice over last year's charges of fraud. It looks like foreign players will be getting their money back, but U.S. players' accounts remain in limbo.

Friday, July 13, 2012

Should poker players embrace new forms of poker?

This post, possibly the last in my series of posts addressing non-adversarial concerns of poker players, was quite difficult for me to put together because I changed my mind about the answer. I used to think that embracing new forms of poker was a good thing, but after considering it more carefully I now think most players are justified in their reluctance to spend time on a new game.

As I was gearing up to write this article, I convinced myself that my affinity for new games came mostly from the fact that my advantage comes from my superior fundamentals and creativity. After all, playing a new game requires players to draw on fundamental, general principles of poker as opposed to the knowledge of the peculiarities of a particular game. I concocted an analogy between a poker player who plays the same form of poker each day and a golfer who plays the same course each day. Sure, such a golfer could probably establish a profitable advantage over other players on that one course, but if you were truly a good golfer, you would embrace the challenge of playing a new course. You would need to draw on your creativity and your ability to see parallels with courses you've played before, and having good fundamentals would help carry you through the challenge.

In reality, I doubt any professional golfer would tee off for a tournament without ever having practiced the course, and poker players who insist on practicing a new form of poker before anteing up are being similarly prudent. The truth is, I, too, am hesitant to jump into new games for substantial stakes. Instead, I try the game at low stakes first, which is similar to practicing a golf course before a tournament. I think I was fooling myself in thinking that I was willing to put my fundamentals and creativity to the test to the same extent that I have been willing to put to the test my time-tested skills in games like No Limit Hold'em. In NLHE, I have hundreds of hours of results and statistics to support my decision to play at substantial stakes.

That said, I do think there is substantial value in occasionally playing poker variants for low stakes. For one thing, it can act as practice for the games you play regularly. It forces you to focus on different aspects of poker and might help you to see new strategic parallels. In unfamiliar games, the mistakes of your opponents tend to be far more pronounced, and so you might notice some tendencies that are too subtle to have noticed in NLHE but would still be exploitable. Also, exercising your creativity really is fun, and this can reenergize your poker game in general.

You could also choose to do your homework and become truly superior player at a new game. Spend a few days studying the odds for drawing various hands. Work out the correct amounts to bet, call, or raise in several representative scenarios. Play heads-up with a friend and see what situations call for further study. Then play for a day at the lowest stakes offered and make note of what types of mistakes your opponents make. Go back home and calculate how best to exploit them. Then take a stab at some more substantial stakes. At this point, you are probably going to be one of the best players, because very few people will have gone to all this trouble. They will mostly be like me, having fun venturing into unfamiliar waters with only their wits about them. You will have both your wits and a flashlight to help you see where you are going. Still, take care to observe your opponents' mistakes. If you can't find any and you aren't winning, move back down in stakes. This is probably the only prudent and professional way to play a new game for substantial stakes. Your advantage will probably diminish after a few weeks.

Playing a new game can be fun and even profitable, but, like anything, it carries with it an opportunity cost. If you enjoy doing your own research, you can calculate the odds and exploit the unexperienced players for a while, and this might temporarily give you a higher EV than your opponents. On the other hand, it might not, and you are forgoing the value of playing in your standard game (or doing something else entirely).

One thing I've been trying to do with this series is to consider what effect each proposal would have on the poker community as a whole. So, would embracing new games help the community? It's hard to say, but I can see some potential benefits. It could attract interest from new players. Having the option to play a new game also provides a fun alternative for players like me, who might want a break from NLHE every once in a while. Perhaps most significantly, a new and better game always has a chance to catch on and revolutionize poker. After all, Texas Hold'em and was a new game not so very long ago.

Tuesday, June 12, 2012

Should poker players be willing to play in short-handed games?

Absolutely. Not only should you be willing to play short handed, but short-handed games are actually preferable to full-ring games.

Many players refuse to play unless a game is nearly full. Still more will play if there are five or six players but not if there are fewer than that. Sometimes, while sitting with three or four other players who are unwilling to play until more players arrive, I ask them why they don't like to play shorthanded. One such player told me that short-handed games are too expensive because the blinds come around too often. Sometimes it's simply that they don't want to play shorthanded in a game with me in it. Some players come for the social atmosphere and find that the competition gets too personal with fewer players. Other players seem to just like to sit around folding most of the time while waiting for AA or KK. Still other players probably have other concerns.

So, why do I think short-handed games are not only worthwhile but are actually better for poker players? Let's look at the three main concerns of a poker player: winnings, social experience, and game purity.

Effect on winnings: The old adage that "you need to play more hands when you play short-handed" is overly vague. The truth is that there is a much better way to transfer your strategy from a full-ring game to a short-handed game: When playing X-handed, play exactly as you would play in the same position relative to the button in a 9 handed game after the first (9-X) players fold. As I will now demonstrate, the two scenarios are very similar.

Suppose you are playing in the cutoff or button of a 9-handed game and the first five players after the big blind fold before the flop. If you have an idea of how to play in this situation, then you can play in a 4-handed game. There are only three very minor differences in the two situations. First, the 4-handed scenario would move faster because the deal would be quicker and you wouldn't need to wait for the first five players to fold. Second, the hand in the 4-handed game would be cheaper in most casinos because in most casinos the short-handed game would have a smaller rake and maybe no jackpot drop. (Both scenarios have four players left, so you are about equally likely to win the hand and end up paying the drop.) Third, in the four-handed game, you wouldn't need to worry about any bunching effects, and so the game is slightly easier if you are trying to combinatorially guess your opponents' hands. (As we will see presently, this is probably a negligible concern anyway.) So, the game is faster, cheaper, and easier. Faster and cheaper are clear advantages. Easier is a wash because it applies to your opponents as well as to you.

So, the strategy in a short-handed game has a nearly direct parallel to a situation most full-ring players are already familiar with: the situation where the first several players fold. Consider the implications of this. The first five hands after the blind are the least-often-played hands. They are the spots where you are most often sitting and doing nothing except waiting for your opponents to finish playing (and maybe gathering information to use against them). If you could just eliminate these five spots, you would vastly increase the rate at which you would have decisions to make. That is exactly what happens when you play short-handed. Winning poker players make their money by making better decisions than their opponents, so having more decisions in any given period of time translates directly to a higher win rate.

In addition, short-handed games require players to quickly gain a good sense of their opponent's strategies, because they will be going up against the same opponents in each hand. Also, the nature of short handed games is that they tend to fluctuate in size, requiring an ability to adjust to changing circumstances. These are skills that good players can put to better use in short-handed games than full-ring games.

I anticipate two main objections to my argument that short-handed games are better for your win rate. First, the situations I've described are not exactly the same. After all, in a 9-handed game where the first five players have folded, there is a "bunching" effect: because folded hands are slightly more likely to have contained low cards, the remaining cards are slightly more likely to be high (and thus strong). Just for a quick example, suppose the first five players will each play if and only if they are dealt an ace. Suppose they all fold this hand. If you are in the cutoff and also don't have an ace, then all four aces are still left and there are only 40 cards left (52 minus 12). For each of your opponents, the chance of having pocket aces is now 1 in 130 (4/40 times 3/39), much better than the usual 1 in 221. However, this is an extreme example. In practice, players do play some low cards and they do fold with hands like A2 (most players, anyway). The "bunching" effect is just not all that big a factor. Maybe I'll do a deeper analysis of this later. For now, I'll just say that I don't believe this is a big enough effect to contradict my claim that you can view them as being essentially the same. I concede that it makes sense to be tiny bit more wary of your opponents in the 9-handed game after five folds than in the 4-handed scenario, but making a big adjustment would be a mistake. You would be safe if you made no adjustment at all.

Second, you may argue something like:
Sure, those scenarios are essentially the same, but you are overlooking some real advantages to having those early-position hands that exist only in full-ring games. These afford me important opportunities to apply my superior poker skills. For one thing, I can use the time after I fold these hands to watch my opponents play. Since I'm more observant than my opponents and since I'm better able to apply new information, this represents a real advantage to me. Even ignoring this, my basic strategy in these EP hands is far superior to some of my opponents. The biggest weakness of many of my opponents is that they play too loosely, and this weakness is most pronounced in EP. Why remove these opportunities for my opponents to play badly?
These are reasonably strong arguments. It's true that playing short-handed eliminates some opportunities for strategic advantage, and for a thorough analysis, I would need to consider the value of these strategic advantages. For now, let me just give an intuitive explanation for why I don't think these arguments are strong enough contradict my claim that short-handed games are better. Yes, we are giving up some opportunities to gain value over our opponents through superior use of observation and superior play in EP. However, there is an opportunity cost to these advantages. For the benefit of getting to sit and observe your opponents, you are losing the opportunity to actually be playing more hands and applying your strategic advantages; if you really want extra time to observe your opponents, you can achieve that in a short-handed game by simply sitting out a few rounds and watching. As for your advantage over your opponents who play terribly in EP, this comes at the cost of the advantage you have over your opponents' LP and blinds strategy. Every hand we would get to play in EP is replaced in short-handed games by extra hands in LP and the blinds. Since these are hands that you are much more likely to be playing (rather than folding), it seems to me that your advantage over your opponents here is likely even greater than the advantage you have over your opponents in early position. I agree that it is much easier for your opponents to play terribly in EP, but it is also much easier for you to play great in LP and the blinds, because they often involve lots of decision making deep into hands. Playing "great" in EP basically just means having the discipline to fold a lot.

There are some rational explanations for why a winning player would have a higher EV in full-ring games. Perhaps they really aren't good at playing in the cutoff and on the button compared to their proficiency at playing in early position. Perhaps they thrive on post-flop situations that are multi-handed. Perhaps they don't have the ability to concentrate in the way that is required when you need to make many decisions each hour. Perhaps they make their profit by preying on players who play poorly in early position, or perhaps they play in a venue where such players are particularly prevalent. Perhaps their game does not lower the fees for short-handed games. If these describe your situation, you may have a strong case that you have a better EV when playing full-ring games. However, I don't think these are common characteristics of poker players or venues, and, in any case, any advantage you may have in EV per hand when playing full-ring games would have to outweigh the increased number of hands you are able to play in the faster short-handed games. A 4-handed game likely has twice as many hands per hour than a 9-handed game. Asking a player to make twice as much per hand in a 9-handed game than a 4-handed game is a very tall order.

In the end, I think that with a smaller rake and a greatly increased decision-rate, short handed games make for much more efficient winnings.

Big advantage to short-handed games, assuming you are better than your opponents in late postion and on the blinds.

Effect on social atmostphere: Full-ring games afford players the opportunity to sit back and relax. They chat with their opponents and even discuss poker strategy without worrying too much that the player they are speaking with will play many hands with them. Basically, the game is less contentious. On the other hand, they can sometimes get boring and players get impatient with each other for playing slowly.

Small advantage to full-ring games.

Effect on game purity: Smaller rake means slightly less negative effect on the game. Fluctuating game size requires a flexible strategy, which I view as a slight positive. However, some would argue that a full-ring game, with its slower pace and emphasis on patience and observation, is the way "pure" poker was meant to be played.

Very small advantage to short-handed games.

Unless you come mostly for the social experience, you should prefer short-handed games.

Thursday, May 31, 2012

What is the best fee structure for poker players?

(Another in my series of posts addressing what I think poker players should want from a card room.)

In Los Angeles, the rake tends to be $1 taken from the pot before the flop and another $5 after the flop, including $1 for the jackpot drop. In Las Vegas, it used to be as low as $4 with the fourth dollar not being taken out until the pot reached $80 or even $120. In higher-limit games (10-20 NL and above or 100-200 limit or above), the players usually pay "time," which means they pay something like $5-$15 to the house every half hour, but the pots are left unadulterated.

Nobody likes paying these fees, but we all acknowledge that the casino needs money to for all sorts of expenses and would like to make a profit on top of that. This does not mean that players should just accept whatever fees are levied and by whatever means the casino pleases. Not all fee structures are equally bad for players, and, whatever the structure, a smaller fee is clearly better. So, what structure is best for casino poker players? Can we do better? How much does the size of the fee really matter? Should we be "comparison shopping" and pressing the casinos to keep their fees low?


First, let's do a comparison of paying rake versus "time."

Effect on winnings: If you are playing in a 9-handed NLHE game, you will likely play about 30 hands per hour and win about 3. If you play tight and take a break once in a while, this is probably closer to 2.5 hands won per hour. Time games cost about $10-$25 per hour plus maybe $3 in tips. In a raked game, it costs $7 per hand won, including tip. Multiplying by 2.5, this gives $17.50 per hour. This corresponds to a $14.50/hour time game (assuming $3 of tipping per hour). This means that if you are a tight player, most time games are slightly more expensive.

Most players do not chop in time games, but most players do chop in raked games. It's probably better for you if your opponents chop because the game will go faster. This probably adds one or two hands per hour. The downside is that you don't get to watch your opponent's heads-up strategy as often if they are chopping, but I think an extra hand or two should be worth more than this extra information.

As I've said before, taking money from a pot rewards and encourages tighter play, which is bad for the game, especially NLHE. Adding money to the pot has the reverse effect. You are effectively playing higher stakes when you pay time instead of rake.

The advantage here really depends on the size of the rake or time fee. Time fees are usually slightly higher, but this is offset by chopping and increased pot sizes.

Effect on social experience: The time games encourage players to stay at the table, lest they waste hands they already paid for. Most players like this, but I find it annoying. I like taking a few leisurely breaks during a session, and I don't mind if the game becomes shorthanded.

Rake games encourage chopping the blinds, which helps the game go faster. On the other hand, if you don't chop, you might have some upset neighbors in a rake game.

Slight advantage to time games.

Effect on game purity: Time fees preserve the purity of the game. Rake fees alter the pot size and encourage chopping. This is especially problematic in low-limit games where the rake is a large percentage of the pot.

Advantage to time games.

Time games often cost a couple extra dollars per hour to play. I think it's worth it for game purity and social experience, but only if it's not too expensive. In higher-limit games, the rake does not disrupt the game too much and I would only pay an extra $3 or so per hour to play a time game. Even this might be too extravagant. That's an extra $3000 per year if you are a pro playing 1000 hours.


How important is the size of the fee?

If you do some comparison shopping, you can likely find a place that takes $1 or $2 less in rake ($2.50 to $7 or so per hour) or charges $5 or so less per hour in time fees. An amateur player might play 100-200 hours a year, which comes to around $500-$1000. A pro might pay an extra $5000-$10,000 per year. I'd say it's a very significant but not overwhelming concern.


What is the ideal fee structure? Well, I identified problems with both rake and time fees. The rake affects the purity of the game and rewards tighter play. The time fees unduly discourage taking breaks. The following idea fixes both problems:

Make the button pay the fee each hand. Like a "hand fee," only it's paid just by the player who has the best position. The one drawback here is that you can't really adjust the fee to the size of the pot like you can with a rake, and if there is no flop it's still only fair to charge the button the full amount. If this results in the game being too expensive, the casinos can start charging $4/hand instead of $5 (for example).

If someone pays his blinds but skips his button, treat it as if he missed a blind -- that is, he must post or wait for the blinds to reach him before he gets another hand. This fixes the problems with both the rake and time fees.

Are any new problems likely to arise with this solution? Any way players will try to "game the system" other than skipping the button, which I already addressed? I can't think of any.


I am considering playing in the WSOP main event this year. (I might look into selling up to fifty 1% shares in my winnings. Is that legal?) It's something that I almost feel I should do; playing the main event would be a great way to cap off my poker career, and it's something that people always ask me about when they hear I played professionally. Considering that I haven't played recently, my EV is surely lower than ever, but my enjoyment would probably be higher than ever.

Still, Noon to 12:30 am for days on end? That is too much poker!

Friday, May 18, 2012

Should Poker Players Point Out Dealer Errors?

I think so, but this may be specific to my own peculiar view.

At a poker table, it is the dealer's job to make sure the game is being played by the book. Some dealers are better at this than others, and even the best dealers make occasional mistakes. Bets are miscounted, hands are misread, players are directed to play out of turn, anti-collusion rules go unenforced, pots are split incorrectly, and any number of other mistakes can happen. When I notice these things, I like to point them out and get them corrected, but when I do some other players sometimes get upset. Should I be pointing these things out? Let's look at the main factors.

1. Effect on my winnings. 
The only direct effect is that I will usually point out errors even if they were in my favor, such as an opponent putting in two many chips to call a bet. I lose money when I do that.

One indirect factor is the effect of either upsetting or pleasing other players. However, there's not that much they can do about it, and not many people take these things very personally, anyway.

Another indirect factor is that new players might feel more comfortable in the casino, which may help to make the average competition a little softer.

This category is a wash, with maybe a tiny advantage to NOT pointing out errors, especially those errors that directly result in more chips for myself.

2. Effect on the social atmosphere.
Usually, if I don't point out an error, it will go unnoticed by whomever it hurt. So, by pointing out the errors, I might be making the social atmosphere a little more tense.

An indirect effect is that everyone can relax a little more about the whether the rules are being followed. We can trust that somebody else will usually point out any mistakes.

Another indirect effect is that players might trust each other a little more, which I think encourages a better social atmosphere in the long run.

For me, the major reason I like to point out any errors I see is that the alternative is unfair to inexperienced players and players who are new to a casino. For inexperienced players, they obviously are less likely to realize if a mistake has been made. For players new to a casino, they suffer from the fact that the other players are likely to know each other and be inclined to look out for each other. So, errors that were made in the new players' favor are more likely to be pointed out and reversed, putting new players at an unfair disadvantage. When this happens, the social atmosphere becomes much worse. However, these situations are rarely so clear cut as to make a big difference.

Personally, I just feel better if I do what feels like the "right" thing, so I would be particularly uncomfortable if I ignored errors. You may be different.

Advantage to pointing out errors, but this may be partly specific to myself.

3. Effect on the purity of the game. This depends on what you think "pure" poker means. To me, it means a game of poker played by the rules, but other purists might argue that poker should be a purely individualistic game, and no player should say anything that could help another player out, even if it's just to ensure that rules are being followed.

Advantage to pointing out errors, but players with different philosophies may disagree.

I personally would certainly like it if players took a more active role in policing their games, but it doesn't seem likely that we could overturn the prevailing mentality that players should avoid getting involved in other players' hands.


I accepted a spot in the PhD program in statistics at UMBC.


I've been posting on a blog called "Skepolitical," a portmanteau of "skeptic" and "political." My most recent post was on Attachment Parenting.

Sunday, May 13, 2012

Should No Limit Holdem Players Want Antes in Their Games?

Two of the main triggers of the poker boom in the 2000's, the movie Rounders and ESPN's well-produced broadcast of the WSOP (especially the Moneymaker victory), both specifically glorified the game of no-limit holdem. Rounders famously quoted Doyle Brunson calling NLHE the "Cadillac of poker games." Brand-new poker players came to the casinos looking for holdem games, especially no-limit holdem games. Before long, veteran stud players migrated to the no-limit games hoping to prey upon the newbies. The result is that, compared to holdem games, stud games have plummeted in popularity since the 1990's. Today, stud games feel downright antiquated.

One distinguishing feature of stud games is that they use antes, and, as a result, antes now seem as antiquated as the stud games they're used for. Actually, while antes are almost never used in NLHE cash games, they do usually come into play in the later rounds of tournaments. This is cause for consternation among some tournament players, mostly because the antes increase the effect of luck as compared to skill. Perhaps ironically, then, one place you can occasionally see antes in NLHE cash games is in the very high-stakes games, where you might expect the players to want to maximize the importance of skill. The reason they like antes is that many of these top players have recognized the problem I mentioned midway through my previous post on jackpots: standard NLHE has very little action if everyone in the game is playing a strong, solid, tight and aggressive game. To fix this problem, top pros have sometimes decided to add antes to their games. So, should the rest of us be advocating for the introduction of antes into our NLHE games? Probably, but let's look at the major considerations.

1. Maximizing winnings.
2. Having an enjoyable social experience.
3. Having a pure, intellectually stimulating game of poker.

All three factors have opposing forces that I will attempt to weigh against each other.

1. Maximizing winnings: If you are a strong player with a given set of opponents, your EV will probably be slightly improved if you are using an ante. With more action, you will be correct to play more hands, and this will give you more opportunities to use your superior skill against your opponents. Also, there will be more money in each pot, which means more potential profit. There are two major drawbacks, however. First, your expected volatility will certainly rise substantially because the antes directly increase the luck factor and, with more money being bet, you will effectively be playing higher stakes. This will possibly force you to move down to lower stakes. Second, your typical opponent's biggest weakness, playing too many hands, will suddenly become much less of a liability. Your weak opponents will be playing better even if they fail to adjust for the introduction of the ante. This is all subjective, but my guess is that these factors give a bit of a net boost to EV.

The previous paragraph assumes "a given set of opponents," but we must  also consider the effect on the player supply in an ante game versus a no-ante game. In the short run, only good players seem likely to want to use antes. The first players who will want to make the move to "ante NLHE" are those who are confident in their ability to adjust to the new strategic challenges posed by the introduction of an ante and those who recognize the problem I just described with NLHE losing action if you are at a table of solid players. We can expect that these players are better than average, and they will certainly not be novices. Despite this, I think that in the long run, bad players will really enjoy the antes. Having more action and higher volatility is way more fun. If we can get to the point where antes are no longer a novel concept, novices will be happy to play with them. In the long run, which is what I'm primarily concerned with in these blog posts, I think the antes will attract more bad players than good players because of the increased luck factor. Another small net positive for EV.

2. Social experience: For most people, getting to play more hands is more fun. Sure, there will be the odd player who likes to sit back and wait for AA or KK, but who needs those guys anyway? Others will object to the increased luck factor, but just as many will enjoy it. In the short run, some players will be put off by the novelty of antes, but others (such as myself) like thinking about novel strategic situations, and in any case the novelty will wear off. A net positive.

3. Pure, stimulating game of poker: Some purists, including yours truly, are just concerned with having a robust, stimulating, fairly-played game, unencumbered by factors introduced by the casino such as jackpots, rakes, or confusing rules or promotions. The antes affect none of these factors except that they have the potential to engender a much more stimulating game by discouraging tight, nitty play. Some purists additionally want a traditional or low-luck game of poker. For these players, the antes may be a problem. From my perspective, however, the antes represent a major boon to the game itself.

Many of the factors above relate to my personal preferences, which may make it hard to convince other players (or my readers) to come to my side if they are not already so inclined. For example, if you understand the importance of having luck in a poker game (this is what attracts the bad players) but you still think it's better to try to minimize it, there's not much I can do to convince you that antes would be a good thing. Also, my approximations on the effect on EV are certainly up for debate. However, if you agree with me on these factors (and you should!) then you'll agree that introducing antes is a really good idea.

I wonder whether we can ever really make the jump to adding antes in lower stakes games. Perhaps it's like the QWERTY keyboard: research shows it's not optimal, but it's just not worth making the switch. It's not surprising that the high-stakes NLHE games were the first to adopt antes. Nobody playing those stakes is going to have an issue with getting outside their comfort zone to play a slightly novel form of poker. (Well, maybe Andy Beal.) They're not worried about scaring away new players, and they are looking to maximize the amount of action in their games. It's also possible that these high stakes games have fewer action players and are thus more prone to going cold.

All of these factors that encourage the use of antes diminish as you go down in stakes. What I think needs to happen for antes to become prevalent is for enough regular players to realize that the top pros are playing with antes. When that happens, the game will no longer look as weird and novel as a Dvorak keyboard. In the meantime, regular players can advocate for antes by convincing their fellow poker players that antes are a good thing and by asking their floor men to make "interest" lists for ante games.

Sunday, April 29, 2012

Should Poker Players Want Jackpots in Their Games?

This is the second in what I hope will become a series of posts on the things that (good) poker players should look for in an ideal casino game. Regular players in poker rooms hold sway with the casino management, and this series can be viewed as my personal commentary on what I think you should be lobbying for if you are a good poker player.

Entering "jackpot" into the search field on this blog yields many instances of my bemoaning their existence in my games, but in truth my disdain for jackpots has waned recently. (This is decidedly not due to the fact that I've won a substantial amount from jackpots, which many of my casino acquaintances assumed would change my negative opinion of jackpots in general. Talk about results-oriented thinking!) There are many different types of jackpots awarded in poker games at casinos. In Los Angeles, the "Bad Beat Jackpot" is by far the most pervasive, but in Las Vegas, I think the "High-Hand Jackpot" might still be more common. Both usually take $1 out of each pot (sometimes only if there is a flop) and award money to players in rare instances such as losing with a very strong hand (Bad Beat) or just winning with certain types of very strong hands (High Hand).

For this post, I'll be thinking primarily of the "Bad Beat" type of jackpot, which I think is the worse of the two. I'll be looking at how it affects the three main concerns I mentioned in my previous post:

1. Maximizing Winnings.
2. Having an enjoyable social experience.
3. Playing a pure, intellectually stimulating game of poker.

I don't have anything to say about concern #2 here, but some players may have a strong personal preference for or against jackpots. Personally, I don't like them much. Let's look at concern #3 and then #1.

If playing a pure game of poker is your main reason for coming to a casino, you will hate jackpots, especially bad-beat jackpots. For purists, putting finely-tuned poker strategies to work against real opponents is the essence of what makes playing poker worthwhile. It can be a joyous experience to put theory into practice and have it work out. Jackpots destroy this by changing the players' incentive structure, thereby interfering with the logical inferences about your opponents' decisions that characterize a pure game of poker. These disruptions are most evident in Bad Beat Jackpot games during hands where there are two Aces on board, because the easiest way to win a jackpot is for a third Ace to hit the board while one player has the case Ace and the other player holds a large pocket pair. Winning the actual pot becomes insignificant, with players focusing only on making sure they do not miss out on the 1/40 or so chance at winning a few thousand dollars.

There is another, subtler, consequence of jackpots on the purity of the game that is often overlooked. The $1 jackpot fee is taken from each pot, and this affects optimal play. A slightly smaller pot means that it's optimal to play slightly tighter (and, if other players make are making that adjustment, it becomes correct to play more aggressively). This is a minor disruption, but it is made worse by the fact that another $5 is usually being taken out for the casino's rake, and my sense is that each extra dollar taken out is marginally worse than the previous. (Consider, for example, the effect of taking the first dollar out of a $1000 pot compared to taking the thousandth dollar out after already removing the first 999!) In No-Limit Hold'em, which already has a problem of having too little action when everyone in the game is solid, the problem is especially pronounced. A future post may explore the possibility of adding an ante to NLHE games in order to liven them up a bit.

The jackpots introduce opportunities for corrupt practices by players, dealers, and administrators. Honest players now have one more thing to be on the lookout for in order to protect themselves.

When a jackpot is actually hit, the game comes to a screeching halt. Winners celebrate, decks are examined for evidence of cheating, administrators skim off the top of the jackpot (legally and sometimes illegally), ID's are taken out, and forms are filled out for tax purposes. A nightmare for a purist who just wants to sit and play poker.

I hesitate to call myself a purist (after all, it ranks third on my list of concerns), but maybe I am. Certainly, I'm sympathetic to this way thinking, and I consider "game purity" to be the major reason to dislike jackpots. I previously would have told you that Maximizing Winnings is my primary issue with jackpots, but the effect of jackpots on winnings is actually pretty complicated. Let's examine the pros and cons.

Having often argued against jackpots, I'm well-versed in the negatives. The simplest possible analysis is to look at the EV of each dollar paid into the jackpot. In California, I've been assured that the casino is allowed to take 15% for administrative costs, so each dollar returns 85 cents at best. (This is assuming you can trust administrators not to skim off the top.) The money you put in will sit around for months, on average, so the net present value of that money is slightly less than 85 cents. Then, you are expected to tip. (Tipping can be forgone, I suppose, but everyone I know has tipped after their jackpot wins.) Most players tip 5-10%, so our return is now down to about 75%.

Things are still worse than that, though, for several reasons. First, jackpots increase the volatility of our win rate substantially. Second, the deck-checking is unfairly biased towards delaying the jackpot payouts, because they are occasionally cancelled. (Once in a while the deck-check reveals a bad deck and the jackpot is not paid, but is it very rare for a deck to be checked when the jackpot is not paid out. This means sometimes payments have gone into the jackpot drop in hands that would have been voided had the jackpot been won and the deck checked. To be fair, the decks should be checked every time a dollar is paid to the drop, but this is impractical for obvious reasons.) Third, the slightly smaller pots mean tighter play becomes correct, and this can cut into the win rate of strong, creative players. Fourth, when the jackpot is actually won, the game will be delayed, eliminating winnings you expected to have during that time playing poker. These factors are hard to quantify, but I would say that between the EV and volatility issues another 5% of utility is lost. So, we are at about 70% return, assuming there is no cheating or illicit skimming by the casino management.

I've heard a few good arguments for having jackpots amid many weak arguments. The most worthy argument is that jackpots attracts amateur players.  All else being equal, having to play the jackpot drop costs me about $4 an hour and in the long run I get paid back about $3 in jackpot winnings. So, ignoring strategic effects and time delays, it really only costs me about $1 per hour. On the flip side, a single fish at the table is certainly worth much more than this. Even just a slightly weak player can make up for that $1/hour jackpot loss. Moreover, a good player will tend to play hands that have a good chance at making a jackpot, such as high pocket pairs or big Aces. This means that, for good players, the return on investment should be slightly higher than for weaker players. My sense is that this is a very minor effect, but I could be wrong. It is something, at least.

In conclusion, I would say that the only very significant effect of jackpots on any relevant concern is on the purity of the game. Jackpots are unmitigated disasters for game purity. However, your bankroll will benefit if the jackpot scares off the other poker purists. Purists tend to be good players. If your only concern is for making money, the jackpot might actually be helping you in the long run by attracting worse players to the game. Keep in mind, however, that if these worse players are not in the game at any particular time, you would certainly be better off without the jackpot drop.


I did not get into the UMD College Park Applied Math department. I am leaning towards accepting the position in the PhD program in Statistics at UMBC.

Thursday, April 19, 2012

Advice That Will Help Both My Opponents and Myself

Most of the advice and analysis on this blog could easily be used against me if readers found me at their poker table. (Indirectly, it can hurt me even if we never play against each other by marginally improving the play of the average poker player.) I enjoy doing strategy and hand analysis on this blog, and I think it's been worth any small amounts of EV I may have lost.

A commenter (Rick) suggested that I give some advice that would actually help me if it were followed by my opponents. This sounds easy: Just give bad advice! An intriguing idea, but it wouldn't make much difference because my poker-playing readers can mostly discern bad advice from good, anyway. Fortunately, there is another way: Give advice that helps not only me but also my opponents. This is clearly the angle Rick was suggesting. This seems like a good idea, so I'm going to devote a few posts to encouraging behavior that will improve the culture of casino poker.

When I'm in a poker room, I have three main concerns. Players will surely differ on the relative importance of these three factors, but I think nearly all players are implicitly concerned with these three things. For me, I would rank them as follows.

1. Maximizing my winnings. This is an explicit goal of most players, and the main concern of most poker pros. Like other poker players, I tend focus on ways in which I can win money from other players, but there are also plenty of things players can do to help not only themselves but also other players (either all the other players or some subset).

2. Having an enjoyable social experience. Poker is a social game, after all. Occasionally, I will come across players for whom this seems to be the primary goal of their poker games.

3. Playing an interesting game of poker. This is the concern of the poker purists, who play for the love of the game.

The first piece of advice I want to give is conventional wisdom but is very difficult for many people to follow: Be nice to the bad players. This helps the other players fulfill Concern #1 because the bad players are likely to stick around for longer. It usually also helps the bad players fulfill Concern #2. Unfortunately, poker players are often too immature to resist castigating bad players for bad beats and the like. Personally, I also wish that people were nicer to the good players, but that is not necessarily good for fulfilling Concern #1. There are a few of players at the Bike who are so unpleasant that I tend to try to avoid them, and I imagine it is good for their win rate to get me out of their games.

That's it for today. Stay tuned for my next attempt to help improve the culture of casino poker.


I've been taking an online course on game theory run by two professors at Stanford.


I got into the PhD Statistics programs at UMBC and George Washington, but without funding. I'm still waiting on UMD College Park's PhD program in Applied Math, Applied Statistics, and Scientific Computation.

Monday, April 02, 2012

What is Your Biggest Weakness as a Poker Player?

This is another interview-style question that seemed like the type I might get after my Mathematical Poker talk back on February 14. Since I haven't been playing poker recently, these questions have provided a good excuse to keep this blog alive for the past several weeks. I hope to address some other poker issues in the coming weeks, but this will probably be the last in this question-answer format unless a commenter has another question worth answering.

The one thing I think would most help my poker income would be to put more effort into game selection. I'm not sure if this qualifies as a "weakness": most players neglect game selection as much as I do, so I'm not actually particularly weak. Doing game selection has some drawbacks, especially in live poker: it is conspicuous to scout out various tables before playing, it cuts into the time you could be playing, and it annoys the floorpeople if you keep changing tables (especially at the Commerce, in my experience). Still, the effect of having a good game can overwhelm any effect of marginal improvements in my own strategy when it comes to my win rate. I state this without data; perhaps I'll find the motivation to do a bit of analysis to back up (or falsify) this idea. Drawing from my memory, however, it really does seem that some tables at a casino can be clearly seen to be better than others, I am pretty confident that selecting a good game is far more important to my winnings than any small fluctuations in my own play or adding a few extra minutes of playing to my session. In a similar vein, I have rarely tried to make stabs at higher limits, despite my belief that this can be a useful endeavor, and I've had several strong players tell me I should be playing higher stakes. I guess I just don't consider myself much of a "gambler" and I would like to keep it that way.

Historically, my approach to game selection has been as follows: spend 20 seconds scanning the room for known fish or for a table seeming to have an unusually good time. (Occasionally, it helps to play with players who are good but who are particularly skilled at making other players play badly. Rarely, it can also help to notice recognize a player I know focuses on game selection, and I can be confident that any game he is in will be a good one.) Then, when I'm in a game, I am rather aggressive about selecting against staying there. That is to say, I will ask for a table change within 5 minutes if the game is not great. (This can annoy the floorpeople and gives your opponents some information about the type of player you are.) To improve my table selection would require that I spend an extra couple of minutes watching a few hands at each potential game until I find one that is quite juicy, and there are usually one or two of these if you look hard enough. If I don't find a juicy game, I should still be able to select one that is at least pretty good.

At the table, my biggest weaknesses are probably concentration and exploiting strong players, which are related. Against weak players, I am perfectly capable of focusing and probing their weaknesses, but I tend to just model strong players as "perfect" and try to play optimally against them in a game-theory sense. This creates a sort of feedback loop of being distracted from the game if I'm up against only solid players, because I don't feel the need to concentrate on them and this creates boredom. In truth, I do think even good players are exploitable, and this becomes especially interesting once they start trying to exploit me; I tend to be a step behind the competition in such situations (not a big deal, since I think my standard game is unusually difficult to exploit in the first place). I think the problem is that finding opportunities to exploit these weaknesses seldom arise, and it takes an awful lot of patience for the effort to pay off. Perhaps other players are fooling themselves into thinking that it's more worthwhile than it truly is, but the bottom line is that most other players seem to have deeper wells of patience and concentration to draw from than I do when it comes to studying their opponents.

Sunday, March 25, 2012

What are some common weaknesses of your opponents?

This is another question I was NOT asked at my poker talk last month, but that I figured would make for an interesting blog post.

This question is basically the same as the following: what do you do as a poker player that sets you apart from most other players and enables you to win? It's not strictly necessary to be able to answer this question in order to be a +EV player. For example, it could be that your income comes entirely from the 5% of players who are truly terrible, and that against most players you have no real strategic advantage. In practice, though, a winning poker player will try to identify and exploit weaknesses in all his opponents.

Below I list several common weaknesses of players. You will notice a common theme of players being conflicted between the "correct" goal of maximizing EV and some other goal, usually related to psychological satisfaction. I believe one of my primary advantages over other players is that I am not an emotional player. To the extent that my emotions are involved in my play, they are usually tied to my ability to make +EV plays, since it gives me satisfaction to think I am playing well.

The most common weakness of players is to play too many hands. Any player who has heard even a little poker advice knows that they should be playing very few hands. To a new player in a nine-player NLHE game, it is shocking how often they should be folding, and it often takes a while for them to really believe get used to it. Among weaker players, I think another problem is that they have trouble reconciling conflicting motives: they want to make money but they also want to have fun. Folding is not fun, so they play lots of hands even if they know they shouldn't.

Another common weakness I see is that players overestimate their skill level. This often manifests itself in the first weakness I mentioned: playing too many hands. Players think they can make more hands win than they really can. In good players, overconfidence can also result in "Fancy Play Syndrome," which means deviating too much from standard play, usually in an attempt to make a "hero call" or a big bluff. These plays are psychologically extremely rewarding when they work, which suggests that good players, too, succumb to conflicting motives.

A more specific weakness is that players are reluctant to call with hands that probably losing but are +EV because of good pot odds. A classic example is if you hold QQ and you figure your opponents has raised with AA, KK, or AK. You are behind your opponent's range here but you will likely want to call if you are getting good pot odds. (This is one reason why I am a big fan of semi-bluffing with AK before the flop.) Again, I think this can be traced back to a problem of conflicting motives. Good players often care deeply about their reputation, and since it can be embarrassing to call with a hand that is behind, they are reluctant to do so.

Finally, I think good players spend too little effort considering their own hand ranges and too much trying to "outthink" their opponents by thinking one "level" higher. It's much more efficient to just make sure you have balanced your play in a game-theoretical sense. For example, before you check on the river with a weak hand consider your hand range given the play so far. If your hand range contains some hands that you would like to value bet with, it should also contain some hands that you will bluff with. In fact, for those who saw my talk at Swarthmore or who have read The Mathematics of Poker by Chen and Ankenman, you know that there is a specific ratio of the number of hands you should be betting to the number you should be bluffing. Unless you are trying to exploit a suspected weakness of your opponent (for example, you think he calls too much on the river), you should balance your range in agreement with an optimal strategy. (As an aside, I think that this approach is one reason why people's assessment of my play tends to be polarized, with many people thinking my strategy is carefully measured, and other thinking I'm maniacally aggressive because I find opportunities to bluff in situations that most players wouldn't bother. These assessments seem contradictory, but both are essentially correct.) I think this weakness usually stems from the fact that most players simply haven't learned to think about poker in this way. However, for some players it may be that this is yet another example of conflicting motives like we saw in the first few examples. That is, it is certainly fun to try to outsmart your opponents (rather than just balancing your own range), and so it seems likely that players will put a bit more effort into that aspect of the game than is really called for.

Wednesday, March 14, 2012

What is one piece of advice you would give to a beginning player?

I've been using this blog to answer questions that I got during the Mathematical Poker talk I gave last month. In the coming week, I'll answer two or three other questions that I did NOT get. They are sort of standard interview-type questions that I thought I might have to answer during the talk, but they didn't come up. I feel like answering them anyway. The first one I'll address is how what advice I would give to beginning players. I am assuming they will be playing no limit holdem.

If I really had to give only one piece of advice, it would be to play as low stakes as possible and fold almost everything as soon as possible. Most new players play way too many hands, most of which they will have no idea what to do with. Even good players would lose if they played that many hands, and new players will probably lose way more with them.

However, the answer really depends on what you hope to get out of poker. The above advice is good if your goal is to play and lose as little money as possible. However, many players will have other goals. For example, if you have played very little poker and your goal is to:

1. Make money. My advice is: don't play poker. You'll probably lose because your opponents are probably better than you.

2. Get better at poker. First, read a lot. If I can give more than one piece of advice: think about your own hand ranges with each action you take. (If your opponent knew your strategy, would he be able to figure out what you have?) Third, keep track of your results and, if you play online, keep track of your statistics.
Fourth, play lots of hands and raise a lot. (This puts you in the action and gives you lots of experience and you will learn how your opponents react to you. The downside is you will probably lose a lot of money in the meantime.) Fifth, play high stakes. (Again, you'll lose a lot, but this is the fastest way to learn how to win at these stakes.)

3. Get better without losing so much. Same as the previous answer, but skip the fifth point above and moderate the fourth point. I would still advise playing hands that yield slightly -EV because this is a good way to gain experience.

4. Have fun but don't lose too much. Think hard to try to figure out what your opponents have and try to exploit them. If this isn't fun for you, you probably do not like poker. Don't try to trick your opponents too often, because this will lose you money. Play very low stakes, fold a lot, and raise a lot. Folding a lot is not fun, but it is absolutely essential to avoid losing a lot. Make your raises bigger than the size of the pot. If this means putting in more than one quarter of your stack or your opponent's stack, just go all-in. This makes it very hard for better players to take advantage of you.


I didn't get into UPenn Wharton statistics or UMD economics. Those, along with JHU biostat, were probably my only chances at an academic career. I'm still waiting to hear back from three other PhD programs that are less competitive. If it doesn't work out, I always have poker to fall back on! Perhaps I could become a professional blogger. (Or I could try to get a late application in somewhere, like GW econ or UMD Law.)


I signed up for a free Game Theory course offered by Stanford.

Thursday, March 08, 2012

Has mathematical analysis changed the game a lot in the past few years?

This is similar to one of the last questions I got after my Mathematical Poker talk last month. Unless a commenter asks another question, I think this will be the last one I answer here on the blog.

The game has indeed changed a lot in the past several years, but it's hard to tell how much of that change is really attributable to mathematical analysis. Certainly, the games have gotten tougher in during the years I played, but I think the main factor may just be natural selection. I would guess that most of the players int the games I was playing in Los Angeles do not know the game theory results I presented in the talk. Ten years ago, I think there really was a Moneymaker-aided poker "craze", which was the inspiration for this blog's name. That brought in a lot of new players, and so games were easy to beat. The ensuing years weeded out the bad players, while the good players were more likely to stick around. This process is pretty hard to disentangle from the fact that the good players were also getting better with practice and study, so in order to guess at the influence of analytics, I need to rely upon conversations I've had with players. My impression from such conversations is that new players tend to have a good sense of the analytical fundamentals of the game, much better than almost anybody had ten years ago. Meanwhile, the older players tend to be mostly those who had a good intuitive feel for the game and were able to survive the natural selection process. Most of the best players today (especially the young players) seem to have a very strong analytical foundation, and that is where I think analytics have caused some of the biggest and most visible changes in poker. In light of that, the continued success of Doyle Brunson is all the more impressive to me.

Another area analytics seems to have made a big difference is in tournaments. I haven't been playing tournaments much, so I can't speak from experience, but tournaments seem more ripe for mathematical analysis. Also, my poker discussions with tournament players gave me the impression that they are more keen on the technical aspects of the game. 

Monday, March 05, 2012

Do players at the casinos usually know who the props are?

This was another of the questions from my Swarthmore math talk, which I'm revisiting and answering on the blog.

To varying degrees, all of the props at the casinos in Los Angeles try to blend in with the customers. Some will outright lie to customers about whether they are props, while others might make it obvious without even being asked. In general, none of the props wear any identification, and the casinos operate under the assumption that it's better if customers don't know that there are any props at all. I think we were technically supposed to tell people the truth if we were asked, and I know that the floorpeople needed to inform customers of who the props were if asked. Beyond that, there was a lot of secrecy. Shortly after I started at the Bike, we had a meeting in which one of the supervisors told us that if someone asks us if someone else is a prop, we should just say we don't know. "It's not really lying because for all you know, he quit that morning and isn't a prop anymore." If you are concerned about who the props are, just go ask a floorman.

In practice, the regular players at a casino do know who the props are, but new players usually do not. In fact, the new players usually don't even know that there are any props at all. I didn't know when I started going to casinos.