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.

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.

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.

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.

How often do you raise?

This was the simplest question I got after my talk. However, I didn't know the answer; I simply don't keep track of my play that closely. I probably should have been more prepared for this question, because the last third of my talk was about how we can use Bayesian statistics to model our opponents' strategies, and I used raising rates as an example. In truth, a player's raising rate is (for most players) highly dependent on the situation. The same exact situation never really presents itself twice (at least if we take into account stack sizes and meta-game issues), so it is difficult to gather relevant data. We need to look at similar situations and hope that they are relevant to each other. Poker players do this intuitively: if player A raises way too often in one situation, we guess that he will raise too often generally. I think a very interesting research topic would be to develop a better model of how to generalize from one situation to another, and how to quantify the "similarity" between two different situations. The best analysis I've seen in this regard simply looks at how often players raise given a particular seat position (eg "on the button"), without regard to other relevant factors such as opponents and stack sizes.

An interesting anecdote is that there were a few players at the Bike's 20-40 limit game who thought that I intentionally raised whenever it was their turn to put in the blind bet, and they would call and reraise me more than they would against other players; in turn, I actually did start raising their blinds slightly more often (that is, with slightly weaker hands than I would normally) in order to maximize my EV against their relatively weak calling and raising ranges.

At the talk, I interpreted this question as referring to raising before the flop in no-limit holdem. Even given this rather narrow interpretation of the question, I considered it too broad to give an accurate answer (I didn't venture a guess at the time, but if I had to now, I would say 15%). Instead, I explained two of the most important factors that go into my raising rate. First, the number of players and my position at the table. If I have only one or two players I need to beat, I will raise with way more hands than if I have seven or eight players I need to beat. In the latter scenario, the chances are just too good that someone else has a hand stronger than mine. This position-based thinking is a basic poker concept that should be familiar to any self-respecting poker player. The other factor I mentioned during the talk is the skill level of my opponents. If my opponents are very weak, I will play a lot more hands. Against stronger opponents, many of those hands would probably yield negative EV if I tried raising with them. One thing I forgot to consider in my answer is the possibility of just calling before the flop. I do this so rarely that in my mind I equated "raising" with "not folding," but I do limp sometimes, especially if there are limpers in front of me and my opponents are weak and are unlikely to raise behind me.

In closing, I admitted that I should probably keep better track of how I play. If I played online I would be more likely to keep track, but in live poker it would be very distracting to record all the relevant data.

Live at the Bike

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

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.

I've Been Laid Off

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

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

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.

Slow Days at the Bike

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.

Keeping the Props

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.

Potpourri

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.

Chairs, Dealers, Lawsuit, and the Full Tilt Book

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.

Poker Future?

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"

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

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

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

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.

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

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.