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.

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.

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. 

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.

Why don't I play tournaments?

This is another question I got after my Mathematical Poker talk: Why don't you play tournaments?


I think tournaments are actually full of opportunities to apply mathematical principles. Any situation where your opponents' decisions are relatively unimportant is likely to be solvable mathematically, because you don't need to get bogged down in much game theory. For example, there are situations where you should go all in with any hand, and it is very useful to know when you are in such a situation.  I used to play tournaments quite a bit back in Las Vegas. I even had some success. However, I stopped playing nearly as much once I got to Los Angeles. 


The first reason I gave during the talk was that tournaments and cash games have slightly different skill sets. I was doing both for a while, but once I was hired by the casino to play cash games for 40 hours a week, I rarely felt like playing more in my free time. After a year or two of that, my tournament skills became very rusty. For example I do not know when exactly I should be pushing all-in with specific hands. Meanwhile, new frontiers seem to have been explored in tournament poker research. The top players seem to have integrated a knowledge of the implications of ICM into their strategies. It seems like it would take quite a bit of work to get back up to speed and make myself a solid winning tournament player again. 


The second reason I gave during the talk is that there seems to be a culture of cheating in tournaments, and I think cheating works better in tournaments. Specifically, collusion is more effective in tournaments because knocking another player out helps all the other players left. I actually think I overstated this point, because it is rather hard to ensure you end up at a table with one of your cronies.


In restrospect, I think the main reason I stopped playing so many tournaments was that the fees just seemed too high (I forgot to mention this during the talk). It was harder to find big tournaments in LA, and the smaller tournaments would take as much as 30% fee plus 1-5% for the staff... and then you are supposed to tip, as well. It's tough to overcome that. 


Some other factors I neglected to mention:


Tournaments just don't fit into a schedule very well. You might play for five minutes or twelve hours. I don't like playing longer than eight hours at a time. If it seemed like the tournament might take longer than ten hours to win, I wouldn't join it.


I don't like the deal-making at the end of tournaments. This is actually a bigger problem than it seems. When everyone else at a final table wants to make a deal and I am the last holdout, I become a target to get knocked out. This lowers my EV (actually increases the EV of tournament chips, but also increases my volatility, which lowers my payout EV) and is socially uncomfortable, too.


The bigger tournaments, especially the main event of the WSOP probably yield the best win rates. So, these are the most likely to be worthwhile. However, if I get to the money I will be playing for tens of thousands or even millions of dollars. At these levels, my utility curve will really start to bend, meaning my overall expected utility may be less than what $EV would suggest. Although I generally assume that maximizing the EV of my winnings is the "right" way to play poker, in truth this depends on large sample theory and the idea that we are playing for the long run. This breaks down in situations where you might get fewer than ten really big payouts over a career as a tournament player. Furthermore, I just have a constitutional preference for not having to think about money while I'm playing. This is something I could probably overcome if I wanted to.


Very similar to the previous point: Tournament winnings probably have a much higher volatility than cash games. I haven't verified this, but it is conventional wisdom, and it seems very plausible. I think it's true.


Playing online tournaments actually eliminates many of these problems. If you can play a few single table tournaments online at once, you maximize the value of mathematical play, you multiply win rate without increasing volatility, and you probably won't be asked to make deals at the end. This might actually be the ideal way for a mathematician to win at poker. The only problem is figuring out how to get money onto a poker site in America...


*****


Despite being invited to the JHU Biostatistics PhD recruitment weekend, I was not accepted. I'm still waiting on five other programs.