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.
4 comments:
This is a very interesting post. The only thing I disagree with you is about the dealmaking. In my limited experience, you can really make a lot of equity with savvy dealmaking. Often tournaments encourage proportional chip deals, which very heavily favor the chip leader. Waiting til you're the chip dealer and then making such a deal can be hugely profitable. I had one tournament where I had 40% of the chips in play with like 6 players left. Mathematically, unless I was way better or worse than the others, I only had about a 40% chance of winning 1st place. However, the chip deal granted be practically 1st place money!
Rick
That's a very good point. I began the post by saying that tournaments have many opportunities to apply mathematical principles, but I failed to mention that one of those opportunities is in dealmaking. (I did actually put this on one of my last slides for the talk.) I know this is fertile ground for mathematicians to gain an advantage, but I didn't realize just how big those advantages were! First place money for 40% of the chips? Wow!
A related point: my aversion to dealmaking stems from my aversion to being forced to think about the actual real-life monetary/utility consequences of poker while I'm playing. However, I think I could solve this problem if I were simply to view dealmaking as an extension of the strategic aspect of the game.
Its funny, my dad, in his retirement, has become a regular tournament poker player, typically $65 tournaments in Atlantic City. He always talks about chopping, which he does fairly often, and speaks with rage or contempt when someone refuses to chop. I don't have the heart to tell him my feelings on deals, especially the ones he makes, where the last 6-8 people split the prize money fairly evenly. I have never made a deal unless I was in 1st place, and even then I really only do it to keep the peace. If I'm say, 6th in chips at the Final Table and everyone wants to deal, I'll usually say something like "wait until you guys knock me out, then you can split up the rest of the money," to let them know that it's not ego so much as my personal philosophy that leads me to want to hold out.
Yeah, it really is in the culture of tournaments to chop, perhaps especially in casinos that have daily tournaments where there are lots of regular players. My first encounter with this was at the Sahara. A few people at the final table were furious with me and told me that they would be trying to knock me out.
As Rick says, it's probably best to just take a deal as long as you know what your equity should be and you get at least that much. I guess this can be quite an advantage at times. Still, I think it's kind of sad, because the end of tournaments are so much fun to play. Nothing in my poker career quite compares to the few times I've won tournaments (only once live).
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