Tuesday, January 30, 2007

The Long Run and Regret

One reason I thought it would be satisfying to play poker full time is that I would be able to actually realize the "long run," as in "it all evens out in the long run." Actually it doesn't ever truly even out. Thinking this way is just one manifestation of what is known as the Gambler's Fallacy. Luck just seems to even out because it all kind of runs together in your memory when enough time has passed. The truth is though that if you lose a $1000 pot you "should" have won, you are out $1000. No matter what happens for the rest of your life, you would have been $1000 richer if your opponent in that hand had not given you a "bad beat." This is a slight oversimplification since your loss of this hand actually can effect some other factors that can influence the actual poker game; for instance, if you get AA next hand and only have $100 in front of you rather than the $1100 you would have had if you'd won the previous hand, you can expect a different outcome. However, these factors aren't likely to help you win your $1000 back, and they certainly don't validate the gambler's fallacy.

Still, there is some sense in which luck actually does even out in the long run. However, that requires looking at "luck" in a different sort of way: averaged over your entire playing career. Luck averages out for your win rate, not your total winnings. For example, if you play just one hand of 20-40 limit, it's quite unlikely you'll lose $1000, but it's not unlikely that you will lose $200, making your win rate -$200/hand. If you play 99 more hands, it's now much more likely you will have lost $1000, but you are very, very unlikely to still have a win rate as low as -$200/hand. So luck actually does even out with respect to your win rate.

Playing every day and keeping close track of my win rate helps me to focus on my win rate rather than my bottom line. After playing 3000 hours, you need to lose $3000 just to change your win rate by $1. I like to think in terms of pot equity, which I think is the most direct way to arrive at appropriate pot- and implied-odds decisions. For example, in limit poker, players will often say things like "it didn't matter that I didn't bet on the turn, because he would have called and hit his flush anyway. I just would have lost more money if I'd bet there." While true, this type of comment shows a lack of understanding of either randomness or pot equity. The correct analysis would be something like this: "There were 44 possible cards that could come on the river. I win when 35 of them come out, and my opponent wins when the other 9 come out. Therefore a $40 bet here is worth about $40 * (35/44) - $40 * (9/44) , or about $24." So in fact, the player with the best hand is missing out on $24 worth of pot equity if he doesn't bet. Thinking in terms of pot equity also helps to put "bad beats" into perspective. The inclination to think "I should have won that pot" fades away. For instance, if the player who hit his two-outer was all-in on the flop, then he probably actually had about a 8.5% chance to win the $1000 pot. So really I only had $915 equity. I was unlucky to lose, but only $915 unlucky, not $1000 unlucky. Interestingly, even most good players fail to see the game this way and lose their cool at the slightest misfortune.

To get back to my original point, I think a big part of my advantage over common players is my ability to naturally think about poker decisions this way. It also helps to see just how little control a poker player has over his results in a particular session. Sure, I bet the turn which is technically a $24 EV play, but the "luck" factor is what ultimately determines who wins the $240 pot. It takes a while for even quite profitable plays like this one to make a big difference in your bottom line.

The reason I wanted to bring all this up is that something occurred to me a few months ago while I was reading The Paradox of Choice by my college professor Barry Schwartz. His thesis is essentially that although we generally think of choice as a good thing, there are many aspects of our lives where we've reached a sort of critical mass of choice beyond which any additional options are actually deleterious to our well-being. Part of his argument is that having choices forces people to consider opportunity costs. In other words, having to consider the question "what am I missing?" actually makes it harder for us to enjoy whatever we are doing. I've noticed that thinking about poker in a rational way has become more difficult now that I have other viable choices. In Las Vegas there was almost nothing for me to do except get up and go play poker every day. On the weekends I would occasionally get a call from friends inviting me to a club or lounge, but because the running shoes I always wear prohibit me from entering most clubs, I didn't experience much ambivalence about staying in my poker game. Now that I live in Los Angeles, where the weather permits my being outside for more than 5 minutes at a time and where I have a girlfriend and another friend who like to hang out on the weekends, playing poker is no longer my only option. I find myself thinking, "if I turn down hanging out with my friends in favor of playing poker, what a waste it would be if I don't even win!" All of a sudden I'm thinking in terms of the short-run again! Worse, I suspect that having to consider more significant opportunity costs may be lessening my enjoyment of playing. An overall increase in the quality of my options seems to be hindering my enjoyment of any of them.

If I'm making decisions about when to play based on avoiding regret, am I in danger of starting to make decisions on how to play based on avoiding regret? Will I make plays that maximize volatility when I'm losing and minimize it when I'm winning? Will I become the guy who bets $100 into a $15 pot with his set of aces just to avoid the chance someone will draw a flush? Or maybe the guy who will keep playing until he finally gets back to even for the day? I can't really imagine it ever coming to that, but I'm still a bit disappointed that I'm concerning myself with short term results in any capacity.


Lauren said...

Haha, very interesting. Was The Paradox of Choice anything like his speech at your commencement? I thought that was a snooze, and it made me a little angry too (though I don't remember why).

I don't really see why you would start changing your decision making process while you're playing since your extra choices are not at all involved. The two seem unrelated. Though I do understand how your enjoyment of your choice can be lessened. I'm definitely experiencing that with the choice of the book I'm reading now.

I'm not really sure why you think that you are not thinking about poker in a rational way just because you feel that playing poker is not as good if you lose when you could have been doing something with your friends. I mean, to me, that says you should go do something with your friends if you are making excuses not to play; unless you are also thinking that it would be a waste to do something with your friends if you were to win. Besides, having a fun weekend often makes me a better worker.

Hehe, one more thing: Whenever your girlfriend suggests you go do something with her, you sould probably just do it. It may seem like a short term choice, but that's only because men don't generally think like women.

Keith said...

Yes, Schwartz's book was actually a lot like his speech. I can't imagine what about it would have made you angry!

I think you're right that there's no reason to worry that my poker decisions will be affected by any of this. I'm pretty sure this does happen to a lot of players, though. I just wanted to acknowledge (to myself, mostly), that I'm not immune to this sort of "irrationality", even if it's very unlikely to ever spill over into poker.

I think I break your girlfriend advice at least once a day. I like to think my girlfriend should be able to just tell me when something is important, and then I'll do it. If you're expecting Ben to "read between the lines" and making him feel guilty when he doesn't, well... Shame on you! I suppose you have Ben pretty well trained, though.

Wonjae said...

fuck y'all

Wonjae said...

not really - interesting read. now i'm going back to work.

Lauren said...

Oh man, I looked back at that speech, and I pretty much disagreed with everything he said. Except, oddly enough, the main point. His explanations about maximizers and his suggestion to let other people make decisions for you seemed ridiculous.

Haha, I think my girlfriend advice is good for Ben, but I'm nuts. I pretty much like to be left alone, so if I suggest to Ben we do something, he should sit up and take notice, because it generally happens less than once a week. Besides, Ben is pretty much incapable of reading between any lines. You should see him during movies where the plot is not completely obvious.

Keith said...

Is it that you agreed with his observation that too much choice can be overwhelming, but you disagree with his advice on how to deal with it?