“Am I playing well?”, and Poker variance

by PokerAnon ~ August 15th, 2011. Filed under: Philosophy and approach, Poker psychology.

Say you play tennis with a regular opponent. You are slightly better at tennis than your opponent. In the first ten matches that you play, you win 6 out of 10. Neither of you work on your game and then after 50 matches you’ve won 31 and lost 19. Seem reasonable?

Now say that both of you lose your rackets and have to borrow rackets from a community center. Sometimes you get a good one and other times the racket is partially broken or chipped or it’s a kid’s racket and is undersized. Your opponent is subject to the same random variations and might have a good racket when you have a broken one or vice versa. Now you expect the results of your matches to vary more because your starting situation is now varying. For every 10 matches under these conditions you aren’t surprised if you have won 8 when you had the good racket often or 4 when you had the kid’s racket often.

Now imagine that the court is closed down and you have to play on a multipurpose playground that is covered with small, smooth gravel. The ball sometimes goes where you expect but also may very well veer off slightly or widely from where it would go if the court were flat. There are also a few holes so if the ball catches the edge of one of these the ball may fly off in any direction. And the balls are not even round anymore. Sometimes you get ones with dents in them, like ping pong balls that have been stepped on. You’ll swing a beautiful stroke only to catch the edge of the dent in the ball and have it go straight into the ground or flying out of bounds. Now the game is really unpredictable. How often do you expect to win under these conditions?

Then you have to share the equipment and can’t play the same opponent all the time. You are put in a pool of 6 players and randomly you play one of the other 5. According to the community center tennis rankings you are slightly better than all your opponents, but sometimes they mis-book you and you end up playing two opponents at once. How often do you expect to win now?

Finally, put yourself in some post-apocalyptic future where this last version of tennis is the situation when you first try to learn the game. Random opponents from a selected group, sometimes more than one, lopsided balls, randomly assigned rackets, unpredictable playing surface and you’re trying to learn the game. How confident would you be in your abilities?

Compare this with your development as a poker player. You have randomly dealt pocket cards. You have rotating position. You have 5, 6, sometimes more potential opponents in any one given hand. Sometimes your beautiful play with a big pocket pair hits, sometimes you get an awful result with two callers and a JT8 with a flush draw flop. Sometimes your double barrel on a dry board works, other times you are betting for value with a decent hand but a passive player suddenly gets aggressive on an innocuous looking turn card. Sometimes you get it in with a draw and hit, other times you get it in with a dominating hand and get sucked out on.

I put all these unpredictable elements (random quality rackets, lopsided ball, uneven surface) into the tennis game to emulate the variance of the cards in poker. And I’ve intentionally added them gradually to push the concept of just how much this variance can be a factor in the results. You can imagine the poor tennis player who was used to winning 7, 6, or 5 out of any 10 matches in optimal playing situations now expecting almost any result after any 10 matches. The distribution of results is going to be extremely wide and even after 100 matches the tennis player might be happy with 75 wins or 45 wins and still believe that they should be winning 60% of the time.

But what of the post-apocalyptic player who tries to learn tennis under the unpredictable situations? He might have a coach that tells him “you’re good enough to win at this level 60% of the time”, but in reality his results are skewed wildly because of the unpredictability and randomness of the playing conditions. He’ll go on winning streaks where it seems that he can’t lose, but how much of it is due to skill and how much due to chance? He’ll go on losing streaks of the same length and wonder the same thing. How does he develop his game under these circumstances, and how does he develop confidence in his game?

This is the difficulty facing the poker learner. If your coach, or a player who has similar skills as you or better, can look at a hand and say “you played that as well as you could given the range of hands that this particular opponent might have in this particular situation and give the odds of various cards coming in the future streets”, that’s all you can do regardless of how the hand worked out. Sometimes you hit the dent in the ball, or the stone on ground, or you get the racket with the missing strings. And sometimes you don’t. Sometimes you’ll go on long streaks of being card dead preflop, sometimes you’ll go on long streaks of missing the flop, sometimes you’ll go on long streaks of facing opponents who fire back at you, and sometimes you don’t. Imagine how tough it is for the tennis player on the uneven court with the lopsided balls and random rackets, and keep that in mind when you try to figure out whether you’re playing your poker game well or not.

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