Saturday, March 14, 2009

Mistakes They Make

This is an old article I did a while back and published on a now defunct website. I'm reprinting it as is
Mistakes They Make
by Gary Carson
September 20, 2000

In the last few essays we explored the conflict between the theory of poker that poker is a struggle among the players for the ante and the theory that money simply flows from the bad players to the good players. We saw how blending those ideas with the theory that poker is a betting game of choosing the right odds can help reconcile the conflict.

There are myriad theories of poker that you can bring to bear to develop a perspective for the game. As we go on in this series of essays we'll be talking about a lot more theoretical perspectives. It's important to keep the various ideas in mind. So far we've discussed:

Ante Theory. Poker is a struggle among the players for the rights to the ante.

Bad Player Theory. In poker, the money flows from the bad players to the good players. Good players win money from the bad players.

Odds Theory. Poker is about choosing bets where the odds you get on the bet are an overlay to your odds of winning.

This essay introduces a fourth theoretical view of poker -- a theory of poker as a game of mistake control.

Mistake Theory. The player who makes the fewest mistakes wins.

Looking at the game this way suggests that the road to winning poker is to keep your mistakes to a minimum. That leads to a game theory type approach with an objective that's more defensive than offensive. But, we can expand on a Mistake Theory.

Mistake Theory. The player who makes the fewest mistakes wins. The more mistakes your opponents make, the larger your win.

Now this leads us to the idea that we can win by playing defensively, but we can win big by actively exploiting our opponents' mistakes.

If you want to maximize your playing profits you must actively identify and exploit your opponents' mistakes. This approach can be risky, it usually is. But, it's the road to maximizing the net win.

To exploit your opponents' mistakes you have to know what they are. And, even knowing what mistakes they make isn't enough if you don't know when they make the mistakes. Sometimes you have to be able to predict mistakes. For example, if you know a player has a high likelihood of making a certain kind of mistake on the flop then you might call a bet preflop with a very wide range of hands, just so you'll later be in a position to exploit an opponent mistake.

So, knowing why a player tends to make mistakes can be critical. Knowing why often helps us predict mistakes.

This leads us to the importance of knowing your opponents. Not just general knowledge, but specific knowledge can have value. You need to know something about the kind of information you need to gather to develop strategies that will optimally exploit opponents' mistakes. This is not an easy thing to do, and it varies a lot from opponent to opponent.

Many proponents of a game theory approach to poker believe that players make mistakes because they don't know any better. They think that if players knew correct game theory strategies that no one would make mistakes and the games would die out. This argument is used to justify the idea that a defensive game theory approach to the game is optimal.

I think that belief is wrong. I think many players make mistakes, not because they don't know any better, but because they don't care. Players raise because it's fun. They call because they want to chase the illusive thrill of getting lucky. It's not about the money to most players. It's about the fun and the thrill.

This presumption that players only make mistakes because they don't know any better leads to mathematical and logical arguments are used to develop a strategy that has the characteristic that it is the best way to play against a player who plays well.

In a heads-up match against a player who plays well, that's probably a good approach. But, I'm not sure why anyone would want to be in that situation. In a full game, even when all the players are players who play well, I'm not so sure. Mathematically no one has ever found a game theory solution to such a multi-player game (they have to some multi-player games, just not any that look like poker). No one has even proved that any stable game theory solution exists to a multi-player poker game.

In a real poker game, against real people who are making real mistakes, the key is to identify those mistakes, predict when they'll make the mistakes, and act to exploit the mistakes.

I haven't said anything yet about how to accomplish any of this. That's not always easy to do. But, the first step is to identify what it is you want to accomplish. Only after that's done can you figure out how to accomplish it.

If you're playing heads-up, against an opponent who doesn't understand what a minimax strategy is, you can often play a minimax strategy and let him flail around trying to beat you and that might be the best way to play. Such an approach will certainly guarantee a profit. If you're heads-up against such a player who'll just keep playing until one of you is broke, then such a defensive approach will eventually get all the money.

But, that's not a typical poker situation. A typical situation pits you against many players, some of which call to much on the river, some of which fold to much on the river. So against some of the you don't want to bluff often but do want to make marginal value bets. Against others you might want to bluff a lot. Your tactics in a particular situation depend on the kinds of mistake your opponents tend to make, and that's often much more important information than the cards you happen to hold.

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