3/13/2006

03-14-06 [poker] - 1

03-14-06 [poker]

Why is pot control so good? On the one hand, it's an obvious idea that you will win in the long run if you can play big pots when you have big hands, and small pots when you have weak hands, eg. pot size is proportional to hand strength. On the other hand, isn't it correct to just get the most money in as possible when you have the best hand? eg. if you have one pair (a pretty weak hand), but think he has a worse hand and will call, shouldn't you go ahead and play a big pot to maximize profit? These are like macro and micro views of the same problem. The macro view (pot control) is an overall play strategy. The micro view just looks at each individual choice (fold, call, raise), and says for that choice you should take the option which maximizes EV, which could in theory conflict badly with pot control. How do we reconcile these two pictures ?

First of all, recall that you should be playing Bayesian Poker (see previous articles, etc.). Bayesian Poker at each decision point assigns your opponent a probability for every possible hole, P[H], and also an opponent model of what he'll do if you do certain actions, P(A|H,S). For this to be complete, these probabilities must include the chance that he's playing really weird this hand, that he's being tricky, that he mis-read his hole cards or the board, that he's just not paying attention, that he mis-clicked a button online, etc. etc. In practice, we don't actually think of all that when we do "hand reading". What we do in practice is just to think of their primary play style and figure out what hand they would play that way. eg. based on the play so far and the board, I put him on hand X, or perhaps hand Y. I'm not actually thinking of a full range of probabilities and all these other possibilities, because it's just too much to go through.

Now, this type of "deterministic" opponent model is pretty good, it's right 90% of the time, and if you make decisions just based on "putting him on a hand", you will most of the time make the right decision. The problem is those few times he's deviated from it, you might make the wrong decision. Now, those events are rare, so they're not a big deal, right? Well, in Limit Hold'em, that's true and we can just stop the discussion. In No Limit, however, the pot size can vary, so that a rare event can be disastrous.

Just as a quick example, let's say you decide you're never going to fold the second nuts. Most of the time that's a fine strategy and you'll win many pots that way. Once in a rare while, though, he'll have the true nuts. If you lose a huge pot in that case, it may be disastrous to your EV even though it's incredibly rare.

Pot Control is a way to hedge against these rare disasters. It means you only play big pots with good hands, which makes it even less likely that your opponent can have a good hand when you play a big pot (because the chance of you both having very good hands is very rare). If you will play a big pot with one pair, there might be 300 holes (out of 1200) that make better hands, but if you only play a big pot with a set or better, there are usually 50 or fewer holes that make better hands.

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