[Jerrod Ankenman]

Here's a short answer about applying game theory to poker.

You have a strategy for playing poker. That strategy includes what you would do in all the various possible situations you might find yourself in, from "you're on the button with A9s" to "the action has gone r50r150c;8h 2h 7s/b300c;Js/kk;Tc/b700" and it's up to you.

Now your opponent has a strategy too. And if we had those strategies and a fair amount of computer power, we could find your expectation in the game (just assume headsup for a moment).

I divide all non-exploitive poker play (which is what game theory is about) into two ideas: aggression and balance.

Aggression is, put succinctly, the hands that you play for value. You can have different levels of aggression. For example, I've played with some people whose idea of "aggressive" was raising tens in the cutoff in limit holdem. I've played with some people whose aggression-o-meter didn't run out until I got all their money (and some who got some of mine!). But the idea is that there is a set of hands you bet, raise, check-raise, etc, for value.

The other concept is balance. To understand what balance is about, suppose you had a book with your opponent's strategy in it, and he would play that strategy and not deviate. Could you make money? You probably could, although it would be a little harder than most people think. You'd construct a strategy that maximally exploited his. We call that the nemesis strategy.

Now there's a particular strategy where you COULDN'T make money. That strategy is called optimal, because it is the strategy which does the best (EV-wise) against its own nemesis. We'd love to have the optimal strategies for no-limit, but it's computationally intractable.

But you can understand this concept of balance now - suppose you have a strategy S. Now evaluate that strategy against 1) its nemesis - call that value S#, and 2) the optimal strategy - call that value S%.

If S# is close to S%, then the strategy is balanced. If it's far away, then it's unbalanced. Balance is a measure of the exploitability of a strategy. Now some strategies lose money because they are too tight, loose, aggressive, passive, whatever. Others lose because they don't properly balance their play. If you never bluff, the exploitive response is to fold mediocre hands. Bluffing isn't a value action - it's a balance action.

Now the optimal strategy is perfectly balanced with the precisely proper level of aggression. This is what game theory tells us.

This "picking a card to bluff on" stuff isn't game theory. I mean, it's inspired by game theory and it's sorta the beginning of an idea about game theory. But why don't you do this instead. Think about your own strategy. Think about the actions you take, the bets you make. Think about how you would smash yourself if you were your own opponent. Then change the way you play so that this can't happen any more. Bluff appropriately. Semibluff appropriately, and so on.

Most of the existing literature in game theory is going to talk about the prisoner's dilemma. That doesn't help you with poker, unfortuantely. it's important in life, but it just normally isnt relevant to poker. There will be a book in the not-so-distant future that will have more information about this. Now I have to go work on it some more.

Hope this helps.

Jerrod Ankenman