solutions poker texas hold'em

Question

Is there any equation that characterizes the poker game in terms of variables such as the strength of the hand, the amount of betting money in the pot, etc? Is there any solution that says what the best move?

Answer 1

There is no one equation. There is a large field of theory, for example calculating the chance that a given hand will win. Unfortunately, that chance changes depending on what you think the other player's hands might be. The subject is part of game theory.

If it were easy, people wouldn't play the game.

Answer 2

It is a finite incomplete information game, so we know a Perfect Bayesian Equilibrium exists. Note that, since this is a game, the "solution" is not based on optimality but rather on consitency between the strategies of the players. There is no "solution" that specifies the best move: there is only an equilibrium strategy that specifies the best response given your cards and your beliefs about the strategies of others. The game is too complicated for the best response to be expressed succinctly.

Answer 3

For a discussion of a stripped-down version of poker (no, it's not strip poker), cf here. Now imagine how much more complex the real game of poker is. Computing the probabilities is the easy part.