[sjb]

There's one point that I think some folks miss here. Hold 'Em is (discouting the rake) a zero sum game. The only asymmetry in the game is position, so the "value" of the game, as determined by game theory can only differ by position, and the sum of the values across all positions must be zero.

Therefore, the "optimal" stragety identified by a Nash equilibrium for the game really only tells you how to to break even. So, if you're going to build a poker bot that *wins*, you'd have to make it so it can recognize when other players deviate from one of the equilibrium strategies and then determine how to best capitalize on that deviation - that's where the money would come from. Game theory doesn't tell you how to do that, because one of the fundamental assumptions in game theory is that all players are equally able to analyze the game to determine their optimal strategies.

So, to build a "perfect poker bot", you'd have to go way beyond a game-theoretic optimal strategy (Nash equilibrium) to work out a model of how the other players at the table *actually* play. That problem is *way* underdetermined. Hence, I'd argue that no such bot is possible.