[AaronBrown]

Echoing rufus' point from another angle, the number of possible outcomes of one hand understates what you have to consider to solve Poker. Every player at the table can select any probability distribution of actions for any situation, and can change that for each hand.

For example, consider a much simpler game betting on how many heads we have between us. Each of us flips a coin and looks at it, but doesn't show it to the other. I say either zero or one. If I say one, you either say challenge or two. I win if I say zero and there are no heads between us, or if I say one and you challenge and there is at least one head between us, or if I say one, you say two and there are fewer than two heads between us. Otherwise, you win.

This game has four intitial states, HH, HT, TH and TT, and three possible sets of actions: zero, one/challenge and one/two. That's 12 possible combinations. But I can pick any p from 0 to 1 as the probability of saying zero with either H or T; that's two continuous numbers. Moreover, I can pick different p's for each hand, either independently or dependent on previous outcomes. Solving this 12 state game is not trivial. Multiply by 10^14 and you have a difficult problem even with a lot of computer power.