Strategy

A basic decision facing any poker player, given that a bet is on the table, is whether to call or fold one's hand (ignoring the possibility of raising for now). Assuming probability p of winning the pot if the hand is played to a showdown, n-1 opponents remain in the game and an expected cost k of reaching the showdown, then the threshold probability of winning required to make the decision to call a bet can be worked out from the pot odds.

This assumes that the final size of the pot minus the current player's future contribution will be the current size of the pot plus equal contributions by all other players. The calling threshold $\theta$ identifies the probability of winning at which the expected values of calling a bet versus folding are equal. As shown in [Korb, Nicholson, and JitnahKorb et al.1999], the relation between probability and odds, $\theta$ is:

$$\theta \frac{k}{c + 2k -1}$$ = (1)

If we can compute an accurate probability of winning, then by comparison with $\theta$ we can make reasonable decisions about whether to call or fold. By extension -- considering the degree to which our estimated winning probability exceeds that threshold when it does -- we can make reasonable decisions about bets and raises as well.