![]() There are only a finite number of possible hands, after all, so each probability is a rational number. Therefore, I set out to compute the exact answers. If we’re going to fritter away time analyzing simplified poker games, we might as well do an excellent job while we’re at it. ![]() However, their data only has six significant digits, which, frankly, is not cool. Initially, we were using the table from for this purpose. In order to compute the Nash equilibrium, we need to know the probability of Alice or Bob winning for each pair of possible poker hands (there are 169 unique two card hands). If Alice bets, Bob then looks at his cards and decides in turn. Alice looks at her two cards, and decides whether to bet or fold. As in the previous post, consider two players Alice and Bob, where Bob posts a blind of 1. ![]() To keep the problem manageable, we considered only “preflop” betting, after the private hands have been dealt but before the shared cards are known. For those who don’t know the details, in Texas holdem each player is dealt two cards face down, followed by five cards face up which are shared between all players (with betting at various points in between these cards). Brief summary in case you just want the data: here’s a table of exact win/loss/tie probabilities for every pair of two card preflop hands in Texas holdem:Įugene d’Eon and I have been playing around computing Nash equilibria for extremely simplified versions of heads-up Texas holdem poker. ![]()
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