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: exact.txt Eugene d’Eon and I have been playing around computing Nash equilibria for extremely simplified versions of heads-up Texas holdem poker. 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).

Consider the following poker-like game, played with two players: Alice and Bob. Bob posts a blind of 1. Both players are dealt a single, continuous hand chosen uniformly at random from $[0,1]$. Alice can fold, call, or raise any amount $b \gt 0$ (calling means $b = 0$). Bob either calls or folds. My original plan was to work out the Nash equilibrium for this game, and therefore derive interesting smooth curves describing the optimal way for Alice to bluff and generally obscure her hand.