A near-optimal strategy for a heads-up no-limit Texas Hold'em poker tournament

Abstract

We analyze a heads-up no-limit Texas Hold'em poker tournament with a fixed small blind of 300 chips, a fixed big blind of 600 chips and a total amount of 8000 chips on the table (until recently, these parameters defined the heads-up endgame of sit-n-go tournaments on the popular Party-Poker.com online poker site). Due to the size of this game, a computation of an optimal (i.e. minimax) strategy for the game is completely infeasible. However, combining an algorithm due to Koller, Megiddo and von Stengel with concepts of Everett and suggestions of Sklansky, we compute an optimal jam/fold strategy, i.e. a strategy that would be optimal if any bet made by the player playing by the strategy (but not bets of his opponent) had to be his entire stack. Our computations establish that the computed strategy is near-optimal for the unrestricted tournament (i.e., with post-flop play being allowed) in the rigorous sense that a player playing by the computed strategy will win the tournament with a probability within 1.4 percentage points of the probability that an optimal strategy (allowing post-flop play) would give.