Abstract

against diseases), (cyber)security, and other domains. On page 145 of this issue, Bowling et al. ( 1) report on having computed a strat-egy for two-player limit Texas Hold’em poker that is so close to optimal that, at the pace a human plays poker, it cannot be beaten with statistical significance in a lifetime. While strong strategies have been computed for larger imperfect-information games as well (2–6), this is, to my knowledge, the larg-est imperfect-information game essentially solved to date, and the first one competi-tively played by humans that has now been essentially solved. The general leading approach for solv-ing imperfect-information games is shown in the figure; for a review, see ( 7). First, the game is abstracted to generate a smaller but strategically similar game, reducing it to a size that can be tackled with an equilibrium-finding algorithm. Then, the abstract game is solved for equilibrium or near-equilib-rium. A Nash equilibrium defines a notion of rational play. It is a profile of strategies, one per player, such that no player can in-crease her expected payoff by switching to a different strategy. A strategy for a player states for each information set where it is the player’s turn, the probability with which the player should select each of her available actions. An information set is a collection of game states that cannot be distinguished by the player whose turn it is because of private information of the other players. Finally, the strategies from the abstract game are mapped back to the original game. Cellular stress defense p. 125 China’s aquaculture threatens the oceans p. 133INSIGHTS Playing at a normal human pace, one can’t beat a computer program for limit Texas Hold’em with statistical significance in a lifetime