title: Computer science. Heads-up limit hold'em poker is solved.
abstract: Poker is a family of games that exhibit imperfect information, where players do not have full knowledge of past events. Whereas many perfect-information games have been solved (e.g., Connect Four and checkers), no nontrivial imperfect-information game played competitively by humans has previously been solved. Here, we announce that heads-up limit Texas hold'em is now essentially weakly solved. Furthermore, this computation formally proves the common wisdom that the dealer in the game holds a substantial advantage. This result was enabled by a new algorithm, CFR(+), which is capable of solving extensive-form games orders of magnitude larger than previously possible.
authors.affiliation: Department of Computing Science, University of Alberta, Edmonton, Alberta T6G 2E8, Canada. bowling@cs.ualberta.ca.
authors.forename: Michael
authors.initials: M
authors.lastname: Bowling
authors.affiliation: Department of Computing Science, University of Alberta, Edmonton, Alberta T6G 2E8, Canada.
authors.forename: Neil
authors.initials: N
authors.lastname: Burch
authors.affiliation: Department of Computing Science, University of Alberta, Edmonton, Alberta T6G 2E8, Canada.
authors.forename: Michael
authors.initials: M
authors.lastname: Johanson
authors.affiliation: Unaffiliated; http://jeskola.net.
authors.forename: Oskari
authors.initials: O
authors.lastname: Tammelin