2015/01/09 by Michael Bowling, Neil Burch, Michael Johanson +1 · 351 citations
Computer Science · Economics, Econometrics and Finance · Social Sciences · Mathematics · #Artificial Intelligence in Games #Sports Analytics and Performance #Digital Games and Media #Perfect information #Limit (mathematics) #Imperfect #Computation #Computer science #Combinatorial game theory #Mathematical economics #Extensive-form game #Sequential game #Complete information #Game theory #Theoretical computer science #Mathematics #Algorithm
paper · doi:10.1126/science.1259433
published in Science 347(6218), 145-149 (American Association for the Advancement of Science)
openalex publication_date 2015/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
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.