Heads-up Limit Hold'em Poker is Solved

Michael Bowling, Neil Burch, Michael Johanson, and Oskari Tammelin. Heads-up Limit Hold'em Poker is Solved. Science, 347(6218):145–149, January 2015.




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.

Additional Information

The HTML link is to Science's paywall'd site. The PDF download is our accepted manuscript.


  Title = "Heads-up Limit Hold'em Poker is Solved",
  Author = "Michael Bowling and Neil Burch and Michael Johanson and Oskari Tammelin",
  Journal = "Science",
  Month = "January",
  Year = "2015",
  Volume = "347",
  Number = "6218",
  Pages = "145--149"

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