Heads-up limit hold'em poker is solved
Michael Bowling, Neil Burch, Michael Johanson, Oskari Tammelin, Vern Paxson
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.
- The paper did a good job of giving enough context for the problem of the poker game to understand the significance of the solution in the progression of solving imperfect-information games.
- There was not enough explanation of the CFR and CFR+ algorithms to form a proper understanding of them, so reading the references would be helpful. It was also obviously not the point of the paper to explain the algorithms.
- The illumination of the results was very impressive in that the computed strategy both confirmed and disproved several conventional notions about optimal strategy for the poker variant.