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Science. 2015 Jan 9;347(6218):145-9. doi: 10.1126/science.1259433.

Computer science. Heads-up limit hold'em poker is solved.

Author information

1
Department of Computing Science, University of Alberta, Edmonton, Alberta T6G 2E8, Canada. bowling@cs.ualberta.ca.
2
Department of Computing Science, University of Alberta, Edmonton, Alberta T6G 2E8, Canada.
3
Unaffiliated; http://jeskola.net.

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.

PMID:
25574016
DOI:
10.1126/science.1259433
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