Title |
Heads-up limit hold’em poker is solved
|
---|---|
Published in |
Science, January 2015
|
DOI | 10.1126/science.1259433 |
Pubmed ID | |
Authors |
Michael Bowling, Neil Burch, Michael Johanson, Oskari Tammelin |
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. |
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Geographical breakdown
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Japan | 221 | 22% |
United States | 78 | 8% |
Canada | 21 | 2% |
United Kingdom | 14 | 1% |
Spain | 7 | <1% |
Germany | 6 | <1% |
France | 5 | <1% |
Australia | 3 | <1% |
China | 3 | <1% |
Other | 41 | 4% |
Unknown | 588 | 60% |
Demographic breakdown
Type | Count | As % |
---|---|---|
Members of the public | 904 | 92% |
Scientists | 72 | 7% |
Science communicators (journalists, bloggers, editors) | 5 | <1% |
Practitioners (doctors, other healthcare professionals) | 5 | <1% |
Unknown | 1 | <1% |
Mendeley readers
Geographical breakdown
Country | Count | As % |
---|---|---|
United States | 4 | 1% |
Germany | 3 | 1% |
United Kingdom | 3 | 1% |
France | 3 | 1% |
Italy | 2 | <1% |
Netherlands | 2 | <1% |
Japan | 2 | <1% |
Estonia | 1 | <1% |
India | 1 | <1% |
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Unknown | 259 | 92% |
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Readers by professional status | Count | As % |
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Researcher | 67 | 24% |
Student > Master | 30 | 11% |
Student > Bachelor | 30 | 11% |
Professor > Associate Professor | 12 | 4% |
Other | 40 | 14% |
Unknown | 35 | 12% |
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Agricultural and Biological Sciences | 30 | 11% |
Engineering | 28 | 10% |
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Other | 55 | 20% |
Unknown | 40 | 14% |