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Abstract

The game of checkers has roughly 500 billion billion possible positions (5 × 1020). The task of solving the game, determining the final result in a game with no mistakes made by either player, is daunting. Since 1989, almost continuously, dozens of computers have been working on solving checkers, applying state-of-the-art artificial intelligence techniques to the proving process. This paper announces that checkers is now solved: Perfect play by both sides leads to a draw. This is the most challenging popular game to be solved to date, roughly one million times as complex as Connect Four. Artificial intelligence technology has been used to generate strong heuristic-based game-playing programs, such as Deep Blue for chess. Solving a game takes this to the next level by replacing the heuristics with perfection.

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References and Notes

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The support of Canada's Natural Sciences and Engineering Research Council (NSERC), Alberta's Informatics Circle of Research Excellence (iCORE), and the Canada Foundation for Innovation is greatly appreciated. Numerous people contributed to this work, including M. Bryant, J. Culberson, B. Gorda, B. Knight, D. Szafron, K. Thompson, and N. Treloar.

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Published In

Science
Volume 317 | Issue 5844
14 September 2007

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Submission history

Received: 20 April 2007
Accepted: 6 July 2007
Published in print: 14 September 2007

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Notes

Supporting Online Material
www.sciencemag.org/cgi/content/full/1144079/DC1
Materials and Methods
Figs. S1 to S4
References

Authors

Affiliations

Jonathan Schaeffer* [email protected]
Department of Computing Science, University of Alberta, Edmonton, Alberta T6G 2E8, Canada.
Neil Burch
Department of Computing Science, University of Alberta, Edmonton, Alberta T6G 2E8, Canada.
Yngvi Björnsson
Department of Computing Science, University of Alberta, Edmonton, Alberta T6G 2E8, Canada.
Akihiro Kishimoto
Department of Computing Science, University of Alberta, Edmonton, Alberta T6G 2E8, Canada.
Martin Müller
Department of Computing Science, University of Alberta, Edmonton, Alberta T6G 2E8, Canada.
Robert Lake
Department of Computing Science, University of Alberta, Edmonton, Alberta T6G 2E8, Canada.
Paul Lu
Department of Computing Science, University of Alberta, Edmonton, Alberta T6G 2E8, Canada.
Steve Sutphen
Department of Computing Science, University of Alberta, Edmonton, Alberta T6G 2E8, Canada.

Notes

*
To whom correspondence should be addressed. E-mail: [email protected]

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