On solving the 7,7,5-game and the 8,8,5-game

Theoretical Computer Science(2020)

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摘要
An mnk-game is a kind of k-in-a-row game played on an m×n board, where two players alternatively mark empty squares with their own colors and the first player who gets k-consecutive marks (horizontally, vertically, or diagonally) wins. In this paper, we present an AND/OR search tree algorithm specifically for proving mnk-games. We first propose three novel methods to reduce the branching factor of AND/OR search trees. We also propose a new method to find pairing strategies, which further accelerate the proof of mnk-games. The combined methods drastically speed up the proof for the 7,7,5-game, which is solved in 2.5 seconds. Moreover, this paper is the first to solve the 8,8,5-game, which is proven as a draw within 17.4 hours.
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关键词
k-in-a-row games,mnk-games,Positional games,Pairing strategy,Relevancy-zone
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