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

Wei-Yuan Hsu, Chu-Ling Ko, Jr-Chang Chen, Ting-Han Wei, Chu-Hsuan Hsueh, I-Chen Wu

Abstract: 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. Previous article in issue Next article in issue