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关于Hex博弈最优获胜策略的一种新方法彭 元 许晓东 罗海鹏 崔岫峰


摘 要:Hex博奕Hex(n)是一种在六边形拼接的n×n棋盘上进行的二人博奕,博奕中二人轮流下红色和蓝色棋子,先构造出一条从一边连到对边的单色路者为胜者。Hex博奕中先手有必胜策略。设δ(n)为Hex(n)中先手能保证获胜所需的最少步数,Garikai Campbell通过研究其他对象间接地证明了δ(n)>n对任意n≥4成立。利用新的方法来分析对称性,给出了δ(n)>n一个直接而简单的证明,并在此基础上利用计算证明了δ(5)=7。
  关键词:Hex博弈; 步数; 最优策略
  中图分类号:TP301.6
  文献标志码:A
  
  文章编号:1001-3695(2010)02-0498-02
  doi:10.3969/j.issn.1001-3695.2010.02.025
  
  New approach on optimal play in Hex game
  
  PENG Yuan1, XU Xiao-dong1, LUO Hai-peng1, CUI Xiu-feng2
  
  (1.Guangxi Academy of Sciences, Nanning 530007, China; 2. Network Information Center, Qiqihar University, Qiqihar Heilongjiang 161006, China)
  
  Abstract:Hex game Hex(n) is a two person game played on an n×n board of hexagonal tiles, in which the players take turns trying to construct paths from one side of the board to the other. There exists a winning strategy for the first player. Let δ(n) be the minimum number of moves that player one must make to guarantee a win in Hex(n),Garikai Campbell proved δ(n)>n for any n≥4 by studying another question. In this note, gave a directed and much simpler proof based on a new approach, based on what proved δ(5)=7 by computing.
  Key words:Hex game; moves; optimal play ......
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