关于Hex博弈最优获胜策略的一种新方法

New approach on optimal play in Hex game

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。

Hex game Hex（n） is a two person game played on an n x 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.