The Max-Welter game

作者：Ho Nhan Bao^*

来源：Discrete Mathematics, 2014, 318: 41-47.

DOI：10.1016/j.disc.2013.11.012

• Welter%26apos
• s game
• Combinatorial games
• Misere games
• P-positions
• Sprague-Grundy values
• Periodicity

On a semi-infinite strip of squares rightward numbered 0, 1, 2,... with at most one coin in each square, in Welter%26apos;s game, two players alternately move a coin to an empty square on its left. Jumping over other coins is legal. The player who first cannot move loses. We examine a variant of Welter%26apos;s game, that we call Max-Welter, in which players are allowed to move only the coin furthest to the right. We solve the winning strategy and describe the positions of Sprague-Grundy value 1. We propose two theorems classifying some special cases where calculating the Sprague-Grundy value of a position of size k becomes easier by considering another position of size k - 1. We establish two results on the periodicity of the Sprague-Grundy values. We then show that the Max-Welter game is classified in a proper subclass of tame games that Gurvich calls strongly miserable.

• 出版日期2014-3-6