Abstract In this paper we study computing Sprague-Grundy values for short impartial games under the normal play convention. We put forward new game-agnostic methods for effective pruning search trees of impartial games. These algorithms are inspired by the α-β, a well-known pruning method for minimax trees. However, our algorithms prune trees whose node values are assigned by the mex function instead of min/max. We have verified the effectiveness of our algorithms experimentally on instances of some standard impartial games (that is Nim, Chomp, and Cram). Based on the results of our experiments we have concluded that: (1) our methods generally perform well, especially when transposition table can store only a small fraction of all game positions (which is typical when larger games are concerned); (2) one of our algorithms constitutes a more universal alternative to the state-of-the-art algorithm proposed by Lemoine and Viennot.

中文翻译：

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论公正博弈搜索树的剪枝

摘要 在本文中，我们研究了在正常游戏规则下计算短时间公平游戏的 Sprague-Grundy 值。我们提出了新的游戏不可知方法来有效修剪公平游戏的搜索树。这些算法的灵感来自 α-β，这是一种著名的极小极大树修剪方法。然而，我们的算法修剪了节点值由 mex 函数而不是 min/max 分配的树。我们已经在一些标准的公正游戏（即 Nim、Chomp 和 Cram）的实例上通过实验验证了我们的算法的有效性。基于我们的实验结果，我们得出的结论是：（1）我们的方法总体上表现良好，特别是当换位表只能存储所有游戏位置的一小部分时（这在涉及较大游戏时是典型的）；