论文标题
通过通行证调查公正游戏
Investigations of Impartial Games With a Pass
论文作者
论文摘要
组合游戏NIM及其变体的研究丰富而多样，但对游戏的传球知之甚少。它是NIM，但是一旦每场比赛，一个玩家就可以跳过轮回，但是只有在剩下非空的堆时才能做到这一点。在本文中，我们为游戏定义了一个新的二进制操作，我们用来证明NIM的新型属性以及通过它的概括。最重要的是，我们在寻找$ \ Mathcal {p} $的位置和游戏的最佳策略方面取得了很小的进步。
The study of the combinatorial game Nim and its variants is rich and varied, but little is known of the game Nim with a Pass. It is Nim, but once per game a player is permitted to skip their turn but this can only be done if a nonempty pile remains. In this paper we define a new binary operation on games which we use to prove novel properties of Nim with a Pass, as well as games which are generalizations of it. Most importantly, we make small progress on finding the $\mathcal{P}$-positions and optimal strategies of the game.
