论文标题
卡游戏战争的组合方面
Combinatorial Aspects of the Card Game War
论文作者
论文摘要
本文在有限的纸牌上研究了纸牌游戏战争的单套件版本。玩家如何将他们赢得的卡片放在手中的卡片有不同的方法，但是我们主要考虑随机将卡片放回原处，并确定性地始终将获胜卡放在丢失卡之前。定义了一个\ emph {passthrough}的概念，这是指从游戏中的特定点上通过所有卡片玩的玩家。我们考虑第二名玩家在第一次传球中获胜的游戏。我们介绍了与游戏相关的几个组合对象：游戏图，损失序列，赢损二进制树和游戏posets。我们展示了这些对象如何相互关系。我们列举状态，具体取决于回合的数量和传球数量。
This paper studies a single-suit version of the card game War on a finite deck of cards. There are varying methods of how players put the cards that they win back into their hands, but we primarily consider randomly putting the cards back and deterministically always putting the winning card before the losing card. The concept of a \emph{passthrough} is defined, which refers to a player playing through all cards in their hand from a particular point in the game. We consider games in which the second player wins during their first passthrough. We introduce several combinatorial objects related to the game: game graphs, win-loss sequences, win-loss binary trees, and game posets. We show how these objects relate to each other. We enumerate states depending on the number of rounds and the number of passthroughs.
