论文标题
带有Modulo获胜条件的概率收集游戏
Probabilistic chip-collecting games with modulo winning conditions
论文作者
论文摘要
令$ a $，$ b $和$ n $为$ 0 <a <b <n $的整数。在某些两人概率的筹码游戏中，爱丽丝扔了一枚硬币，以确定她是收集$ a $ chips还是$ b $芯片。如果爱丽丝收集$ a $芯片，那么鲍勃会收集$ b $芯片，反之亦然。当玩家积累了许多$ n $的筹码时，宣布了获胜者。在本文中，我们解决了与此游戏有关的文献中的两个猜想。
Let $a$, $b$, and $n$ be integers with $0<a<b<n$. In a certain two-player probabilistic chip-collecting game, Alice tosses a coin to determine whether she collects $a$ chips or $b$ chips. If Alice collects $a$ chips, then Bob collects $b$ chips, and vice versa. A player is announced the winner when they have accumulated a number of chips that is a multiple of $n$. In this paper, we settle two conjectures from the literature related to this game.
