具有模获胜条件的概率集片对策
Probabilistic chip-collecting games with modulo winning conditions
摘要：
令$a$、$b$和$n$为整数，其中$0<a<b<n$。在某个双人概率筹码收集游戏中，爱丽丝掷硬币来决定她收集的是$a$筹码还是$b$筹码。如果Alice收集$a$筹码，那么Bob收集$b$筹码，反之亦然。当玩家累积的筹码数是$n$的倍数时，他们就被宣布为赢家。在本文中，我们解决了两个问题，从文献中有关这个游戏。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
