AI 中文总结
针对赌场崩盘游戏，提出一种不受玩家数量和投资金额影响的优化算法，可平衡赌场与玩家利益，还能辅助专业玩家决策，且分析了其计算复杂度与停止乘数统计特性。
AI 中文摘要
崩盘（Crash）是一款广受欢迎的赌场游戏，融合了策略决策、概率与计算分析，尤其从赌场视角来看更是如此。本文提出一种优化算法，旨在最小化赌场的保底正收益，同时最大化给定回合中赢得一定金额的玩家数量。由于崩盘游戏本质上是多玩家游戏，玩家会在不同时间点投入随机的投资金额，这使得任何单个玩家在回合开始前都难以判断其计划投资是相对高还是低，进而难以确定自身实际承担的风险。该算法的核心目标是确定一个最优停止乘数，以平衡赌场与玩家双方的利益。值得注意的是，该算法不受玩家数量变化或投资金额波动的影响，尽管实际中赌场通常会对允许的投资设定固定范围。此外，该算法还能帮助专业玩家就投资金额和可接受的风险程度做出更明智的决策。我们进一步分析了该算法的计算复杂度及其停止乘数的统计数据，以更全面地了解其实际表现。
英文摘要
Crash is a widely played casino game that blends strategic decision-making, probability, and computational analysis, particularly from the perspective of the house. This paper presents an optimization algorithm aimed at minimizing the casino's guaranteed positive earnings while simultaneously maximizing the number of players who win some amount during a given round. Since Crash is inherently a multiplayer game, players place random investment amounts at different points in time, which makes it difficult for any individual player to judge, before the round even begins, whether their intended investment is comparatively high or low, and consequently, how much risk they are actually taking on. The core objective of the proposed algorithm is to determine an optimal stopping multiplier that balances both the casino's and the players' interests. Notably, the algorithm remains unaffected by changes in the number of players or by variation in investment amounts, although in practice casinos typically impose a fixed range on permissible investments. Beyond this, the algorithm can help professional players make more informed decisions about how much to invest and how much risk they are comfortable accepting. We further analyze the algorithm's computational complexity and its stopping-multiplier statistics to give a fuller picture of how it behaves in practice.
Comments11 Pages, 3 figures
