摘要翻译：
Penney的游戏是一个两人零和游戏，每个玩家选择一个正面和反面的三个翻转模式，获胜者是在重复掷一枚公平的硬币中模式出现在第一个的玩家。因为玩家选择顺序，第二个移动者有优势。事实上，对于任何三个翻转模式，都有另一个严格来说更有可能首先发生的三个翻转模式。本文提出了一个新的无套利论点，它产生对应于任何一对不同模式的获胜赔率。由此得到的赔率公式与康威的“领先数”算法生成的赔率公式等价。伴随而来的投注赔率直觉增加了康威算法工作原因的洞察力。证明简单，易于推广到涉及两个以上结果、不相等概率和不同长度竞争模式的对策。关于Penney游戏的预期持续时间的附加结果被提出。包括算法的代码实现和交叉验证。
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英文标题：
《Penney's Game Odds From No-Arbitrage》
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作者：
Joshua B. Miller
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最新提交年份：
2019
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分类信息：

一级分类：Mathematics        数学
二级分类：Optimization and Control        优化与控制
分类描述：Operations research, linear programming, control theory, systems theory, optimal control, game theory
运筹学，线性规划，控制论，系统论，最优控制，博弈论
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一级分类：Economics        经济学
二级分类：Theoretical Economics        理论经济学
分类描述：Includes theoretical contributions to Contract Theory, Decision Theory, Game Theory, General Equilibrium, Growth, Learning and Evolution, Macroeconomics, Market and Mechanism Design, and Social Choice.
包括对契约理论、决策理论、博弈论、一般均衡、增长、学习与进化、宏观经济学、市场与机制设计、社会选择的理论贡献。
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英文摘要：
  Penney's game is a two player zero-sum game in which each player chooses a three-flip pattern of heads and tails and the winner is the player whose pattern occurs first in repeated tosses of a fair coin. Because the players choose sequentially, the second mover has the advantage. In fact, for any three-flip pattern, there is another three-flip pattern that is strictly more likely to occur first. This paper provides a novel no-arbitrage argument that generates the winning odds corresponding to any pair of distinct patterns. The resulting odds formula is equivalent to that generated by Conway's "leading number" algorithm. The accompanying betting odds intuition adds insight into why Conway's algorithm works. The proof is simple and easy to generalize to games involving more than two outcomes, unequal probabilities, and competing patterns of various length. Additional results on the expected duration of Penney's game are presented. Code implementing and cross-validating the algorithms is included.
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PDF链接：
https://arxiv.org/pdf/1904.09888