Abstract

We propose a single loop diagram and use it to devise a single loop matrix method to computationally solve the Penney-Ante game. This method avoids the nuances of repeated use of conditional probability and Markov chain representations. We remove the limitations of Conway’s trick as applied to a fair coin and generalize the method where the coin is allowed to be biased. A uniform random number generator is used to simulate the game and formulate implicit mathematical relations to explore nontransitivity.

中文翻译：

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重新探索 Penney-Ante 博弈

摘要

我们提出了一个单循环图并用它来设计一个单循环矩阵方法来计算解决 Penney-Ante 博弈。这种方法避免了重复使用条件概率和马尔可夫链表示的细微差别。我们消除了适用于公平硬币的康威技巧的限制，并概括了允许硬币有偏差的方法。一个统一的随机数生成器用于模拟游戏并制定隐含的数学关系以探索非传递性。