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Re-exploring the Penney-Ante Game
The American Statistician  (IF8.71),  Pub Date : 2021-08-31, DOI: 10.1080/00031305.2021.1961860


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.