From Unequal Chance to a Coin Game Dance: Variants of Penney's Game

Agarwal, Isha; Borodin, Matvey; Duncan, Aidan; Ji, Kaylee; Khovanova, Tanya; Lee, Shane; Litchev, Boyan; Rastogi, Anshul; Rastogi, Garima; Zhao, Andrew

doi:10.48550/arxiv.2006.13002

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2020

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“…A popular variation uses various other objects in place of a coin, such as a finite deck of cards in Humble & Nishiyama [8] or a roulette wheel in Vallin [10]. Many more variations of this game were studied by Agarwal et al [1].…”

Section: Introductionmentioning

confidence: 99%

The Penney's Game with Group Action

Khovanova¹,

Li²

2020

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We generalize word avoidance theory by equipping the alphabet A with a group action. We call equivalence classes of words patterns. We extend the notion of word correlation to patterns using group stabilizers. We extend known word avoidance results to patterns. We use these results to answer standard questions for the Penney's game on patterns and show non-transitivity for the game on patterns as the length of the pattern tends to infinity. We also analyze bounds on the pattern-based Conway leading number and expected wait time, and further explore the game under the cyclic and symmetric group actions.

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Section: Introductionmentioning

confidence: 99%