Alice and Bob on $\Bbb X$: reversal, coupling, renewal

Geoffrey R. Grimmett

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arXiv · 2409.00732

Alice and Bob on $\Bbb X$: reversal, coupling, renewal

Geoffrey R. Grimmett

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Abstract

A neat question involving coin flips surfaced on $\Bbb X$, and generated an intensive `storm' of `social mathematics'. In a sequence of flips of a fair coin, Alice wins a point at each appearance of two consecutive heads, and Bob wins a point whenever a head is followed immediately by a tail. Who is more likely to win the game? The subsequent discussion illustrated conflicting intuitions, and concluded with the correct answer (it is a close thing). It is explained here why the context of the question is interesting and how it may be answered in a quantitative manner using the probabilistic techniques of reversal, coupling, and renewal.

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Geoffrey R. Grimmett. 2024-09-01. Alice and Bob on $\Bbb X$: reversal, coupling, renewal. https://arxiv.org/abs/2409.00732

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