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

2024/09/01 by Geoffrey Grimmett, Grimmett, Geoffrey R.
Computer Science · #60C05 #Algorithms and Data Compression #Artificial Intelligence in Games #FOS: Mathematics #Logic, programming, and type systems #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2409.00732

openalex publication_date 2024/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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