A proof that HT is more likely to outnumber HH than vice versa in a sequence of n coin flips

2024/05/26 by Simon Segert, Segert, Simon
Economics, Econometrics and Finance · #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR) #Sports Analytics and Performance

paper · pdf · doi:10.48550/arxiv.2405.16660

openalex publication_date 2024/05/26 · openalex created_date 2024/05/29 · openalex updated_date 2026/07/28

Abstract

Consider the following probability puzzle: A fair coin is flipped n times. For each HT in the resulting sequence, Bob gets a point, and for each HH Alice gets a point. Who is more likely to win? We provide a proof that Bob wins more often for every n>=3. As a byproduct, we derive the asymptotic form of the difference in win probabilities, and obtain an efficient algorithms for their calculation.

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