Year: 2025
Type: article
Abstract: A fair coin is flipped n times, and two finite sequences of heads and tails with the same length are given, say A and B . Each time A appears in the sequence of fair coin flips, Alice gets a point, and each time B appears, Bob gets a point. Who is more likely to win? This puzzle is a slight extension of Litt’s game [10]. In this note, we show that the game is fair for any value of n and any two words A , B that have the same auto-correlation structure by building up a bijection that exchanges Bob and Alice scores. It is remarkable that the inter-correlations between A and B do not play any role in this case. Additionally, we propose a conjecture for cases where the game is unfair, providing insights into the underlying structure of the game for a fixed n .
Source: Comptes Rendus Mathématique
DOI: 10.5802/crmath.783
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4400222192