2024/06/28 by Basdevant, Anne-Laure, Hénard, Olivier, Maurel-Segala, Edouard +1
#Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2406.20049
A fair coin is flipped n times, and two finite sequences of heads and tails (words) A and B of the same length are given. Each time the word A appears in the sequence of coin flips, Alice gets a point, and each time the word B appears, Bob gets a point. Who is more likely to win? This puzzle is a slight extension of Litt's game that recently set Twitter abuzz. We show that Litt's game is fair for any value of n and any two words that have the same auto-correlation structure by building up a bijection that exchanges Bob and Alice scores; the fact that the inter-correlation does not come into play in this case may come up as a surprise.