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arXiv · 2406.20049

On cases where Litt's game is fair

Anne-Laure Basdevant·Olivier Hénard·Edouard Maurel-Segala·Arvind Singh
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Abstract

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.

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Anne-Laure Basdevant, Olivier Hénard, Edouard Maurel-Segala, Arvind Singh. 2024-06-28. On cases where Litt's game is fair. https://arxiv.org/abs/2406.20049

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