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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2406.20049 |
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| _version_ | 1866909447319715840 |
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| author | Basdevant, Anne-Laure Hénard, Olivier Maurel-Segala, Edouard Singh, Arvind |
| author_facet | Basdevant, Anne-Laure Hénard, Olivier Maurel-Segala, Edouard Singh, Arvind |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_20049 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On cases where Litt's game is fair Basdevant, Anne-Laure Hénard, Olivier Maurel-Segala, Edouard Singh, Arvind Combinatorics Probability 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. |
| title | On cases where Litt's game is fair |
| topic | Combinatorics Probability |
| url | https://arxiv.org/abs/2406.20049 |