How many coin tosses would you need until you get $n$ Heads or $m$ Tails?
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914187987386368 |
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| author | Janson, Svante Martinez, Lucy Zeilberger, Doron |
| author_facet | Janson, Svante Martinez, Lucy Zeilberger, Doron |
| contents | We harness both human ingenuity and the power of symbolic computation to study the number of coin tosses until reaching $n$ Heads or $m$ Tails. We also talk about the closely related problem of reaching $n$ Heads and $m$ Tails. This paper is accompanied by a Maple package that enables fast computation of expectations, variances, and higher moments of these quantities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07803 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | How many coin tosses would you need until you get $n$ Heads or $m$ Tails? Janson, Svante Martinez, Lucy Zeilberger, Doron Probability Combinatorics 60 (Primary) 05 (Secondary) We harness both human ingenuity and the power of symbolic computation to study the number of coin tosses until reaching $n$ Heads or $m$ Tails. We also talk about the closely related problem of reaching $n$ Heads and $m$ Tails. This paper is accompanied by a Maple package that enables fast computation of expectations, variances, and higher moments of these quantities. |
| title | How many coin tosses would you need until you get $n$ Heads or $m$ Tails? |
| topic | Probability Combinatorics 60 (Primary) 05 (Secondary) |
| url | https://arxiv.org/abs/2512.07803 |