A proof that HT is more likely to outnumber HH than vice versa in a sequence of n coin flips
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916261382848512 |
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| author | Segert, Simon |
| author_facet | Segert, Simon |
| contents | Consider the following probability puzzle: A fair coin is flipped n times. For each HT in the resulting sequence, Bob gets a point, and for each HH Alice gets a point. Who is more likely to win? We provide a proof that Bob wins more often for every n>=3. As a byproduct, we derive the asymptotic form of the difference in win probabilities, and obtain an efficient algorithms for their calculation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_16660 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A proof that HT is more likely to outnumber HH than vice versa in a sequence of n coin flips Segert, Simon Combinatorics Probability Consider the following probability puzzle: A fair coin is flipped n times. For each HT in the resulting sequence, Bob gets a point, and for each HH Alice gets a point. Who is more likely to win? We provide a proof that Bob wins more often for every n>=3. As a byproduct, we derive the asymptotic form of the difference in win probabilities, and obtain an efficient algorithms for their calculation. |
| title | A proof that HT is more likely to outnumber HH than vice versa in a sequence of n coin flips |
| topic | Combinatorics Probability |
| url | https://arxiv.org/abs/2405.16660 |