Alice and Bob on $\Bbb X$: reversal, coupling, renewal
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911139190800384 |
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| author | Grimmett, Geoffrey R. |
| author_facet | Grimmett, Geoffrey R. |
| contents | A neat question involving coin flips surfaced on $\Bbb X$, and generated an intensive `storm' of `social mathematics'. In a sequence of flips of a fair coin, Alice wins a point at each appearance of two consecutive heads, and Bob wins a point whenever a head is followed immediately by a tail. Who is more likely to win the game? The subsequent discussion illustrated conflicting intuitions, and concluded with the correct answer (it is a close thing). It is explained here why the context of the question is interesting and how it may be answered in a quantitative manner using the probabilistic techniques of reversal, coupling, and renewal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_00732 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Alice and Bob on $\Bbb X$: reversal, coupling, renewal Grimmett, Geoffrey R. Probability 60C05 A neat question involving coin flips surfaced on $\Bbb X$, and generated an intensive `storm' of `social mathematics'. In a sequence of flips of a fair coin, Alice wins a point at each appearance of two consecutive heads, and Bob wins a point whenever a head is followed immediately by a tail. Who is more likely to win the game? The subsequent discussion illustrated conflicting intuitions, and concluded with the correct answer (it is a close thing). It is explained here why the context of the question is interesting and how it may be answered in a quantitative manner using the probabilistic techniques of reversal, coupling, and renewal. |
| title | Alice and Bob on $\Bbb X$: reversal, coupling, renewal |
| topic | Probability 60C05 |
| url | https://arxiv.org/abs/2409.00732 |