How to Answer Questions of the Type: If you toss a coin n times, how likely is HH to show up more than HT?
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911884673810432 |
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| author | Ekhad, Shalosh B. Zeilberger, Doron |
| author_facet | Ekhad, Shalosh B. Zeilberger, Doron |
| contents | On March 16, 2024, Daniel Litt, in an X-post, proposed the following brainteaser: "Flip a fair coin 100 times. It gives a sequence of heads (H) and tails (T). For each HH in the sequence of flips, Alice gets a point; for each HT, Bob does, so e.g. for the sequence THHHT Alice gets 2 points and Bob gets 1 point. Who is most likely to win?" We show the power of symbolic computation, in particular the (continuous) Almkvist-Zeilberger algorithm, to answer this, and far more general, questions of this kind. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_13561 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | How to Answer Questions of the Type: If you toss a coin n times, how likely is HH to show up more than HT? Ekhad, Shalosh B. Zeilberger, Doron Combinatorics Probability On March 16, 2024, Daniel Litt, in an X-post, proposed the following brainteaser: "Flip a fair coin 100 times. It gives a sequence of heads (H) and tails (T). For each HH in the sequence of flips, Alice gets a point; for each HT, Bob does, so e.g. for the sequence THHHT Alice gets 2 points and Bob gets 1 point. Who is most likely to win?" We show the power of symbolic computation, in particular the (continuous) Almkvist-Zeilberger algorithm, to answer this, and far more general, questions of this kind. |
| title | How to Answer Questions of the Type: If you toss a coin n times, how likely is HH to show up more than HT? |
| topic | Combinatorics Probability |
| url | https://arxiv.org/abs/2405.13561 |