How reactive gambling can backfire: ruin probability is increasing in $p$, Hölder continuous in initial fortune
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915669568651264 |
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| author | Roy, Aditya Guha Peres, Yuval Qin, Shuo Zuo, Junchi |
| author_facet | Roy, Aditya Guha Peres, Yuval Qin, Shuo Zuo, Junchi |
| contents | A gambler with an initial fortune $x$ starts by betting a dollar, then doubles the bet after every win and halves the bet after every loss. Let $p\in (0,1)$ be the probability of winning for each round. We show that the gambler survives with positive probability if and only if $p < 1/2$ and $x > 2$. Moreover, the ruin probability is increasing and real-analytic in $p$, but a singular, Hölder continuous function of $x$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10754 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | How reactive gambling can backfire: ruin probability is increasing in $p$, Hölder continuous in initial fortune Roy, Aditya Guha Peres, Yuval Qin, Shuo Zuo, Junchi Probability A gambler with an initial fortune $x$ starts by betting a dollar, then doubles the bet after every win and halves the bet after every loss. Let $p\in (0,1)$ be the probability of winning for each round. We show that the gambler survives with positive probability if and only if $p < 1/2$ and $x > 2$. Moreover, the ruin probability is increasing and real-analytic in $p$, but a singular, Hölder continuous function of $x$. |
| title | How reactive gambling can backfire: ruin probability is increasing in $p$, Hölder continuous in initial fortune |
| topic | Probability |
| url | https://arxiv.org/abs/2512.10754 |