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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.10294 |
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| _version_ | 1866912481638612992 |
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| author | Clay, Alexander |
| author_facet | Clay, Alexander |
| contents | We investigate a one-time single shelf shuffle by establishing the position matrix explicitly. In some cases, we prove a no-feedback optimal guessing strategy. A general no-feedback strategy is conjectured, and asymptotics for the expected reward are given. For the complete-feedback case, we give a guessing strategy, prove that it is optimal and unique, and find the expected reward. Our results prove a conjecture of Diaconis, Fulman, and Holmes in a special case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_10294 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Guessing Strategies for Shuffling Machines Clay, Alexander Probability Combinatorics We investigate a one-time single shelf shuffle by establishing the position matrix explicitly. In some cases, we prove a no-feedback optimal guessing strategy. A general no-feedback strategy is conjectured, and asymptotics for the expected reward are given. For the complete-feedback case, we give a guessing strategy, prove that it is optimal and unique, and find the expected reward. Our results prove a conjecture of Diaconis, Fulman, and Holmes in a special case. |
| title | Guessing Strategies for Shuffling Machines |
| topic | Probability Combinatorics |
| url | https://arxiv.org/abs/2507.10294 |