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| Hovedforfatter: | |
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| Format: | Preprint |
| Udgivet: |
2026
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| Fag: | |
| Online adgang: | https://arxiv.org/abs/2601.16607 |
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| _version_ | 1866908828521463808 |
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| author | Kuba, Markus |
| author_facet | Kuba, Markus |
| contents | We consider a card guessing game with complete feedback. An ordered deck of $n$ cards labeled $1$ up to $n$ is riffle-shuffled exactly one time. Given a value $p\in(0{,}1)\setminus\{\frac12\}$, the riffle shuffle is assumed to be unbalanced, such that the cut is expected to happen at position $p\cdot n$. The goal of the game is to maximize the number of correct guesses of the cards: one after another a single card is drawn from the top, and shown to the guesser until no cards remain. We provide a detailed analysis of the optimal guessing strategy and study the distribution of the number of correct guesses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16607 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Card guessing after an asymmetric riffle shuffle Kuba, Markus Combinatorics Probability 05A15, 05A16, 60F05, 60C05 We consider a card guessing game with complete feedback. An ordered deck of $n$ cards labeled $1$ up to $n$ is riffle-shuffled exactly one time. Given a value $p\in(0{,}1)\setminus\{\frac12\}$, the riffle shuffle is assumed to be unbalanced, such that the cut is expected to happen at position $p\cdot n$. The goal of the game is to maximize the number of correct guesses of the cards: one after another a single card is drawn from the top, and shown to the guesser until no cards remain. We provide a detailed analysis of the optimal guessing strategy and study the distribution of the number of correct guesses. |
| title | Card guessing after an asymmetric riffle shuffle |
| topic | Combinatorics Probability 05A15, 05A16, 60F05, 60C05 |
| url | https://arxiv.org/abs/2601.16607 |