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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2303.15601 |
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| _version_ | 1866911869821779968 |
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| author | Ottolini, Andrea Tripathi, Raghavendra |
| author_facet | Ottolini, Andrea Tripathi, Raghavendra |
| contents | Consider a well-shuffled deck of cards of $n$ different types where each type occurs $m$ times. In a complete feedback game, a player is asked to guess the top card from the deck. After each guess, the top card is revealed to the player and is removed from the deck. The total number of correct guesses in a complete feedback game has attracted significant interest in last few decades. Under different regimes of $m, n$, the expected number of correct guesses, under the greedy (optimal) strategy, has been obtained by various authors, while there are not many results available about the fluctuations. In this paper, we establish a central limit theorem with Berry-Esseen bounds when $m$ is fixed and $n$ is large. Our results extend to the case of decks where different types may have different multiplicity, under suitable assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_15601 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Central limit theorem in complete feedback games Ottolini, Andrea Tripathi, Raghavendra Probability 62L99, 60G40, 92A25 Consider a well-shuffled deck of cards of $n$ different types where each type occurs $m$ times. In a complete feedback game, a player is asked to guess the top card from the deck. After each guess, the top card is revealed to the player and is removed from the deck. The total number of correct guesses in a complete feedback game has attracted significant interest in last few decades. Under different regimes of $m, n$, the expected number of correct guesses, under the greedy (optimal) strategy, has been obtained by various authors, while there are not many results available about the fluctuations. In this paper, we establish a central limit theorem with Berry-Esseen bounds when $m$ is fixed and $n$ is large. Our results extend to the case of decks where different types may have different multiplicity, under suitable assumptions. |
| title | Central limit theorem in complete feedback games |
| topic | Probability 62L99, 60G40, 92A25 |
| url | https://arxiv.org/abs/2303.15601 |