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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.20932 |
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| _version_ | 1866909925484003328 |
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| author | Phan, Vu Ugarcovici, Ilie |
| author_facet | Phan, Vu Ugarcovici, Ilie |
| contents | We investigate the expected number of calls required to achieve Bingo in a generalized (n,m)-Bingo game, where each n x n card is filled by sampling n numbers from m possible values per column. Using the inclusion-exclusion principle, we derive exact formulas for the probability distribution and the expected game length. Our main theoretical result proves that the expected number of calls is a linear function of m. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20932 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Expected Duration of a Generalized Bingo Game Phan, Vu Ugarcovici, Ilie Combinatorics Probability 05 We investigate the expected number of calls required to achieve Bingo in a generalized (n,m)-Bingo game, where each n x n card is filled by sampling n numbers from m possible values per column. Using the inclusion-exclusion principle, we derive exact formulas for the probability distribution and the expected game length. Our main theoretical result proves that the expected number of calls is a linear function of m. |
| title | On the Expected Duration of a Generalized Bingo Game |
| topic | Combinatorics Probability 05 |
| url | https://arxiv.org/abs/2511.20932 |