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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.19178 |
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| _version_ | 1866909364687732736 |
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| author | Ju, Haoru Leifer, Daniel Miller, Steven J. Padmanabhan, Sooraj A. Sun, Chenyang Tichi, Luke Tocher, Benjamin Wallace, Kiley |
| author_facet | Ju, Haoru Leifer, Daniel Miller, Steven J. Padmanabhan, Sooraj A. Sun, Chenyang Tichi, Luke Tocher, Benjamin Wallace, Kiley |
| contents | We study variants of a stochastic game inspired by backgammon where players may propose to double the stake, with the game state dictated by a one-dimensional random walk. Our variants allow for different numbers of proposals and different multipliers to the stake. We determine the optimal game state for proposing and accepting, giving analytic solutions in many variants. We also introduce a 3-player generalization of the game and prove basic results about its behavior, in addition to providing a simulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_19178 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Doubling Thresholds in Backgammon-like Stochastic Games Ju, Haoru Leifer, Daniel Miller, Steven J. Padmanabhan, Sooraj A. Sun, Chenyang Tichi, Luke Tocher, Benjamin Wallace, Kiley Optimization and Control Probability We study variants of a stochastic game inspired by backgammon where players may propose to double the stake, with the game state dictated by a one-dimensional random walk. Our variants allow for different numbers of proposals and different multipliers to the stake. We determine the optimal game state for proposing and accepting, giving analytic solutions in many variants. We also introduce a 3-player generalization of the game and prove basic results about its behavior, in addition to providing a simulation. |
| title | Optimal Doubling Thresholds in Backgammon-like Stochastic Games |
| topic | Optimization and Control Probability |
| url | https://arxiv.org/abs/2410.19178 |