Relationship between misère NIM and two-player GOISHI HIROI
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912145294229504 |
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| author | Abuku, Tomoaki Fukui, Masanori Katayama, Shin-ichi Suetsugu, Koki |
| author_facet | Abuku, Tomoaki Fukui, Masanori Katayama, Shin-ichi Suetsugu, Koki |
| contents | In combinatorial game theory, there are two famous winning conventions, normal play and misère play. Under normal play convention, the winner is the player who moves last and under misère play convention, the loser is the player who moves last. The difference makes these conventions completely different, and usually, games under misère play convention is much difficult to analyze than games under normal play convention. In this study, we show an interesting relationship between rulesets under different winning conventions; we can determine the winner of two-player GOISHI HIROI under normal play convention by using NIM under misère play convention. We also analyze two-player GOISHI HIROI under misère play convention. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03996 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relationship between misère NIM and two-player GOISHI HIROI Abuku, Tomoaki Fukui, Masanori Katayama, Shin-ichi Suetsugu, Koki Computer Science and Game Theory Combinatorics In combinatorial game theory, there are two famous winning conventions, normal play and misère play. Under normal play convention, the winner is the player who moves last and under misère play convention, the loser is the player who moves last. The difference makes these conventions completely different, and usually, games under misère play convention is much difficult to analyze than games under normal play convention. In this study, we show an interesting relationship between rulesets under different winning conventions; we can determine the winner of two-player GOISHI HIROI under normal play convention by using NIM under misère play convention. We also analyze two-player GOISHI HIROI under misère play convention. |
| title | Relationship between misère NIM and two-player GOISHI HIROI |
| topic | Computer Science and Game Theory Combinatorics |
| url | https://arxiv.org/abs/2412.03996 |