Misere Connect Four is Solved
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929718161309696 |
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| author | Steele, Robert Larremore, Daniel B. |
| author_facet | Steele, Robert Larremore, Daniel B. |
| contents | Connect Four is a two-player game where each player attempts to be the first to create a sequence of four of their pieces, arranged horizontally, vertically, or diagonally, by dropping pieces into the columns of a grid of width seven and height six, in alternating turns. Misere Connect Four is played by the same rules, but with the opposite objective: do not connect four. This paper announces that Misere Connect Four is solved: perfect play by both sides leads to a second-player win. More generally, this paper also announces that Misere Connect $k$ played on a $w \times h$ board is also solved, but the outcome depends on the game's parameters $k$, $w$, and $h$, and may be a first-player win, a second-player win, or a draw. These results are constructive, meaning that we provide explicit strategies, thus enabling readers to impress their friends and foes alike with provably optimal play in the misere form of a table-top game for children. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05551 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Misere Connect Four is Solved Steele, Robert Larremore, Daniel B. Combinatorics Computer Science and Game Theory Connect Four is a two-player game where each player attempts to be the first to create a sequence of four of their pieces, arranged horizontally, vertically, or diagonally, by dropping pieces into the columns of a grid of width seven and height six, in alternating turns. Misere Connect Four is played by the same rules, but with the opposite objective: do not connect four. This paper announces that Misere Connect Four is solved: perfect play by both sides leads to a second-player win. More generally, this paper also announces that Misere Connect $k$ played on a $w \times h$ board is also solved, but the outcome depends on the game's parameters $k$, $w$, and $h$, and may be a first-player win, a second-player win, or a draw. These results are constructive, meaning that we provide explicit strategies, thus enabling readers to impress their friends and foes alike with provably optimal play in the misere form of a table-top game for children. |
| title | Misere Connect Four is Solved |
| topic | Combinatorics Computer Science and Game Theory |
| url | https://arxiv.org/abs/2410.05551 |