Chess is hard even for a single player

Show simple item record Aravind, N. R. Misra, Neeldhara Mittal, Harshil 2022-04-06T05:31:53Z 2022-04-06T05:31:53Z 2022-03
dc.identifier.citation Aravind, N. R.; Misra, Neeldhara and Mittal, Harshil, "Chess is hard even for a single player", arXiv, Cornell University Library, DOI: arXiv:2203.14864, Mar. 2022. en_US
dc.description.abstract We introduce a generalization of "Solo Chess", a single-player variant of the game that can be played on this http URL. The standard version of the game is played on a regular 8 x 8 chessboard by a single player, with only white pieces, using the following rules: every move must capture a piece, no piece may capture more than 2 times, and if there is a King on the board, it must be the final piece. The goal is to clear the board, i.e, make a sequence of captures after which only one piece is left. We generalize this game to unbounded boards with n pieces, each of which have a given number of captures that they are permitted to make. We show that Generalized Solo Chess is NP-complete, even when it is played by only rooks that have at most two captures remaining. It also turns out to be NP-complete even when every piece is a queen with exactly two captures remaining in the initial configuration. In contrast, we show that solvable instances of Generalized Solo Chess can be completely characterized when the game is: a) played by rooks on a one-dimensional board, and b) played by pawns with two captures left on a 2D board. Inspired by Generalized Solo Chess, we also introduce the Graph Capture Game, which involves clearing a graph of tokens via captures along edges. This game subsumes Generalized Solo Chess played by knights. We show that the Graph Capture Game is NP-complete for undirected graphs and DAGs.
dc.description.statementofresponsibility by N. R. Aravind, Neeldhara Misra and Harshil Mittal
dc.language.iso en_US en_US
dc.publisher Cornell University Library en_US
dc.subject Chess en_US
dc.subject Strategy en_US
dc.subject Board games en_US
dc.subject NP-complete en_US
dc.title Chess is hard even for a single player en_US
dc.type Pre-Print en_US
dc.relation.journal arXiv

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