License: 
Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FUN.2022.5
URN: urn:nbn:de:0030-drops-159753
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/15975/
Aravind, N.R. ;
Misra, Neeldhara ;
Mittal, Harshil
Chess Is Hard Even for a Single Player
Abstract
We introduce a generalization of "Solo Chess", a single-player variant of the game that can be played on chess.com. The standard version of the game is played on a regular 8 × 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.
BibTeX - Entry
@InProceedings{aravind_et_al:LIPIcs.FUN.2022.5,
author = {Aravind, N.R. and Misra, Neeldhara and Mittal, Harshil},
title = {{Chess Is Hard Even for a Single Player}},
booktitle = {11th International Conference on Fun with Algorithms (FUN 2022)},
pages = {5:1--5:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-232-7},
ISSN = {1868-8969},
year = {2022},
volume = {226},
editor = {Fraigniaud, Pierre and Uno, Yushi},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/15975},
URN = {urn:nbn:de:0030-drops-159753},
doi = {10.4230/LIPIcs.FUN.2022.5},
annote = {Keywords: chess, strategy, board games, NP-complete}
}
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Keywords: |
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chess, strategy, board games, NP-complete |
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Collection: |
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11th International Conference on Fun with Algorithms (FUN 2022) |
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Issue Date: |
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2022 |
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Date of publication: |
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23.05.2022 |
