Solving Bicoloring-Graph Games on Rectangular Boards - Part 1: Partisan Col and Snort

J.W.H.M. Uiterwijk

doi:10.1007/978-3-031-11488-5_9

Solving Bicoloring-Graph Games on Rectangular Boards - Part 1: Partisan Col and Snort

J.W.H.M. Uiterwijk^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

Abstract

In this paper we give an overview of results obtained for solving the combinatorial games of Col and Snort on rectangular boards.For Col on boards with at least one dimension even we give a strategy guaranteeing a win for the second player. For Col on general odd x odd boards we found no applicable strategy, though all experimental data show second-player wins. For Linear Col we were able to prove using Combinatorial Game Theory (CGT) that all chains, including odd-length chains, are second-player wins.A similar strategy as for Col guarantees for Snort on boards with both dimensions even a win for the second player and with at least one dimension odd a first-player win. Snort therefore is completely solved.

Original language	English
Title of host publication	ADVANCES IN COMPUTER GAMES, ACG 2021
Publisher	Springer International Publishing AG
Pages	96-106
Number of pages	11
ISBN (Print)	9783031114878
DOIs	https://doi.org/10.1007/978-3-031-11488-5_9
Publication status	Published - 2022
Event	17th International Conference on Advances in Computer Games (ACG) - Virtual Duration: 23 Nov 2021 → 25 Nov 2021

Publication series

Series	Lecture Notes in Computer Science
Volume	13262
ISSN	0302-9743

Conference

Conference	17th International Conference on Advances in Computer Games (ACG)
Period	23/11/21 → 25/11/21

Access to Document

10.1007/978-3-031-11488-5_9

Cite this

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title = "Solving Bicoloring-Graph Games on Rectangular Boards - Part 1: Partisan Col and Snort",

abstract = "In this paper we give an overview of results obtained for solving the combinatorial games of Col and Snort on rectangular boards.For Col on boards with at least one dimension even we give a strategy guaranteeing a win for the second player. For Col on general odd x odd boards we found no applicable strategy, though all experimental data show second-player wins. For Linear Col we were able to prove using Combinatorial Game Theory (CGT) that all chains, including odd-length chains, are second-player wins.A similar strategy as for Col guarantees for Snort on boards with both dimensions even a win for the second player and with at least one dimension odd a first-player win. Snort therefore is completely solved.",

author = "J.W.H.M. Uiterwijk",

note = "Funding Information: We greatfully acknowledge our cooperation with Ewan Demeur. Some of the strategies found were inspired by and formulated during discussions of his thesis research and lead to a deeper insight into the topics of this paper. Publisher Copyright: {\textcopyright} 2022, Springer Nature Switzerland AG.; 17th International Conference on Advances in Computer Games (ACG) ; Conference date: 23-11-2021 Through 25-11-2021",

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N1 - Funding Information: We greatfully acknowledge our cooperation with Ewan Demeur. Some of the strategies found were inspired by and formulated during discussions of his thesis research and lead to a deeper insight into the topics of this paper. Publisher Copyright: © 2022, Springer Nature Switzerland AG.

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N2 - In this paper we give an overview of results obtained for solving the combinatorial games of Col and Snort on rectangular boards.For Col on boards with at least one dimension even we give a strategy guaranteeing a win for the second player. For Col on general odd x odd boards we found no applicable strategy, though all experimental data show second-player wins. For Linear Col we were able to prove using Combinatorial Game Theory (CGT) that all chains, including odd-length chains, are second-player wins.A similar strategy as for Col guarantees for Snort on boards with both dimensions even a win for the second player and with at least one dimension odd a first-player win. Snort therefore is completely solved.

AB - In this paper we give an overview of results obtained for solving the combinatorial games of Col and Snort on rectangular boards.For Col on boards with at least one dimension even we give a strategy guaranteeing a win for the second player. For Col on general odd x odd boards we found no applicable strategy, though all experimental data show second-player wins. For Linear Col we were able to prove using Combinatorial Game Theory (CGT) that all chains, including odd-length chains, are second-player wins.A similar strategy as for Col guarantees for Snort on boards with both dimensions even a win for the second player and with at least one dimension odd a first-player win. Snort therefore is completely solved.

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T3 - Lecture Notes in Computer Science

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BT - ADVANCES IN COMPUTER GAMES, ACG 2021

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