Journal of Information Processing
Online ISSN : 1882-6652
Cannibal Animal Games: a new variant of Tic-Tac-Toe
Jean CardinalSébastien ColletteHiro ItoMatias KormanStefan LangermanHikaru SakaidaniPerouz Taslakian
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2015 Volume 23 Issue 3 Pages 265-271

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Abstract

This paper presents a new partial two-player game, called the cannibal animal game, which is a variant of Tic-Tac-Toe. The game is played on the infinite grid, where in each round a player chooses and occupies free cells. The first player Alice can occupy a cell in each turn and wins if she occupies a set of cells, the union of a subset of which is a translated, reflected and/or rotated copy of a previously agreed upon polyomino P (called an animal). The objective of the second player Bob is to prevent Alice from creating her animal by occupying in each round a translated, reflected and/or rotated copy of P. An animal is a cannibal if Bob has a winning strategy, and a non-cannibal otherwise. This paper presents some new tools, such as the bounding strategy and the punching lemma, to classify animals into cannibals or non-cannibals. We also show that the pairing strategy works for this problem.

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© 2015 by the Information Processing Society of Japan
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