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Cannibal Animal Games: a new variant of Tic-Tac-Toe by Cardinal, Jean; Collette, Sébastien; Ito, Hiro; Korman, Matias; Langerman, Stefan; Sakaidani, Hikaru; Taslakian, Perouz is a scholarly article available to read on EtoBox.

What is Cannibal Animal Games: a new variant of Tic-Tac-Toe about?

This paper presents a new partial two-player game, called the \emph{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 \emph{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 \emph{cannibal} if Bob has a winning strategy, and a \emph{non-cannibal} otherwise. This paper presents some new tools, such as the \emph{bounding strategy} and the \emph{punching lemma}, to classify animals into cannibals or non-cannibals. We also show that the \emph{pairing strategy} works for this problem.

Author

Cardinal, Jean; Collette, Sébastien; Ito, Hiro; Korman, Matias; Langerman, Stefan; Sakaidani, Hikaru; Taslakian, Perouz

Published

2013

Language

EN