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Cannibal Animal Games: A new variant of Tic-Tac-Toe

par Cardinal, Jean ;Collette, Sébastien ;Ito, Hiro;Korman, Matias ;Langerman, Stefan ;Sakaidani, Hikaru;Taslakian, Perouz
Référence Journal of Information Processing, 23, 3, page (265-271)
Publication Publié, 2015

Article révisé par les pairs

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Résumé :

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.