Geodesic
A pairing strategy for tic-tac-toe on the integer lattice with numerous directions
The electronic journal of combinatorics, Tome 15 (2008)
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We consider a tic-tac-toe game played on the $d$-dimensional integer lattice. The game that we investigate is a Maker–Breaker version of tic-tac-toe. In a Maker–Breaker game, the first player, Maker, only tries to occupy a winning line and the second player, Breaker, only tries to stop Maker from occupying a winning line. We consider the bounded number of directions game, in which we designate a finite set of direction-vectors ${\cal S} \subset{\Bbb Z}^d$ which determine the set of winning lines. We show by a simple pairing strategy that Breaker can win this game if the length of each winning line is at least $3|{\cal S}|.$ It should be noted that Breaker's winning strategy can be used as a drawing strategy for Player 2 in the strong version of this game.
DOI : 10.37236/917
Classification : 91A46 
@article{10_37236_917,
     author = {Klay Kruczek and Eric Sundberg},
     title = {A pairing strategy for tic-tac-toe on the integer lattice with numerous directions},
     journal = {The electronic journal of combinatorics},
     year = {2008},
     volume = {15},
     doi = {10.37236/917},
     zbl = {1160.91008},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/917/}
}
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Klay Kruczek; Eric Sundberg. A pairing strategy for tic-tac-toe on the integer lattice with numerous directions. The electronic journal of combinatorics, Tome 15 (2008). doi: 10.37236/917

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