Harary's generalized tic-tac-toe

Harary's generalized tic-tac-toe is an even broader generalization of tic-tac-toe than m,n,k-games are. Instead of the goal being limited to "in a row" constructions, the goal can be any polyomino (Note that when this generalization is made diagonal constructions are not considered a win). It was devised by Frank Harary in March 1977.

Like many other two-player games, strategy stealing means that the second player can never win. All that is left to study is to determine if the first player can win, on what board sizes he may do so, and in how many moves it will take.

Results

Square boards

Let b be the smallest size square board on which the first player can win, and let m be the smallest number of moves in which the first player can force a win, assuming perfect play by both sides.

References

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