Harary's generalized tictactoe
This article relies largely or entirely on a single source. (December 2016)

Harary's generalized tictactoe is a generalization of the game tictactoe, defining the game as a race to complete a particular polyomino on a square grid of varying size, rather than being limited to "in a row" constructions. It was devised by Frank Harary in March 1977, and is a broader definition than that of an m,n,kgame.
Harary's generalization does not include tictactoe itself, as diagonal constructions are not considered a win.^{[citation needed]}
Like many other twoplayer 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.
 monomino: b = 1, m = 1
 domino: b = 2, m = 2
 straight tromino: b = 4, m = 3
 Ltromino: b = 3, m = 3
 squaretetromino: The first player cannot win
 straighttetromino: b = 7, m = 8
 Ttetromino: b = 5, m = 4
 Ztetromino: b = 3, m = 5
 Ltetromino: b = 4, m = 4
References
 Gardner, Martin. The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems: Number Theory, Algebra, Geometry, Probability, Topology, Game Theory, Infinity, and Other Topics of Recreational Mathematics. 1st ed. New York: W. W. Norton & Company, 2001. 286311.