This generalization of Tic-Tac-Toe is called m,n,k-game. (the goal is to get k in a row on a (m,n) board).
Some known bounds: (source wikipedia)
- (5,5,4) is a draw.
- (6,6,5) is a draw.
- (7,7,5) and (8,8,5) are draws.
- (15,15,5) is a win.
- (9,6,6) and (7,7,6) are both draws via pairings.
When the goal is 9 or larger (k>=9) the second player can force a draw:
When k = 9 and the board is infinite, the second
player can draw via a "pairing strategy". A draw on an infinite board
means that the game will go on forever with perfect play. A pairing
strategy involves dividing all the squares of the board into pairs in
such a way that by always playing on the pair of the first player's
square, the second player is ensured that the first player cannot get
k in a line. A pairing strategy on an infinite board can be applied to
any finite board as well - if the strategy calls for making a move
outside the board, then the second player makes an arbitrary move
inside the board.