[1][2][4][5] If one player creates a line of length n of their symbol (X or O) they win the game.
[4] The (n > 0, 0) or (1, 1) games are trivially won by the first player as there is only one space (n0 = 1 and 11 = 1).
A game with d = 1 and n > 1 cannot be won if both players are playing well as an opponent's piece will block the one-dimensional line.
[2][6] For any width n, at some dimension d (thanks to the Hales-Jewett theorem), there will always be a winning strategy for player X.
There will never be a winning strategy for player O because of the Strategy-stealing argument since an nd game is symmetric.