Tic-Tac-Toe

The usual game of tic-tac-toe (also called ticktacktoe) is 3-in-a-row on a $3\times 3$ board. However, a generalized n-in-a-row on an $u\times v$ board can also be considered. For $n=1$ and 2 the first player can always win. If the board is at least $3\times 4$, the first player can win for $n=3$.


However, for tic-tac-toe which uses a $3\times 3$ board, a draw can always be obtained. If the board is at least $4\times 30$, the first player can win for $n=4$. For $n=5$, a draw can always be obtained on a $5\times 5$ board, but the first player can win if the board is at least $15\times 15$. The cases $n=6$ and 7 have not yet been fully analyzed for an $n\times n$ board, although draws can always be forced for $n=8$ and 9. On an $\infty\times\infty$ board, the first player can win for $n=1$, 2, 3, and 4, but a tie can always be forced for $n\geq 8$. For and $4\times 4\times 4$, the first player can always win (Gardner 1979).