My TicTacToe Hypothesis

I've long wondered about the relation of the size of a TicTacToe grid and the number of squares to the outcome of a game.  For example, a 2x2 grid will always be won by the first player:

The odd numbers are the first player's moves, and the even are the second player's moves.

Part one of my hypothesis is that an n to the nth grid will always be won by the first player.  So far, so good!

If we now try a 3x3 (n+1 to the nth+1) grid, we get the following result:

Many people know that in 3x3 TicTacToe game that either the first player will win or a tie will result, especially if the first player always starts from the center.  In the above example, we have a tie because neither player has any moves that will lead to a win. The red numbers are blocking moves.  The only way player two would lose is by making his or her next move in the lower left corner.


Now let's try a three-dimensional game.  If the grid is 3x3x3, then player one can always win with careful play:

Again the red numbers are blocking moves and the green numbers are the winning moves.  The second player has only two choices for the fourth move (8), as shown or where the first player made the winning move (9).  Neither would have prevented the first player's win.

OK, let's try a 4x4x4 game.  After several tries where the first player won, I found one where the second player won, even though the first player kept trying to take the initiative:

The two red X's are the only choices the first player has, either of which still allows the second player to make the winning move.  Can you find which move by the second player put the first player on the defensive?

And thus goes my hope of a grand theory of TicTacToe crashing to the ground, pulled down by the weight of contrary evidence.  My hypothesis is that I went too long to test my TicTacToe hypothesis and kept getting my hopes higher and higher.