Try playing against the AI first and once you’re confident of your skills, challenge your friend to a game and use the screen as a smart board that calls the winner.
The board of the 3D version of Tic-Tac-Toe is a familiar shape of a cube, so you should start with this game. In the cube of size 3, i.e., a cube of size 3 × 3 × 3, there is a winning strategy for the first player. Can you find it and beat the AI every time? How about a larger version of the cube: 4 × 4 × 4? Can you always win?
For more dimensions we call the shape of the board a hypercube. Can you think in 4 dimensions and win in a 4 × 4 × 4 × 4 game?
And if your head is spinning from playing in too many dimensions, you can always try the good old 3 × 3 game.