3-D, 4-D, and higher-dimensional Tic-Tac-Toe

[Asymptote]

I used to play 3D and 4D tic-tac-toe (also called noughts and crosses), and it was actually fairly fun. It re-kindled my interest in an otherwise very stale game for a while. Has anybody else ever played it?

[pat]

Yes... I've even played arbitrary-dimension tic-tac-toe. Add dimensions as needed....

But, you need to go with more than three-in-a-row to make it worth it.

[Asymptote]

Yeah...I tried playing a couple of 3-D games by myself, and I noticed that there were some strategies where one player (usually the one who went first) could set it up so that a win was inevitable, and impossible to block, since they would have three-in-a-row on two different fronts.

[moonlord]

I've found the game balanced on 5^3 and 7^4 boards. Don't know if this holds for higher dimensions.

[Asymptote]

I've found the game balanced on 5^3 and 7^4 boards. Don't know if this holds for higher dimensions.

Do you still employ the "three-in-a-row" rule?

[PWrong]

I've played it a few times. It's balanced on 3^n boards if you have n players. I don't know about larger boards.

Yeah...I tried playing a couple of 3-D games by myself, and I noticed that there were some strategies where one player (usually the one who went first) could set it up so that a win was inevitable, and impossible to block, since they would have three-in-a-row on two different fronts.

That's possible in 2D. It's a solved game, so the 1st player can always win or draw.

[moonlord]

You need to complete a row, column, [something] or a diagonal to win. Not only three.

[pat]

That's possible in 2D. It's a solved game, so the 1st player can always win or draw.

In the 3² case, player one can guarantee at least a draw. In the 3³ case (with only two players), player one can guarantee a win.

[Asymptote]

That's possible in 2D. It's a solved game, so the 1st player can always win or draw.

In the 3² case, player one can guarantee at least a draw. In the 3³ case (with only two players), player one can guarantee a win.

That's what I'd expected. It's very easy to set up an almost-complete row and column at the same time, so that your opponent can block one, but on the next turn, you complete the other.

[d.m.falk]

Now if only someone were to make such a tic-tac-toe game that actually looks like a 3 or 4-dimensional playing field.....

d.m.f.