2

I recently discovered playing tic-tac-toe on a torus; I have not been able to achieve a draw. Is there a proof using game theory that says that tic-tac-toe on torus cannot end in draw?

Shaun
  • 47,747
ved jain
  • 88
  • 2
    I don't think this has anything to do with game theory. Instead, it is simple geometrical constraints. – David G. Stork Aug 23 '21 at 18:21
  • 2
    If it's only 3x3 you should be able to just check the entire game tree – Jair Taylor Aug 23 '21 at 18:23
  • 4
    It's very quick to check. Every starting square is the "center" square! There are only two possible responses for the second player, and each one leads quickly to a forced win. One can even make the case-checking quicker by noticing that the torus variant is just looking for lines in $\Bbb F_3^2$, and linear transformations preserve that structure—so there's really only one possible first-move for the second player up to symmetry. – Greg Martin Aug 23 '21 at 18:25
  • Thank you @GregMartin. It is quite simple. – ved jain Aug 23 '21 at 18:27
  • 4
    @GregMartin Should probably convert that to an answer :) – Alan Aug 23 '21 at 18:27
  • 2
    https://math.stackexchange.com/questions/576864/prove-that-a-game-of-tic-tac-toe-played-on-the-torus-can-never-end-in-a-draw-g more mathematical proof. – Shiv Tavker Aug 23 '21 at 18:28
  • It would help if you would visualize how this game works. – Peter Aug 23 '21 at 18:58
  • Moreover, you should clarify whether you mean a legal game ending in a draw, or whether perfect play will end in a draw. This could be the same after all here, but nevertheless... – Peter Aug 23 '21 at 19:02

0 Answers0