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        riddles >> general problem-solving / chatting / whatever >> 3D Tic-Tac-Toe
        
(Message started by: BNC on Aug 8^th, 2006, 6:41am)

Title: 3D Tic-Tac-Toe
Post by BNC on Aug 8^th, 2006, 6:41am

Here (http://www.mivzakon.co.il/fun/flash/games.aspx?g=342)

I think it's worse than the 2D version, as I believe a win may be assured for one player.

Title: Re: 3D Tic-Tac-Toe
Post by Aravis on Aug 8^th, 2006, 8:01am

Yeah, a win is guaranteed forr the person who goes first. As far as I can tell (no real mathematical proof for this) if you are playing on a ND board, you need a grid with N+1 squares on each side ie 3x3 for 2D, 4x4x4 for 3-d (trying to get 4 in a row). However, I think that this will always leads to a draw. Perhaps ith a time limit for play, the larger N will become tough, because you can't keep trackof it all in your head.

Title: Re: 3D Tic-Tac-Toe
Post by SMQ on Aug 8^th, 2006, 9:15am

Hmm, I'm not sure your hypothesis generalizes to higher dimensions. I agree that 3x3x3 is always a win for player 1, but I played a lot of 4x4x4x4 back in school and if there's a winning strategy for either player it's certainly not obvious...

--SMQ

Title: Re: 3D Tic-Tac-Toe
Post by rmsgrey on Aug 8^th, 2006, 9:45am

The hypothesis doesn't even get into 3D - 4*4*4 is a first player win (according to Wikipedia (http://en.wikipedia.org/wiki/Qubic))

It's obvious that such games can never be a second player win - the first player's extra move can never be a liability.