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Ultimate Tic Tac Toe

mathwithbaddrawings.com

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Re: Ultimate Tic Tac Toe

#41

Post by dreen »

There is another great variant of Tic Tac Toe you can play on a Torus (a donut shape): http://upload.wikimedia.org/wikipedia/commons/1/17/Torus.png

The way to play is to "warp" each side of the board to the side opposite of it. For instance, playing on a 6x6 board with a win condition of length 5:

    .|X|.|.|.|.
    X|.|.|.|.|.
    .|O|.|.|.|.
    .|O|.|.|X|.
    .|.|O|X|.|.
    .|.|X|O|.|.
is a win for X, because the upper and lower ends of the board are synonymous.

I can't find any material about this on the net, I just played it in school on boring lessons (but more commonly we played for 5 in a row on an infinite board, I personally prefer the Torus)

Re: Ultimate Tic Tac Toe

#42

Post by speeder »

yarekt wrote: post #34

http://graffitiwall.co.uk/ultimatetictactoe My quick implementation of this game Edit: For anyone who arrived 10 seconds after i posted that link, The board resembled the ultimate tic tac toe, and then quickly degraded into a paint fight

Interesting that hackers instead of working or reading HN are very interested in fighting over the board (ie: gray color people try to erase it, pink color try to draw a board, and blue color trying to play the game...)

Re: Ultimate Tic Tac Toe

#43

Post by arh68 »

> Whichever square he picks, that’s the board you must play in next.

And what about the dual of this game, where whichever board you pick determines the square he plays next?

Re: Ultimate Tic Tac Toe

#44

Post by triangleman83 »

neruson wrote: post #28
quesera wrote: post #23

I think the Orwin gambit can be extended to win the game every time. - Force opponent to fill center miniboard, as he describes. - Force opponent to fill (e.g.) northeast corner in the same way. Opponent now has taken two miniboards, and you have none, but you are one turn away from taking each of the remaining seven. - Pick SW corner of SW corner. You have taken SW corner miniboard. Opponent is forced to play in sam…

Unless I'm missing something, this wouldn't work because the Orwin gambit gives initiative back to the opponent by sending them back to the center board when it's already full. They would have the chance to employ the strategy back against you before you could pull this off.

The Orwin Gambit actually doesn't go quite so far as to force the win, however if you forget about filling that last center and instead go for a corner, then you can continue to force them back to the same corner over and over. So the Gambit is fallible, but if you back it up one step, it can continue the force to the inevitable win.

Re: Ultimate Tic Tac Toe

#45

Post by frogpelt »

There's a way to prevent the Orlin gambit. Allow the player with the last three in row to take another turn.

This creates a means of alternating who goes first.

I'm not sure whether this gives too much advantage to the other player or not.

Re: Ultimate Tic Tac Toe

#46

Post by chasb »

triangleman83 wrote: post #44
neruson wrote: post #28

Earlier quoted context omitted.

Unless I'm missing something, this wouldn't work because the Orwin gambit gives initiative back to the opponent by sending them back to the center board when it's already full. They would have the chance to employ the strategy back against you before you could pull this off.

The Orwin Gambit actually doesn't go quite so far as to force the win, however if you forget about filling that last center and instead go for a corner, then you can continue to force them back to the same corner over and over. So the Gambit is fallible, but if you back it up one step, it can continue the force to the inevitable win.

No. You lost the initiative (the ability to force their next move) when you sent them to an open board.

Re: Ultimate Tic Tac Toe

#47

Post by speeder »

When my dad was at university he made just out of curiosity a AI to play Tic Tac Toe that started knowing nothing about the game, and tried to learn from playing against the player, until it became impossible to beat it.

Later someone complained with university administrators that my dad was "playing games" in the computer lab, and he got banned from it :/

But I guess this version might be even more interesting to make a AI test or something!

Re: Ultimate Tic Tac Toe

#48

Post by cilo »

yarekt wrote: post #34

http://graffitiwall.co.uk/ultimatetictactoe My quick implementation of this game Edit: For anyone who arrived 10 seconds after i posted that link, The board resembled the ultimate tic tac toe, and then quickly degraded into a paint fight

Who needs comments, all posts should just have a graffiti wall. What could go wrong?

Re: Ultimate Tic Tac Toe

#49

Post by triangleman83 »

chasb wrote: post #46
triangleman83 wrote: post #44

Earlier quoted context omitted.

The Orwin Gambit actually doesn't go quite so far as to force the win, however if you forget about filling that last center and instead go for a corner, then you can continue to force them back to the same corner over and over. So the Gambit is fallible, but if you back it up one step, it can continue the force to the inevitable win.

No. You lost the initiative (the ability to force their next move) when you sent them to an open board.

I don't believe you will ever send them to an open board. O makes all its 8 initial moves in the center, and the 9th move for X will be in the last empty board. I think that it depends on what their last move in the center board is. If they send you to a corner, I believe you can force the win. If they send you to the SW corner, you make the first move in that square to the SW corner. This forces them to reply in the same SW corner. Wherever they go, you make your move in the next square in the SW corner, bringing them back to that corner again.

Re: Ultimate Tic Tac Toe

#50

Post by nmat »

quesera wrote: post #23

I think the Orwin gambit can be extended to win the game every time. - Force opponent to fill center miniboard, as he describes. - Force opponent to fill (e.g.) northeast corner in the same way. Opponent now has taken two miniboards, and you have none, but you are one turn away from taking each of the remaining seven. - Pick SW corner of SW corner. You have taken SW corner miniboard. Opponent is forced to play in sam…

I got confused with the notation so I used paintbrush: http://imgur.com/a/tZPjl

The standard strategy (without optimization) seems to work perfectly. You gain control by forcing the oponent to fill out the miniboards. The last move on the second exhausted miniboard will allow you to choose any miniboard, so it's an easy win.

EDIT: like 3pt14159 pointed out, O might cause you problems if he immediately picks the center in the NW miniboard. This needs further testing...

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