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Ultimate Tic Tac Toe
21–30 of 129 posts
Re: Ultimate Tic Tac Toe
#22My favorite "mathematician game" is Sprouts: http://nrich.maths.org/2413 First heard about it in a column in Scientific American by A. K. Dewdney. The rules are simple and it is rather fun. In one of his columns he talked about playing a toroidal version where a line going off one edge of a rectangular page comes back in on the opposite side.
My Dad, a physicist, taught me that game as a kid. I have great memories of him producing a pen at any restaurant we might have been at, and he and I passing any waiting time playing sprouts on napkins or paper scraps. I since play it with my kids.
Did you ever learn about the variant called 'Brussels Sprouts' and the trick to winning?
Re: Ultimate Tic Tac Toe
#23I 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 same SW miniboard, already won by you.
- Pick SW corner of S. You have taken S miniboard. Opponent is forced to play in SW corner again, already won by you.
- Pick SW corner of SE corner. You have taken SE corner miniboard.
- Done. You win.
Like regular tictactoe, there is an advantage to going first. Unlike regular tictactoe, the advantage can't be compensated for. Otoh, the second player can use the same strategy with a little more carefulness, as long as they start early.
So either player can force the other into a protracted certain loss, unless there's an agreement or a rule against it. That's no fun.
EDIT: actually, you can win every time, in far fewer moves, and not using the Orwin gambit at all. It's not necessary to force your opponent to fill any of the miniboards, not even the center.
I think this will win in ten moves and never lose driver control (excuse the notation): C/C, C/SW, C/S, [opponent takes C], C/SE, NE/SW, NE/S, NE/SE, [opponent takes NE], SW/SW [you take SW], SW/S [you take S], SW/SE [you take SE, and win]. A variation can be used by either player early in the game, but whoever starts with control would be foolish to lose it.
If this is a game played by mathematicians, either I'm wrong, or there are additional rules. :)
EDIT2: C/C (first move above) is unnecessary. Nine moves. Perfect inning.
Re: Ultimate Tic Tac Toe
#24Neat variant. I made something similar for the last ludum dare: http://madelfino.github.io/LD26/postcompo.html
Nice! Managed to beat it, but it wasn't easy: http://dl.dropbox.com/u/1127246/Screenshots/5ths.png
Re: Ultimate Tic Tac Toe
#25I 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…
"Fill center, as he describes. Fill (e.g.) northeast corner in the same way."
I don't think you can force that. When you have the nine center squares of each square and he has the 8 non-center squares of the center square, it is your opponent's move.
The 'force-fill the center square' only works because, in your first move, you occupied the center square. That move prevents your opponent from ever picking the center of the center, thus forcing you to move in the center square.
Re: Ultimate Tic Tac Toe
#26Earlier quoted context omitted.
My Dad, a physicist, taught me that game as a kid. I have great memories of him producing a pen at any restaurant we might have been at, and he and I passing any waiting time playing sprouts on napkins or paper scraps. I since play it with my kids.
Did you ever learn about the variant called 'Brussels Sprouts' and the trick to winning?
Please explain :)
Re: Ultimate Tic Tac Toe
#27My favorite "mathematician game" is Sprouts: http://nrich.maths.org/2413 First heard about it in a column in Scientific American by A. K. Dewdney. The rules are simple and it is rather fun. In one of his columns he talked about playing a toroidal version where a line going off one edge of a rectangular page comes back in on the opposite side.
I particularly liked his Core War game too. Its still around, although admittedly quite low-key: http://en.wikipedia.org/wiki/Core_War
Re: Ultimate Tic Tac Toe
#28I 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.
Re: Ultimate Tic Tac Toe
#29My daughters play a variant of tic-tac-toe with a physical board and just three stones each. I brute-forced this with a little lunchbreak program and the visualisation output from graphviz was ... 340 MEGAPIXELS! I blogged about it: http://williamedwardscoder.tumblr.com/post/35858593837/tic-t...
That's how we used to play as kids, there's an algorithm so that the first mover always wins.
Re: Ultimate Tic Tac Toe
#30I 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…
"Fill center, as he describes. Fill (e.g.) northeast corner in the same way." I don't think you can force that. When you have the nine center squares of each square and he has the 8 non-center squares of the center square, it is your opponent's move. The 'force-fill the center square' only works because, in your first move, you occupied the center square. That move prevents your opponent from ever picking the center…
Instead of filling the center square on the last board, you can fill the corresponding square and then start forcing your opponent to win that board.