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Ultimate Tic Tac Toe

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121–129 of 129 posts

Re: Ultimate Tic Tac Toe

#121

Earlier quoted context omitted.

After that it's pretty easy to force a win. Whatever square they send you to, you just send them back to one of those two squares.

I challenge you to a game where you are X then. Because I can't figure out how you force a win like that.

I take it back. The key is to line up three master blocks with x's free move. Then the game is perfectly won by x.

Re: Ultimate Tic Tac Toe

#122
post #88

Earlier quoted context omitted.

Here's an implementation that pretty much does exactly that. If someone can beat this bot, lemme know: https://www.khanacademy.org/cs/in-tic-tac-toe-ception-perfec... And here's James Irwin's original implementation, auto-set to a Monte-Carlo AI and with a rules variation that (to my knowledge) prevents Perfect Bot from winning. Play with the config variables at the top for some other AIs and 2-player games and whatn…

There are definitely bugs- I played the 2nd link and on several moves the AI moved in the wrong region. I played in the SW block in the E square and then the AI played in the same SW block as me, then did the same thing on the next turn playing in the wrong region.

Could it be because of the rules variation? See the comments on rule 5b to negate Perfect Bot's strategy: if forced to an already-won region, the player may choose any region.

Re: Ultimate Tic Tac Toe

#123

A weird version of tic-tac-toe my friends and I came up with years ago: you play without a board. Any move is valid so long as you could superimpose a standard tic-tac-toe grid over the results. (You assume the marks are at the center of their respective squares; you allow the board to be at any scale or angle, but you can't skew it.) The first two moves have no constraint, so you can just start with an X and O alrea…

Somebody posted another tic tac toe variant on HN some time ago, where the squares were numbered 1-9 and the goal was to get any three squares that summed to 15. It turns out this is equivalent to playing tic tac toe with sides that wrap around (like a torus).

No, that's 100% equivalent to tic tac toe (http://en.wikipedia.org/wiki/Tic-tac-toe#Variations)

(To see why no torus version exists: on a '3x3' torus, all squares are identical, so you have must four ways to get three in a row from each starting number. Also, the row/column/diagonal sum must be 15. However, starting with 9, there are only two ways to get 15 with: 1 and 5 and 2 and 4)

The variant with nine words, where selecting three words that share a letter wins the game, IMO is even better.

Re: Ultimate Tic Tac Toe

#124

Earlier quoted context omitted.

Somebody posted another tic tac toe variant on HN some time ago, where the squares were numbered 1-9 and the goal was to get any three squares that summed to 15. It turns out this is equivalent to playing tic tac toe with sides that wrap around (like a torus).

No, that's 100% equivalent to tic tac toe ( http://en.wikipedia.org/wiki/Tic-tac-toe#Variations ) (To see why no torus version exists: on a '3x3' torus, all squares are identical, so you have must four ways to get three in a row from each starting number. Also, the row/column/diagonal sum must be 15. However, starting with 9, there are only two ways to get 15 with: 1 and 5 and 2 and 4) The variant with nine words, wh…

I may have misremembered the details of the game, or conflated it with another game.

What I remember clearly is that the game was equivalent of tic tac toe on a torus -- one could win with a "diagonal" of the form

.|x|.

x|.|.

.|.|x

as well as any of the traditional tic tac toe win conditions.

Re: Ultimate Tic Tac Toe

#125

Earlier quoted context omitted.

No, that's 100% equivalent to tic tac toe ( http://en.wikipedia.org/wiki/Tic-tac-toe#Variations ) (To see why no torus version exists: on a '3x3' torus, all squares are identical, so you have must four ways to get three in a row from each starting number. Also, the row/column/diagonal sum must be 15. However, starting with 9, there are only two ways to get 15 with: 1 and 5 and 2 and 4) The variant with nine words, wh…

I may have misremembered the details of the game, or conflated it with another game. What I remember clearly is that the game was equivalent of tic tac toe on a torus -- one could win with a "diagonal" of the form .|x|. x|.|. .|.|x as well as any of the traditional tic tac toe win conditions.

Tic tac toe on toruses is fairly popular as an educational toy, and there also is serious research on it, for example http://www.ux1.eiu.edu/~kwolcott/TTT.pdf. You might have mixed the 'on a torus' part with the 'using a magic square' part. No problem, but the two do not mix that way (maybe, on larger boards? That 4x4 Dürer square (http://mathworld.wolfram.com/DuerersMagicSquare.html) has zillions of 'add up to 34' sets of cells. There may be even better ones of larger size)

Re: Ultimate Tic Tac Toe

#126
post #82

Earlier quoted context omitted.

> I think this is more like the difference between checkers and chess I'm not sure what you mean by this? BTW are you aware that despite it has only one type of stone and simpler rules, checkers is in fact the more complex game, to write an AI for?

I guess you refer to International checkers (being from the Netherlands). Still a challenge for computers, given that the brute-force solution for American checkers doesn't work well for this larger board. Much harder to program an AI for than chess, certainly. The computer never managed to beat the world champion in a match last year.

Cool, I didn't know there were multiple versions of checkers. I'll have to check (hah) out that solution for the American version though, always interesting (as well as what the differences in rules are). Off to Wikipedia, I guess ;-)

Re: Ultimate Tic Tac Toe

#127
I created a version of this game back in 2008, for the 3 major mobile platforms and PC:

PC: http://www.tictactoeten.com/play

iOS: https://itunes.apple.com/us/app/tic-tac-toe-ten/id317168510?...

Android: https://play.google.com/store/apps/details?id=com.livelovele...

Windows Phone: http://www.windowsphone.com/en-us/store/app/tictactoe10/d84e...

Re: Ultimate Tic Tac Toe

#128
My team and I have implemented what you call Ultimate Tic Tac Toe as what we call Tic Tac Toe Ten. We put it out for iOS, Android, Windows Phone and have made board game sets to go into school districts with starting in 2008. If any of you in this community are interested in helping us to build out the backend analytics infrastructure to help us make the academic breakdown of this game useful for teachers and students please visit our community at https://www.facebook.com/tictactoeten and drop me a message or DM us on Twitter (@tictactoeten) ... we are also always looking for volunteers at our school tournaments where we pit kids against each other March Madness style with brackets and give out prizes to the winners ... we are here in the Bay Area, hope to meet some of you guys soon :)

cheers, @bware218

Re: Ultimate Tic Tac Toe

#129

Earlier quoted context omitted.

I challenge you to a game where you are X then. Because I can't figure out how you force a win like that.

I take it back. The key is to line up three master blocks with x's free move. Then the game is perfectly won by x.

I'm not entirely sure how to do it anymore, but playing with the perfect AI posted somewhere else in this threat convinces me it's impossible to win if you don't start first.
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