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Ultimate Tic Tac Toe

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Re: Ultimate Tic Tac Toe

#71

Post by alphaoverlord »

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…

Perhaps the game makes more sense if you can choose any board as soon as the board is won - not when it is filled. Then, you can only force 3 moves before you have to give up control.

Re: Ultimate Tic Tac Toe

#72

Post by alphaoverlord »

Perhaps the game is less deterministic if you can choose any board as soon as the board is won - not when it is filled. Then, you can only force 3 moves before you have to give up control. Then approaches like the Orwin gambit would not work (it is too costly to lose a board if it only lets you choose three spots.)

Re: Ultimate Tic Tac Toe

#73

Post by gamegoblin »

Another interesting way to play tic-tac-toe that makes it a lot harder:

There is a bag of numbers 1-9. Players take turns moving numbers from the central bag to their own private bags, removing that number from play. Whenever a player has a subset of exactly 3 numbers that sums to 15, they win.

This is isomorphic to tic-tac-toe since the magic square for a 3x3 board has rows/columns/diagonals that sum to 15.

Re: Ultimate Tic Tac Toe

#74

Post by sudhirj »

Can anyone else hear the quiet roar of a thousand not-so-silent fans as they struggle to dissipate heat caused by furious Xcode and RubyMotion compilations?

Re: Ultimate Tic Tac Toe

#75

Post by shawabawa3 »

tripzilch wrote: post #59
lucb1e wrote: post #6

Earlier quoted context omitted.

A "small" update? I think this is more like the difference between checkers and chess. But yes, relevant xkcd

> 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?

> checkers is in fact the more complex game, to write an AI for?

I'm almost certain that's false. Checkers is weakly solved (There are AI's that will never lose, only win or draw)

I assume you meant Go, not checkers. And that's mainly harder for AI because the board is 5 times bigger.

Re: Ultimate Tic Tac Toe

#76

Post by lotharbot »

shardling wrote: post #61

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).

Re: Ultimate Tic Tac Toe

#77

Post by saalweachter »

tripzilch wrote: post #59
lucb1e wrote: post #6

Earlier quoted context omitted.

A "small" update? I think this is more like the difference between checkers and chess. But yes, relevant xkcd

> 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?

Checkers has been solved. Both players can draw with perfect play.

The usual caveat with checkers is that you are probably not good at it. Even if it is simpler and smaller than chess, being a good chess player gives you no advantage and the game is still sufficiently complex that you can't quickly brute force it without years of practice. A chess master will get their ass handed to them by a skilled yokel.

Re: Ultimate Tic Tac Toe

#78

Post by rdsubhas »

quesera wrote: post #57
antoko wrote: post #38

Earlier quoted context omitted.

either I'm wrong TLDR: you're wrong. C/C, C/SW, C/S, [opponent takes C], C/SE, NE/SW, NE/S ... after C/SE, your opponent has control and can go anywhere that is available in the center board they've already won, so you can't assume you're next play will be NE. More importantly after you've sent them to the SW board with NE/SW they can go anywhere except the middle and so they then have the initiative. Hmm, It looks l…

Ouch, yes. My EDIT passages are totally wrong. Sorry, I oversimplified the rules there. The initial idea (extending Orwin Gambit) should still be leverageable into a much better position. This might fall short of a certain win though, if the opponent plays a proper response strategy -- which we should probably assume if the contestants are peer mathematicians. :)

How about an addition to the rules:

| The very first move in the game must not be in the center board (or more specifically CC)

So player has to pick some other board. If they choose C in that board, then they're fucked, the next player will end up playing the Orwin Gambit. So both players will avoid C like the plague until they're sure the Orwin Gambit is no more applicable.

Even if I start with some board (say NE), and in the first move itself I play a C and thereby giving the other player an option of taking the Orwin Gambit, it still can't be effectively used. Because I can later play NE again in the C table, thereby outplaying the gambit (since the C inside NE is already used).

Edit: Formatting

Re: Ultimate Tic Tac Toe

#79

Post by chinpokomon »

willvarfar wrote: post #27
michaelfeathers wrote: post #10

My 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

I've committed countless hours to Core Wars and variations of the game. It is fantastic.

Re: Ultimate Tic Tac Toe

#80

Post by h4pless »

I haven't tested all the cases but this method seems to win every time I've tested it against myself:

Start on an edge-center container [N,E,S,W], marking it with it's corresponding sub-board space. Employ the Orwin gambit to fill the initial edge container. When your opponent selects the last space in the first container, wherever you are sent: pick it's corresponding sub-board space and then employ the Orwin gambit again and then repeat the routine until the game is finished. Your opponent gets to pick your next moves but because they eventually must send you to a filled square on the second and third rounds, you have the ability to control the game's end.

Starting in the center gives you a tactical disadvantage because it only leaves you 4 paths to victory compared to your opponents 8 with him/her in a position affecting 4 lines, whereas by starting on a side piece, you have 7 paths to victory and your opponents position only benefits him on 2 lines.

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