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Ultimate Tic Tac Toe

786 点作者 sid6376将近 12 年前

35 条评论

quesera将近 12 年前
I think the Orwin gambit can be extended to win the game every time.<p>- Force opponent to fill center miniboard, as he describes.<p>- 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.<p>- 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.<p>- Pick SW corner of S. You have taken S miniboard. Opponent is forced to play in SW corner again, already won by you.<p>- Pick SW corner of SE corner. You have taken SE corner miniboard.<p>- Done. You win.<p>Like regular tictactoe, there is an advantage to going first. Unlike regular tictactoe, the advantage can&#x27;t be compensated for. Otoh, the second player can use the same strategy with a little more carefulness, as long as they start early.<p>So either player can force the other into a protracted certain loss, unless there&#x27;s an agreement or a rule against it. That&#x27;s no fun.<p>EDIT: actually, you can win every time, in far fewer moves, and not using the Orwin gambit at all. It&#x27;s not necessary to force your opponent to <i>fill</i> any of the miniboards, not even the center.<p>I think this will win in ten moves and never lose driver control (excuse the notation): C&#x2F;C, C&#x2F;SW, C&#x2F;S, [opponent takes C], C&#x2F;SE, NE&#x2F;SW, NE&#x2F;S, NE&#x2F;SE, [opponent takes NE], SW&#x2F;SW [you take SW], SW&#x2F;S [you take S], SW&#x2F;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.<p>If this is a game played by mathematicians, either I&#x27;m wrong, or there are additional rules. :)<p>EDIT2: C&#x2F;C (first move above) is unnecessary. Nine moves. Perfect inning.
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michaelfeathers将近 12 年前
My favorite &quot;mathematician game&quot; is Sprouts: <a href="http:&#x2F;&#x2F;nrich.maths.org&#x2F;2413" rel="nofollow">http:&#x2F;&#x2F;nrich.maths.org&#x2F;2413</a><p>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.
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willvarfar将近 12 年前
My daughters play a variant of tic-tac-toe with a physical board and just three stones each.<p>I brute-forced this with a little lunchbreak program and the visualisation output from graphviz was ... 340 MEGAPIXELS!<p>I blogged about it: <a href="http:&#x2F;&#x2F;williamedwardscoder.tumblr.com&#x2F;post&#x2F;35858593837&#x2F;tic-tac-toe" rel="nofollow">http:&#x2F;&#x2F;williamedwardscoder.tumblr.com&#x2F;post&#x2F;35858593837&#x2F;tic-t...</a>
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shardling将近 12 年前
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&#x27;t skew it.)<p>The first two moves have no constraint, so you can just start with an X and O already on the board. And after a few moves there might be only one implied board possible, after which it reduces to the normal game. But I always thought it was an interesting twist.
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dreen将近 12 年前
There is another great variant of Tic Tac Toe you can play on a Torus (a donut shape): <a href="http:&#x2F;&#x2F;upload.wikimedia.org&#x2F;wikipedia&#x2F;commons&#x2F;1&#x2F;17&#x2F;Torus.png" rel="nofollow">http:&#x2F;&#x2F;upload.wikimedia.org&#x2F;wikipedia&#x2F;commons&#x2F;1&#x2F;17&#x2F;Torus.png</a><p>The way to play is to &quot;warp&quot; 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:<p><pre><code> .|X|.|.|.|. X|.|.|.|.|. .|O|.|.|.|. .|O|.|.|X|. .|.|O|X|.|. .|.|X|O|.|. </code></pre> is a win for X, because the upper and lower ends of the board are synonymous.<p>I can&#x27;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)
arh68将近 12 年前
&gt; Whichever square he picks, that’s the board you must play in next.<p>And what about the dual of this game, where whichever board you pick determines the square he plays next?
nawitus将近 12 年前
Does anyone else play the &#x27;infinite board&#x27; tic-tac-toe which requires you to get five in a row? It&#x27;s what I used to play as a student, and it&#x27;s pretty well-known at least where I live. Nobody bothers with the 3x3 version, but the five in a row version is pretty exciting and requires plenty of strategy and thinking ahead.
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Delfino将近 12 年前
Neat variant. I made something similar for the last ludum dare: <a href="http:&#x2F;&#x2F;madelfino.github.io&#x2F;LD26&#x2F;postcompo.html" rel="nofollow">http:&#x2F;&#x2F;madelfino.github.io&#x2F;LD26&#x2F;postcompo.html</a>
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speeder将近 12 年前
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.<p>Later someone complained with university administrators that my dad was &quot;playing games&quot; in the computer lab, and he got banned from it :&#x2F;<p>But I guess this version might be even more interesting to make a AI test or something!
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mrspeaker将近 12 年前
I don&#x27;t understand the clarifying rule #2: &quot;What if my opponent sends me to a board that’s full?&quot; Isn&#x27;t that impossible, as there is a maximum of 9 ways to be sent to each local area?
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joeyrobert将近 12 年前
Another quick implementation of this game: <a href="http:&#x2F;&#x2F;joeyrobert.org&#x2F;projects&#x2F;ultimatetictactoe&#x2F;" rel="nofollow">http:&#x2F;&#x2F;joeyrobert.org&#x2F;projects&#x2F;ultimatetictactoe&#x2F;</a>
alphaoverlord将近 12 年前
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.)
Kurtz79将近 12 年前
<a href="http:&#x2F;&#x2F;xkcd.com&#x2F;832&#x2F;" rel="nofollow">http:&#x2F;&#x2F;xkcd.com&#x2F;832&#x2F;</a><p>Randall Munroe could do a &quot;small&quot; update to this based on these rules... although it would take some time.
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yashg将近 12 年前
This is brilliant! Has anybody created an online version of this?
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deletes将近 12 年前
Important question, can this game be solved, like ordinary tic-tac-toe. Is there a solution that always leads to draw of defeat.
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jjcm将近 12 年前
The one I play with my friends is usually a 4-in-a-row, 4 level board. You can win on any individual level, or by creating a straight line of 4 that intersects plays on each level (so playing in the top right of each level would net you a win, for instance). It forces the players to keep a three dimensional model in their head and opens up the board for more counters&#x2F;strategy.<p>Anyone care for a game?<p><pre><code> level 1 level 2 level 3 level 4 .|.|.|. .|.|.|. .|.|.|. .|.|.|. .|.|.|. .|.|.|. .|.|.|. .|.|.|. .|.|.|. .|.|.|. .|.|.|. .|.|.|. .|.|.|. .|.|.|. .|.|.|. .|.|.|.</code></pre>
ronaldx将近 12 年前
I made a quick HTML demo for playing through the game at <a href="http:&#x2F;&#x2F;xoxo.gl&#x2F;ultimate" rel="nofollow">http:&#x2F;&#x2F;xoxo.gl&#x2F;ultimate</a>
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irunbackwards将近 12 年前
We made this into an Android application about a year ago: <a href="http:&#x2F;&#x2F;superttt.com" rel="nofollow">http:&#x2F;&#x2F;superttt.com</a>
lkozma将近 12 年前
I recall seeing this before, called &quot;crazy&quot; tic tac toe:<p><a href="http:&#x2F;&#x2F;tictactoe-cssi.appspot.com&#x2F;" rel="nofollow">http:&#x2F;&#x2F;tictactoe-cssi.appspot.com&#x2F;</a> via: <a href="http:&#x2F;&#x2F;neil.fraser.name&#x2F;news&#x2F;2011&#x2F;07&#x2F;16&#x2F;" rel="nofollow">http:&#x2F;&#x2F;neil.fraser.name&#x2F;news&#x2F;2011&#x2F;07&#x2F;16&#x2F;</a>
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h4pless将近 12 年前
I haven&#x27;t tested all the cases but this method seems to win every time I&#x27;ve tested it against myself:<p>Start on an edge-center container [N,E,S,W], marking it with it&#x27;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&#x27;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&#x27;s end.<p>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&#x2F;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.
tictactoeten将近 12 年前
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 <a href="https:&#x2F;&#x2F;www.facebook.com&#x2F;tictactoeten" rel="nofollow">https:&#x2F;&#x2F;www.facebook.com&#x2F;tictactoeten</a> 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 :)<p>cheers, @bware218
baritonehands将近 12 年前
I created a version of this game back in 2008, for the 3 major mobile platforms and PC:<p>PC: <a href="http:&#x2F;&#x2F;www.tictactoeten.com&#x2F;play" rel="nofollow">http:&#x2F;&#x2F;www.tictactoeten.com&#x2F;play</a><p>iOS: <a href="https:&#x2F;&#x2F;itunes.apple.com&#x2F;us&#x2F;app&#x2F;tic-tac-toe-ten&#x2F;id317168510?mt=8" rel="nofollow">https:&#x2F;&#x2F;itunes.apple.com&#x2F;us&#x2F;app&#x2F;tic-tac-toe-ten&#x2F;id317168510?...</a><p>Android: <a href="https:&#x2F;&#x2F;play.google.com&#x2F;store&#x2F;apps&#x2F;details?id=com.livelovelearn.tictactoeten&amp;hl=en" rel="nofollow">https:&#x2F;&#x2F;play.google.com&#x2F;store&#x2F;apps&#x2F;details?id=com.livelovele...</a><p>Windows Phone: <a href="http:&#x2F;&#x2F;www.windowsphone.com&#x2F;en-us&#x2F;store&#x2F;app&#x2F;tictactoe10&#x2F;d84eac98-7a6f-e011-81d2-78e7d1fa76f8" rel="nofollow">http:&#x2F;&#x2F;www.windowsphone.com&#x2F;en-us&#x2F;store&#x2F;app&#x2F;tictactoe10&#x2F;d84e...</a>
AUmrysh将近 12 年前
What if you played it where the square selected is the direction you move to go to the next board. If the player selects the center square on a board, that board must be played again. If the player selects the left square, the board to the left must be played next. If a corner square is picked, you play the board to that diagonal direction.<p>If the corner is not attached to a board, you roll the board around as though the ends are connected (or as though it&#x27;s an infinitely repeating tiling of the same game). For example, the bottom right square on the bottom right board makes the next board the top left.<p>The center-right square on the center-right board would result in the next board being the center-left board, and so on.<p>Would there be a gambit in this ruleset?<p>edit: So, it looks like the same gambit applies, instead of selecting the center piece you just pick the one pointing toward the center every time.
yarekt将近 12 年前
<a href="http:&#x2F;&#x2F;graffitiwall.co.uk&#x2F;ultimatetictactoe" rel="nofollow">http:&#x2F;&#x2F;graffitiwall.co.uk&#x2F;ultimatetictactoe</a><p>My quick implementation of this game<p>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
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frogpelt将近 12 年前
There&#x27;s a way to prevent the Orlin gambit. Allow the player with the last three in row to take another turn.<p>This creates a means of alternating who goes first.<p>I&#x27;m not sure whether this gives too much advantage to the other player or not.
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GotAnyMegadeth将近 12 年前
My friends used to play something similar with connect 4. You don&#x27;t expect to meet people who are good at connect 4, but these two guys beat me 100% of the time...
gwern将近 12 年前
Reminds me a bit of <a href="http:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Fire_and_Ice_%28board_game%29" rel="nofollow">http:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Fire_and_Ice_%28board_game%29</a> &#x2F; <a href="http:&#x2F;&#x2F;www.boardgamegeek.com&#x2F;boardgame&#x2F;4643&#x2F;fire-and-ice" rel="nofollow">http:&#x2F;&#x2F;www.boardgamegeek.com&#x2F;boardgame&#x2F;4643&#x2F;fire-and-ice</a> - look at the board.
sudhirj将近 12 年前
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?
gamegoblin将近 12 年前
Another interesting way to play tic-tac-toe that makes it a lot harder:<p>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.<p>This is isomorphic to tic-tac-toe since the magic square for a 3x3 board has rows&#x2F;columns&#x2F;diagonals that sum to 15.
solox3将近 12 年前
It happened a while back, when Bobby Kehres told my colleague and I about the game. <a href="https:&#x2F;&#x2F;github.com&#x2F;1337&#x2F;Tic-Tac-Toe-Extreme" rel="nofollow">https:&#x2F;&#x2F;github.com&#x2F;1337&#x2F;Tic-Tac-Toe-Extreme</a>
rfisher1968将近 12 年前
I made this a while back. It a HTML5 game made with construct2. <a href="http:&#x2F;&#x2F;jenpop.com&#x2F;game.php?gurl=games&#x2F;uttt" rel="nofollow">http:&#x2F;&#x2F;jenpop.com&#x2F;game.php?gurl=games&#x2F;uttt</a>
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crimzonphox将近 12 年前
My favorite Mathematics game is: <a href="http:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Connect_Six" rel="nofollow">http:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Connect_Six</a><p>Mathematically fair
randren将近 12 年前
Kid-tested. The 7-year-old loves it. Thank you for saving me from plain-old Tic Tac Toe games with my kid.
minikomi将近 12 年前
What happens to the game if you switch order when you take a board?
iguana将近 12 年前
Someone needs to write a JavaScript implementation of this!