*Updated 7/16/2013 – See Original Here*

Once at a picnic, I saw mathematicians crowding around the last game I would have expected: Tic-tac-toe.

As you may have discovered yourself, tic-tac-toe is terminally dull. There’s no room for creativity or insight. Good players always tie. Games inevitably go something like this:

But the mathematicians at the picnic played a more sophisticated version. In each square of their tic-tac-toe board, they’d drawn a smaller board:

As I watched, the basic rules emerged quickly.

- Each turn, you mark one of the small squares.
- When you get three in a row on a small board, you’ve won that board.
- To win the game, you need to win three small boards in a row.

But it took a while for the most important rule in the game to dawn on me:

**You don’t get to pick which of the nine boards to play on. **That’s determined by your opponent’s previous move.** Whichever square he picks, that’s the board you must play in next. **(And whichever square

*you*pick will determine which board

*he*plays on next.) For example, if I go here…

Then your next move must be here…

This lends the game a strategic element. You can’t just focus on the little board. You’ve got to consider where your move will send your opponent, and where his next move will send you, and so on.

The resulting scenarios look bizarre. Players seem to move randomly, missing easy two- and three-in-a-rows. But there’s a method to the madness – they’re thinking ahead to future moves, wary of setting up their opponent on prime real estate. It is, in short, vastly more interesting than regular tic-tac-toe.

A few clarifying rules are necessary:

*What if my opponent sends me to a board that’s already been won?*In that case, congratulations – you get to go anywhere you like, on any of the other boards. (This means you should avoid sending your opponent to an already-won board!)*What if one of the small boards results in a tie?*I recommend that the board counts for**neither**X nor O. But, if you feel like a crazy variant, you could agree before the game to count a tied board for**both**X and O.

When I see my students playing tic-tac-toe, I resist the urge to roll my eyes, and I teach them this game instead. You could argue that it builds mathematical skills (deductive reasoning, conditional thinking, the geometric concept of similarity), but who cares? It’s a good game in any case.

Anyway, that’s Ultimate Tic-Tac-Toe. Go play! Let me know how it goes!

*11/18/13: See the follow-up post!*

*A Partial List of Online Versions and Apps
(Check Comments Below for Others)*

**Tic Tac Toe Ten****Ultimate Tic-Tac-Toe**

**XO9****Nikhil Baliga****Niek Haarman****Kongregate****Inception Tic Tac Toe****Khan Academy**(open-source online version)**Live-coding**of an online version*French, with English subtitles*)**C code**for a strong artificial intelligence

*While you’re here, check out Math Experts Split the Check and the epic rhyming proof-poem A Fight with Euclid.*

This is the greatest.

Someone showed me a cool variation. instead of eliminating boards that have been won from future play, you must still go on that board if forced. However, your move doesn’t affect the outcome of that board. For example, if X wins one of the small boards, and then forces O to move on that board, instead of O getting to choose where to go, O still must go on that board. But no matter which move O makes, X remains the winner of that board.

Be warned: this variation makes the game take much longer, and it makes winning the first board critical.

See the original version:

https://mathwithbaddrawings.com/ultimate-tic-tac-toe-original-post/

This is also a fun variant, but is sadly solved, as explained here:

https://www.joachim-breitner.de/blog/604-Ultimate_Tic_Tac_Toe_is_always_won_by_X

The rule that if you get sent to a board which is already won, you get to choose a board was introduced to break this strategy.

Bossed it!! Great game!

Reblogged this on Shaman's Antics and commented:

O.M.G.

YES.

Reblogged this on nuknoe and commented:

Check out this different variant on #TicTacToe!!!

NÜK

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That looks like a lot of fun! Normally tic tac toe does get boring. Will definitely play this one with my friends. Thank you for posting it:)

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coding it!

I made a super-fast and super-strong computer opponent for this game here: http://www.theofekfoundation.org/games/UltimateTicTacToe/

This also includes 3 new game modes:

Anti Tic Tac Toe: The goal of the game is to make your opponent win😛

Tie Tic Tac Toe: X still wants to win, but O wants to tie😀

And of course, Anti Tie Tic Tac Toe, where O wants to win and X wants to tie😄

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