Ultimate Tic-Tac-Toe

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.

  1. Each turn, you mark one of the small squares.
  2. When you get three in a row on a small board, you’ve won that board.
  3. 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:

  1. 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!)
  2. 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)

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

469 thoughts on “Ultimate Tic-Tac-Toe

    1. Hello Joe, I had a brief look at your link. I am a third year student and I do have tictactor ultimate as one of the projects on my list. Would you mind helping me out if I am take this project? my email is azzum_waqar@hotmail.co.uk, if you are willing to help or lend me a hand. If you want to charge me, i do not mind either.

  1. Hi are using WordPress for your site platform? I’m new to the blog
    world but I’m trying to get started and set up my own.
    Do you require any coding expertise to make your own blog?
    Any help would be greatly appreciated!

  2. Here’s a tic-tac-toe variant I used to play with my brother: stack four grids “on top” of each other, each with four rather than three squares. This is now a three-D cube rather than a flat surface. You win by getting four in a row in any dimension.

  3. This game is super fun! Thanks for sharing it with the community.

    We created our own version as well. We changed it a bit since we thought that the pace at the beginning was too slow for a multiplayer game. I hope you like it!
    You can play either turn-based or online. It has achievements to complete. Some are really difficult (impossible? We’ll see…). We are also preparing the second version, which will include different kind of Tournaments that will add more stars to your ranking!

    Compatible with iOS 5/6/7.

    Try it for free!

  4. Hello, thanks for sharing this, it definitely improves the classic tic-tac-toe game.
    In fact, I liked it so much I wanted to make my own PC version and, alas, after much time invested in it (don’t really have that much free time so I squeezed some code whenever I could 🙂 ), I managed to create something.

    You can find it here:

  5. Hey there! I’m at work browsing your blog from my new apple iphone!

    Just wanted to say I love reading through your blog and look
    forward to all your posts! Keep up the great work!

  6. Ben, we would like to link to your explanation of the rules for Ultimate Tic Tac Toe on our Kickstarter page, would that be ok? Here is a preview of where we would put the link.

  7. WOW. This is honestly the most awesome game that I have ever heard of. Please keep posting cool games like this one:)

  8. Pingback: Quora

Leave a Reply