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.

About these ads

346 thoughts on “Ultimate Tic-Tac-Toe

  1. Pingback: Ultimate Tic-Tac-Toe « Dads for Life Toolbox

  2. Pingback: Ultimate Tic-Tac-Toe | Math with Bad Drawings | How Alan Sees It

  3. Pingback: Your Daily Digest #2 | CraftingReality.

  4. Pingback: Links | Positive Concepts: The Interweb Version

  5. Pingback: Ultimate Tic Tac Toe Series | Memoirs of a Coder

  6. Pingback: Securing tie-tac-toe | Paul's Perambulations

  7. Pingback: Reblog: Ultimate Tic-Tac-Toe | Musings of an exhausted graduate student

  8. 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!

  9. 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.

  10. Pingback: Ultimate Tic-Tac-Toe | Mr. Westers' Website

  11. Pingback: Play an image's melody and 6 other Monthly Music Hackathon projects we loved » Technically Brooklyn

  12. Pingback: Time to Reflect and Regather | A Portrait of the Math Teacher as an Aging Man

  13. Pingback: Paul de Leeuw alweer weg in België | FL CMSFL CMS

  14. Pingback: Tic-tac-toe made much more interesting with a simple tweak | BaciNews

  15. Pingback: Ultimate Tic Tac Toe (July 2013) | rahulmadanahalli

  16. Pingback: Ultimate Tic Tac Toe | rahulmadanahalli

  17. Pingback: Mathematicians’ Tic-Tac-Toe! | Dickson's Up Phone

  18. Pingback: The Latest Game From Bored Children | Aditya Rohan

  19. 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!

    https://itunes.apple.com/WebObjects/MZStore.woa/wa/viewSoftware?id=768959898&mt=8

  20. Pingback: Fun Recreational Math Games | Drawalot.com

  21. Pingback: Mini Projects in C Programming by Computer Engineering students of IOE, Pulchowk Campus 2070 Batch | Review, Reports and Source Code

  22. 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:

  23. Pingback: Bot Sees the Future in Ultimate Tic Tac Toe (In Process) | rahulmadanahalli

  24. Pingback: Bot Sees the Future in Ultimate Tic Tac Toe (In Progress) | rahulmadanahalli

  25. Pingback: Sunjay Varma | Introducing The All New Genius Tic-Tac-Toe

  26. Pingback: “Gamer’s Tic Tac Toe” #GTTT

  27. 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!

  28. Pingback: Tic-Tac-Toe squared | Hihid News

  29. Pingback: Sunjay Varma | How long did it take me to make Genius Tic-Tac-Toe?

  30. 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.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s