There Are Exactly 14 Different Games of Tic-Tac-Toe… Sort Of

How Symmetry and Strategy Reduce Tic-Tac-Toe to Just 14 Games

Tic-Tac-Toe. That innocent-looking grid. That eternal duel of X vs. O. A game we’ve all played, probably a few too many times—on napkins, whiteboards, school desks, maybe even with a calculator app. But here’s the wild thing: there are exactly 14 different games of Tic-Tac-Toe.

Wait—what? Just 14?

Let’s unpack that… with a few asterisks and a whole lot of nerdy logic.

How Many Games Are There, Really?

If we go full-brain-math-mode and calculate every possible sequence of moves, it’s 9 factorial:
9 × 8 × 7 × 6 × … × 1 = 362,880 games.

(Technically 362,880, but not all of those are valid—some finish early when someone wins.)

So we pare that number down a little. Let’s remove games that continue after someone has already won. Now we’re looking at something like 255,168 possible games. Already trimmed, but still massive.

Symmetry: The Great Shrinker of Grids

Here’s where we start getting clever. The Tic-Tac-Toe board has rotational and mirror symmetry. If you play X in the top-left corner, it’s basically the same as playing it in any of the other three corners—just spun around. Same with edges.

So if we factor out symmetrical duplicates, we’re down to 26,830 unique games (according to one set of methods).

But let’s keep slicing.

Let's Assume Players Aren't… Y'know, Terrible

If you play Tic-Tac-Toe and miss an obvious winning move, are you even playing? Most real players will take the win if it’s handed to them and block if they must.

So let’s apply some rules:

1. If there’s a winning move, you take it.
2. If there’s a losing move, you block it.
3. If you can create a “fork” (two win paths), you go for it.

Add all that, and we cut down to 2,936 games. Add some more logic—don’t just throw moves away, try to set up wins—and it drops again to 146 games.

Then if we factor out “essentially the same” games—games where the ending moves are inevitable forks—we’re down to 64 meaningful, strategic games of Tic-Tac-Toe.

But we’re not done yet.

The Sacred 14

If we assume the first player (X) always starts in the center—the most popular and seemingly powerful move—there are just 14 possible games assuming both players play competently.

We’re talking legit matchups here. No “I guess I’ll play in the corner and ignore your double threat” nonsense. Just solid, strategic games.

And here’s how those 14 break down:

• X wins: 5
• O wins: 1
• Draws: 8

That’s right—O only wins one of the 14 solid center-starting games. Brutal.

Wait… Wasn't That a Mistake?

Here’s the twist: the center isn’t actually the best first move.

Plot twist! The corner is actually the optimal opening move. It statistically gives you the best shot at not losing. So if both players play optimally—X goes corner, O goes center—there are only 3 truly unique games that all end in a draw.

Talk about anticlimactic perfection.

So… What's the Real Number?

Is it 362,880?
64?
14?
3?

Yes. It depends on what you mean by “different.” Are we counting symmetry? Strategy? Suboptimal blunders? Human behavior?

Tic-Tac-Toe might be a deceptively simple grid, but it’s hiding a mathematically rich little world. And maybe that’s the biggest twist of all—for such a tiny game, it’s got more complexity than we give it credit for… until we figure it out and realize, yeah:

Tic-Tac-Toe is kind of a dumb game.

Stay sharp, stay strategic, and avoid center if you’re playing someone who knows what they’re doing. For more mind-bending takes on games, logic, and the beautiful nonsense of nerd culture, keep rolling with us at Land of Geek Magazine!

#Board Games #Math Games #TicTacToeStrategy #GameTheory #GeekMath