How many tic tac toe games are possible?
There are 255,168 possible complete games of tic tac toe if you count every order of moves. Distinct board positions reachable in legal play number 5,478, and 26,830 counting every game path separately. Games end in only 138 terminal boards — 91 won by X, 44 by O, and 3 drawn. Treating rotations and reflections as the same position collapses the 5,478 to 765, which is why the game is small enough to solve completely.
The numbers people quote for tic tac toe disagree wildly — 255,168, 26,830, 5,478, 765, 362,880 — and they are mostly all correct. They count different things.
Here is each one, and what it is counting.
362,880 — the wrong answer, and why it is tempting
Nine squares, nine moves, every order possible: 9! = 362,880.
This is the number you get by ignoring the rules. It assumes every game runs the full nine moves, which is false: most games end as soon as someone makes three in a row, and the remaining squares are never filled.
It is the right answer to "how many ways can nine marks be placed in nine squares", and the wrong answer to "how many games of tic tac toe are there".
255,168 — complete games
Count every distinct sequence of legal moves from empty board to finished game, stopping the moment somebody wins:
| Outcome | Games |
|---|---|
| X wins | 131,184 |
| O wins | 77,904 |
| Drawn | 46,080 |
| Total | 255,168 |
This is the figure most people mean. The gap between X's 131,184 and O's 77,904 is the first-move advantage, stated numerically — X does not merely win more often, X has nearly 70% more winning game paths available.
Note what this count still assumes: both players move at random. It is the size of the game tree, not a prediction. Between two players who know what they are doing the real outcome is always the same, which is the subject of the strategy guide.
26,830 — reachable positions, counting paths
Every position that can occur during legal play, counted once per route that reaches it.
Lower than 255,168 because a position is not a whole game, and higher than the next number because the same arrangement of marks arrived at by a different move order is counted twice.
5,478 — distinct legal positions
Every arrangement of X and O on the grid that could legally occur, counted once regardless of how you got there.
This is the number that matters if you are writing the game: it is the size of the state space you would have to store to look up every position. Five and a half thousand is small — small enough to hold in memory on a 1970s computer, which is exactly why tic tac toe was solved so early.
765 — distinct positions up to symmetry
The board has eight symmetries: four rotations, and each of those mirrored. A corner opening is the same opening whichever of the four corners you pick.
Collapse all positions that are rotations or reflections of each other, and 5,478 becomes 765.
That is the real size of tic tac toe. Seven hundred and sixty-five meaningfully different situations, in a game humans have played for roughly two thousand years.
138 — how games actually end
Only 138 board positions are terminal:
- 91 are wins for X
- 44 are wins for O
- 3 are full-board draws
Three. There are exactly three ways for the board to fill up with nobody winning, and between competent players one of those three is where every single game lands.
Why the small numbers matter
A game with 765 meaningful positions can be solved exhaustively — and it has been. Perfect play by both sides is a draw, always, with no exceptions and nothing left to discover.
That is a strange property for a game to have. Chess has roughly 10⁴⁵ positions and remains unsolved; Go is vastly larger still. Tic tac toe fits comfortably in a lookup table, which makes it a superb teaching problem and a poor game between adults.
It is also the reason variants exist. Slide XO Duel keeps three marks per player and lets you move them instead of adding more, so the board never fills — which removes those three drawn terminal positions entirely and makes the state space much larger than 765. The variants guide covers the other common approaches.
Frequently asked questions
How many possible games of tic tac toe are there?
255,168 complete games, counting every legal order of moves and stopping when someone wins. Of those, X wins 131,184, O wins 77,904, and 46,080 are drawn.
How many tic tac toe board positions are there?
5,478 distinct legal positions, or 765 once rotations and reflections are treated as the same position. Counting each position separately per route that reaches it gives 26,830.
Why is 9! = 362,880 wrong?
Because it assumes every game fills all nine squares. Most games end earlier, the moment one player completes a line, so the remaining squares are never played.
How many ways can a tic tac toe game end?
138 terminal positions: 91 wins for X, 44 for O, and 3 drawn boards. Only three full-board arrangements have no winner.
Does X really have an advantage?
Yes, in the raw counts — X has 131,184 winning game paths to O's 77,904. But it is an advantage only against imperfect play. Two players who both play correctly always draw, whoever starts.
Why can tic tac toe be solved when chess cannot?
Size. Tic tac toe has 765 meaningfully distinct positions; chess has something like 10⁴⁵. One fits in a lookup table, the other does not fit in the universe.