How to Win at Tic-Tac-Toe (and Why It Usually Ends in a Draw)
With best play from both sides tic-tac-toe is always a draw, but a short list of rules, a corner opening and a fork let you win whenever the other player slips.
You keep drawing. Sometimes you lose. Is there a way to always win at tic-tac-toe? Not against a player who plays it right. But there is a short list of rules that stops you losing, and lets you pounce when the other player slips.
The short version
- With best play from both sides, tic-tac-toe always ends in a draw. It is a solved game.
- Wins come from forks: one move that makes two threats at once. Learn to make them, and to block them.
- Go first and open in a corner. Go second and answer a corner with the center.
The short answer
No one can force a win from a fair start if the other side makes no mistakes. The best you can do is never lose. The fun part is that most players do make mistakes, and the rules below show you which ones to wait for.
Eight rules, in this order
A player can play a perfect game, to win or at least draw, by choosing the first available move from this list on every turn. It is the list used in Newell and Simon's 1972 tic-tac-toe program.
- Win: with two in a row, place the third.
- Block: if your opponent has two in a row, play the third square yourself.
- Fork: make a move that gives you two ways to win at once.
- Block a fork: stop your opponent’s fork, ideally with a move that makes your own two in a row.
- Center: take the center.
- Opposite corner: if your opponent is in a corner, take the opposite one.
- Empty corner: take any corner.
- Empty side: take a middle square on a side.
If you go first: open in a corner
The first player, X, has only three really different first moves: a corner, an edge or the center. X can win or force a draw from any of them. But a corner gives the opponent the smallest choice of squares that avoid losing.
Here is the catch. Against a perfect O, the corner opening still ends in a draw. Against a normal opponent, it sets a trap, because O’s corner replies and edge replies both lose.
| X | ||
| O | ||
| X |
If O answers your corner with another corner, or with an edge, X is guaranteed to win. Take the picture below: O went to the top right corner, X took the bottom left, and O had to block the left column. Then X takes the last corner and has two threats at once.
| X | O | |
| O | ||
| X | X |
One more note. If your opponent is not perfect, another study found that a center opening is best for X. Both are fine. The corner just makes more mistakes likely.
If you go second: answer the opening
The second player, O, has to answer with care. O must answer a corner opening with the center, and a center opening with a corner. An edge opening can be answered with the center, a corner next to the X, or the edge opposite the X. Any other reply lets X force a win.
After that, follow the list and watch for forks. The board below shows how to block one.
| X | O | |
| O | ||
| X |
Why it nearly always ends in a draw
Count the ways to play. There are 9 possible first moves, 8 replies, and so on, so at most 9! or 362,880 total games. Games can end before the board is full, and an exact count gives 255,168 possible games. Treat rotations and reflections as the same game and only 26,830 remain.
- Upper bound: 9!362,880
- Exact count of games255,168
- Same after rotations and reflections26,830
Sources: Wikipedia, Game complexity; Game tree; Tic-tac-toe.
That is small enough for a computer program to play it perfectly. The result: the game is a draw if no mistakes are made, and no mistake is possible on the opening move.
Look at the finished boards and you see something odd. After taking symmetry into account, there are 138 finished boards when X always moves first. 91 are won by X, 44 by O, and only 3 are drawn. Yet with best play every game is drawn. The count only tells you which boards are possible, not which ones careful players reach.
Side by side
| Best first moves | What to do next | Watch out | |
|---|---|---|---|
| First player (X) | A corner. The center also works well against weaker opponents. | If O takes the center, take the opposite corner. If O answers badly, make a fork. | X can win or force a draw from any opening, but cannot force a win against a flawless O. |
| Second player (O) | Corner opening: take the center. Center opening: take a corner. Edge opening: the center, a corner next to X, or the opposite edge. | Follow the eight rules and block every fork. | Against two opposite corners, do not take a corner. Take an edge. |
What we would pick
Follow the eight rules and you win or at least draw. Then play on a board that makes you slow down and look. Our marble crystal tic-tac-toe set has a square marble board, 26 × 26 cm, with nine grooved squares, and clear crystal crosses and rounds with golden-amber bases. The marble comes in white or black. Wipe it with a soft damp cloth and keep lemon juice, vinegar and wine off it.
If you only want the pieces, look at the crystal tic-tac-toe set, a set of crystal pieces.
Sources
- Tic-tac-toe, Wikipedia: the eight-rule list, the three first moves, how O should reply, the corner traps, and 138 finished boards (91 won by X, 44 by O, 3 drawn).
- Game complexity, Wikipedia: at most 9! or 362,880 games, an exact count of 255,168, and 26,830 after rotations and reflections.
- Game tree, Wikipedia: the game tree for tic-tac-toe has 255,168 leaf nodes.
- Solved game, Wikipedia: tic-tac-toe is a draw with perfect play, and no mistake is possible on the opening move.
