In reverse tic-tac-toe (also called misère tic-tac-toe), completing three in a row of your own marks loses. With perfect play the game is still a draw, but only if X opens in the center: all eight other first moves lose by force. From there, X has a plan that never loses: answer every O mark on the square straight across the center from it. O can't copy that trick, but O can force a win whenever X opens anywhere else.
The rules are the same as normal tic-tac-toe in every other way: a 3 by 3 grid, X goes first, one mark per turn, and a full board with no line is a draw. Some people call it toe tac tic or anti tic-tac-toe. Poozee's Tic-Tac-Toe plays the standard rules, where three in a row wins, so this guide is for games on paper or with a friend. The normal game and its variants are in how to play tic-tac-toe.
Every number here comes from an exact solver that searches the whole reverse game, built on the same rules code as our game, and a test fails if the article and the code ever disagree.
Is reverse tic-tac-toe a draw?
Yes. A game still ends at the first completed line, so reverse tic-tac-toe has the same 255,168 possible games and the same 5,478 positions as the normal game. Only the results flip. X completes the line in 131,184 of those games and loses them, O loses 77,904, and 46,080 are draws.
With perfect play from both sides, the result is a draw. The catch is the first move. In the normal game every opening draws; in the reverse game, only the center does:
Open in a corner or on an edge and a perfect O can force you to complete a line. That's the surprise of the reverse game: the center sits on four lines, more than any other square, yet it's X's only safe start.
How to never lose as X: center, then mirror
The strategy is two rules:
- Take the center with your first mark.
- Mirror every O mark through the center: take the square straight across from it. If O takes a corner, take the opposite corner; if O takes an edge, take the opposite edge.
The mirror square is always empty when you need it, so the rule never gets stuck. We checked it against every possible series of O moves: there are 360 games in which X plays this way, and X loses none of them. O loses 168 and the other 192 are draws.
It isn't just a safe choice, it's usually the only one. After the center and any O reply, all 8 possible ones, the mirror square is X's only second move that doesn't lose:
Over a whole game, X faces 141 positions with more than one empty square, and in 121 of them the mirror move is the only move that doesn't lose. So if you play reverse tic-tac-toe as X, don't improvise: mirror.
Why the mirror works
Every line through the center joins two opposite squares, like the top left and bottom right. You hold the center, and each time O takes one end of an opposite pair you take the other, so you never own both ends of a pair. You can't complete a line through the center.
The other four lines are the outer rows and columns. Each one is the mirror image of the line across from it: the top row mirrors the bottom row, and the left column mirrors the right column. If you ever filled the top row, it would be because O had filled the bottom row first, with each of your marks placed just after O's. O would have completed that line, and lost, before you finished yours.
When the mirror misses a win
The mirror guarantees you won't lose. It doesn't always take a win when one is there. In 8 of the positions X meets, all of them rotations or reflections of this one, X could force a win but the mirror move only draws:
That's the only kind of position where it happens, so mirror without worrying about it, and take a forced win when you can see one.
A worked example
Here is how a game against the mirror goes wrong for O.
- X takes the center.
- O takes the top left.
- X mirrors on the bottom right.
- O takes the top middle. O now has two marks in the top row, so the top right is a dead square for O: taking it would complete O's own line.
- X mirrors on the bottom middle.
- O takes the middle left, which lines up with the top left and makes the bottom left dead too.
- X mirrors on the middle right.
O has no safe square left, so O's fourth mark completes a line and O loses. Notice that X never had to think: every X move was the mirror.
How to play O
Answer an off-center opening and win
If X opens anywhere but the center, X has already lost against perfect play, and you can force X to complete a line. Here is every reply to every opening:
| X opens | Replies that win for O | Replies that only draw | Replies that lose |
|---|---|---|---|
| Corner | Any of the 4 edges | The center and the other 3 corners | None |
| Edge | The 2 nearest edges and the 2 far corners | The 2 corners beside X and the opposite edge | The center |
| Center | None | All 8 | None |
The one reply to avoid is the center after an edge opening, the only losing reply to any first move. X then wins by force with the opposite edge, straight across from its first mark.
Don't mirror as O
Mirroring doesn't carry over to O. If O answers every X mark on the opposite square whenever it's free (and plays its best only when X has taken the center), X can force O to complete a line after any of the nine first moves. In the game below, the trouble starts when X takes the center, the one square O can't mirror:
Holding the draw against the mirror
Against a center opening and a mirroring X you can't win, but you can always draw. Your first two marks are safe anywhere: every one of them keeps the draw. The danger starts with your third mark: 16 of the 24 positions you can reach then have at least one square that loses against perfect play, and so do 16 of the 24 at your fourth mark.
One habit gets you through every time: play a quiet move, a square that isn't dead for you and doesn't line up with one of your marks to create a new dead square. In every game against the mirror, a quiet move is always there, and in all 57 positions O can meet without being lost already, every quiet move holds the draw. In the worked example, the middle right was the only quiet square O had.
That habit is not a general rule, though. Across all positions where the player to move isn't lost yet and has a quiet move, every quiet move keeps the result in only 1,693 of 2,610. Against the mirror it's enough; against other play, look ahead.
Which squares are the most dangerous?
After the opening, the center is the square most likely to throw a reverse game away. We took every position that can come up where the player to move isn't already lost, and checked whether taking each empty square makes the perfect-play result worse:
| Square | Positions where it's empty | Taking it loses or gives up a win | Share |
|---|---|---|---|
| Center | 1,221 | 852 | 69.8% |
| Each corner | 1,250 | 693 | 55.4% |
| Each edge | 1,247 | 515 | 41.3% |
The center sits on four lines, so it's the square most likely to finish one of yours. Edges sit on only two, and they're the safest squares to reach for when you aren't sure. The exception is X's first move, where the center is the only square that doesn't lose.
Pro tip: Before each move, find your dead squares, the ones that would complete a line of your own. You lose when every empty square is dead for you, which happens in 246 of the 4,520 unfinished positions. Keep at least one live square in reserve.
How often careless players lose
Most real games aren't perfect, so we also worked out the exact odds against two careless players: a random player who picks any empty square, and an avoider who never completes a line of its own while another square is open. These are exact chances over every possible game, not samples.
| Matchup | X wins | O wins | Draws |
|---|---|---|---|
| Random vs random | 28.8% | 58.5% | 12.7% |
| Avoider vs avoider | 13.7% | 64.0% | 22.3% |
Going first is a burden here. X places up to five marks to O's four, so X tends to run out of safe squares first, and between two avoiders X loses nearly two games in three.
The mirror never loses, but it's a cautious way to play: against a random O it wins exactly 50.0% of games and draws the rest, and against an avoider it wins 15.3%. An X who looks ahead and picks, among the moves that don't lose, the one most likely to trap O, wins 60.4% against a random O and 37.5% against an avoider. And a perfect O facing a random X wins 99.9% of games, mostly because a random X opens off the center eight times in nine.
Reverse vs normal tic-tac-toe at a glance
| Normal tic-tac-toe | Reverse tic-tac-toe | |
|---|---|---|
| Three in a row | Wins | Loses |
| Perfect play | Draw | Draw |
| Safe first moves for X | All 9 | Only the center |
| X's simple plan | Corner, then look for a fork | Center, then mirror |
The normal game is about making two threats at once, as how to win tic-tac-toe shows. The reverse game is about the opposite: keeping a square you can safely take while your opponent runs out.
Keep playing
- Play Tic-Tac-Toe, standard rules, against the computer or a friend
- How to win tic-tac-toe: forks and the opposite-corner trap in the normal game
- How to play tic-tac-toe: the rules, ties and other variants
- Dots and boxes strategy, another game won by leaving your opponent no safe move
Frequently asked questions
Can you win reverse tic-tac-toe?
Only if your opponent slips. With perfect play the game is a draw, but the first player has to open in the center: every other first move loses by force against a perfect second player.
What is the best first move in reverse tic-tac-toe?
The center, the only first move that doesn't lose. Then answer every O mark on the square straight across the center from it. In all 360 games that strategy can lead to, X never completes a line.
What is toe tac tic?
Another name for reverse tic-tac-toe, also called misère or anti tic-tac-toe. The board and the turns are the same, but the player who completes three in a row of their own marks loses.
How does O win reverse tic-tac-toe?
O can force a win only when X opens off the center. Answer a corner with any edge, or an edge with one of the two nearest edges or a far corner. Against a center opening followed by the mirror, O's best result is a draw.
Can you play reverse tic-tac-toe on Poozee?
No. Poozee's Tic-Tac-Toe plays the standard rules, where three in a row wins. Play the reverse version on paper with a friend, using the strategy in this guide.