Quantum Tic-Tac-Toe

Quantum Tic-Tac-Toe investigates the concept of quantum entanglement through a simple and fun game. It was created by Allan Goff around 2002. This is an original Flash version. See the rules below the game board. There is no computer player or multiplayer; you play both sides.


As in normal Tic-Tac-Toe, the game is played on a 3-by-3 board, and each of two players takes turns placing pieces, trying to get 3 in a row.

But in Quantum Tic-Tac-Toe, you place two "potential" moves at a time, in separate squares. Eventually, one of these will become a real (or classical) move, and the other will not. Potential moves are marked with the numbers of the turns they were played on. Each pair of potential moves is connected.

Only classical moves count toward a win.

The game continues with each player placing their two potential moves per turn, until a special condition comes about. Eventually, multiple pairs of connected, potential moves will form a closed circuit. This closed circuit represents only two possible sets of classical moves. Depending on which of the last pair of moves becomes "real," all the other squares that are involved in the circuit will necessarily go to player 1 or 2.

The player who closes the circuit chooses which of their last two potential moves becomes real, and all the other potential moves that are part of the circuit are automatically converted into real moves, based on their choice. (Note that it looks like this may be a misinterpretation of the rules on my part, but it's how this version works.)

The game ends when there are one or more lines of three pieces in a row of the same color, or when the board is full. Unlike in regular tic-tac-toe, it's possible for both players to get 3 in a row at once, or for one player to get two of them! There can also be a normal win (one player gets 3 in a row) or no win at all.

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Avatar picture for Daniel Thanks for the game, but I'm a little confused on something... Wiki and the article it links to for the rules both say that the person who did NOT complete the circuit gets to choose where the Xs and Os collapse.

Other than that, great.
Avatar picture for dale Very nice. But try this move sequence:
X 1,5 O 5,9
X 1,5

X marks the upper left corner and the center. O sets up a block by marking the center and the lower right corner. X misses the import of what O did, and proceeds to claim the corner and center by forcing a collapse. Sadly, his now-real marks in the corner and center are blocked by a real O in the opposite corner.

Except that your version of the game will not allow X to complete his second move. He can click in the upper right corner and place one spooky mark, but the program will not recognize a click in the center to place the second spooky mark. X's second move, marking squares 1 and 5 again, is legal and should be allowed by this program.

You need not post this comment, it's just a bug report...

Avatar picture for Chris In response to Dale, it is not a bug, it's the way the game works. The idea of placing two X's per turn is that you are 'entangling' two squares of the board. Once X marks squares 1 and 5, they are already entangled for X. You cannot re-entangle two squares that are already entangled, so X cannot mark 1 and 5 again on his second turn.
Avatar picture for Pierre Durand It doesn't respect the rule :

Since it is possible for a single measurement to collapse the entire board and give classical tic-tac-toes to both players simultaneously, the rules declare that the player whose tic-tac-toe has the lower maximum subscript earns one point, and the player whose tic-tac-toe has the higher maximum subscript earns only one-half point.

[Link to en.wikipedia.org]
Avatar picture for dale In response to Chris's response: it is a bug, according to the reference implementation of the game ([Link to www.paradigmpuzzles.com], the inventor's site). There is no rule preventing either player from entangling two squares, and then placing a later move in the same two squares and forcing a collapse.
Avatar picture for Pratik Borude I am actually writing a extended essay on the game theoretical analysis of quantum tic tac toe and finding its nash equilibrium so it would be great if you could send me some strategies or even an opening strategy ...

Thank You :)

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