QuantumTicTacToe
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A version of Tic Tac Toe where all moves are superpositions of two moves—with online multiplayer!
In this game, X cannot play their second move since that would require moving twice on the same square. The game does not recognize this as a tie, though.
The game is pretty complicated, better instructions would go a long way.
Player Y has no more possible moves but is still instructed to go next 
With this users won't have to find people to play with on their own. It shouldn't be too difficult to implement—you would have to add a new "find game" button...