The Maths of Disappearing Tic Tac Toe

Ordinary tic tac toe is solved and drawn with perfect play. Limiting each side to three pieces changes the decision problem.

Classic tic tac toe has 255,168 legal complete game sequences, or 26,830 once rotations and reflections are grouped. These are counts of game sequences, not of board positions.

With fading pieces, a piece is removed six moves after it is placed, so positions can recur and familiar classic strategies become less reliable. A position occurring three times ends the game as a draw.