![]() We also find the quantum blocking move, which consists of a weighted superposition of moves that the opponent could use to win the game, to be very effective in denying the opponent his or her victory. More interestingly, we find that Player 1 enjoys an overwhelming quantum advantage when he opens with a quantum move, but loses this advantage when he opens with a classical move. ![]() In contrast also to most classical two-player games of no chance, it is possible for Player 2 to win. In contrast to the classical tic-tac-toe, the deterministic quantum game does not always end in a draw. We play the quantum tic-tac-toe first randomly, and then deterministically, to explore the impact different opening moves, end games, and different combinations of offensive and defensive strategies have on the outcome of the game. ![]() A player wins when the sums of occupations along any of the eight straight lines we can draw in the $3 \times 3$ grid is greater than three. We also admit interference effects, by squaring the sum of amplitudes over all moves by a player to compute his or her occupation level of a given site. In order for the quantum game to reduce properly to the classical game, we require legal quantum moves to be orthogonal to all previous moves. In this paper, we perform a minimalistic quantization of the classical game of tic-tac-toe, by allowing superpositions of classical moves.
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