  In this paper, we perform a minimalistic quantization of the classical game
of tic-tac-toe, by allowing superpositions of classical moves. 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. 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. 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 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. In contrast to the classical
tic-tac-toe, the deterministic quantum game does not always end in a draw. In
contrast also to most classical two-player games of no chance, it is possible
for Player 2 to win. 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. 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. We then speculate what implications these results
might have on quantum information transfer and portfolio optimization.
