The player who plays second has a strategy that guarantees winning if played correctly; player 1 cannot win, whatever he does, unless player 2 makes a mistake (in the film, M, who always wins at the game, at one stage lets X go first and even allows X to decide which matches M ought to take; but M knows that X does not know the winning algorithm, so he can afford that generosity and revert to his winning algorithm after X's move).
There are pages out there that describe the winning algorithm (I read it on the German wikipedia page, but there does not seem to be an English page describing the algorithm as nicely). If you let the computer play first in that online game and follow the algorithm, you'll win, and you'll get a nice little congratulatory message. Playing the strategy does require a pen and paper first, though (at least it did for me); playing it mentally might take some practice.
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