  We initiate a study of random instances of nonlocal games. We show that
quantum strategies are better than classical for almost any 2-player XOR game.
More precisely, for large n, the entangled value of a random 2-player XOR game
with n questions to every player is at least 1.21... times the classical value,
for 1-o(1) fraction of all 2-player XOR games.
