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We initiate a study of random instances of nonlocal games. We show thatquantum 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 gamewith 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.

Quantum strategies are better than classical in almost any XOR game