Quantum strategies are better than classical in almost any XOR game
  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. 
Andris Ambainis, Arturs Backurs, Kaspars Balodis, Dmitry Kravcenko,   Raitis Ozols, Juris Smotrovs, Madars Virza
quant-ph cs.GT