Every day you play a game with your friend. He hides his hands behind his back, holding an item in one hand. You guess a hand, and he must reveal if you guessed correctly. If you did, you win that round; otherwise you lose. The game lasts three rounds. Some days, your friend likes to cheat at this game, by (possibly switching and) revealing an empty hand all three times. In fact he does this a third of the times you play, although there is no pattern revealing when he'll do it. You've just played a game, and lost all three rounds. What is the probability that your friend cheated