In the case of the 3 other possible input pairs, essentially identical analysis shows that Alice and Bob will have the same win probability of , so overall the average win probability for a randomly chosen input is . Since , this is strictly better than what was possible in the classical case.
In the case of the 3 other possible input pairs, essentially identical analysis shows that Alice and Bob will have the same win probability of , so overall the average win probability for a randomly chosen input is . Since , this is strictly better than what was possible in the classical case.