@Mike Plotz: It’s true that you can’t do better than random in predicting (theoretical nonphysical) coin tosses, but you also can’t do worse than random. As Eliezer pointed out, the claim isn’t “it is always possible to to better than random”, but “any algorithm which can be improved by adding randomness, can be improved even more without adding randomness.”
@Mike Plotz: It’s true that you can’t do better than random in predicting (theoretical nonphysical) coin tosses, but you also can’t do worse than random. As Eliezer pointed out, the claim isn’t “it is always possible to to better than random”, but “any algorithm which can be improved by adding randomness, can be improved even more without adding randomness.”