This still makes no sense to me. Picking a random number C adds no information, so I can't see how it can influence the accuracy of your decision. Just from a n

This still makes no sense to me. Picking a random number C adds no information, so I can't see how it can influence the accuracy of your decision. Just from a naive information theoretic point of view. If it's possible to get some epsilon of advantage by choosing a C once, then... can you do it more? Can you combine or average more of them? Is 1 optimal? Why? I fee like there's some shenanigans here regarding assumptions about the distribution of A, B and C but I can't really put my finger on it.