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Nick_Tarleton comments on Open Thread: February 2010 - Less Wrong
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Let p be the probability that you 2-box, and suppose (as Greg said) that Omega lets P(box A empty) = p with its decision being independent of yours. It sounds like you're saying you only care about the frequency with which you get the maximal reward. This is P(you 2-box)*P(box A full) = p(1-p) which is maximized by p=0.5, not by p infinitesimally small.