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Nick_Tarleton comments on Open Thread: February 2010 - Less Wrong
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Interesting. I was idly wondering about that. Along somewhat different lines:
I've decided that I am a one-boxer,and I will one box. With the following caveat: at the moment of decision, I will look for an anomaly with virtual zero probability. A star streaks across the sky and fuses with another one. Someone spills a glass of milk and halfway towards the ground, the milk rises up and fills itself back into the glass. If this happens, I will 2-box.
Winning the extra amount in this way in a handful of worlds won't do anything to my average winnings-- it won't even increase it by epsilon. However, it could make a difference if something really important is at stake, where I would want to secure the chance that it happens one time in the whole universe.
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.