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AndySimpson comments on Counterfactual Mugging - Less Wrong
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Yes, I'll give Omega the money, because if I'm going to refuse to give Omega the money after the coin toss occurs, Omega knows ahead of time on account of his omniscience. If I had won, Omega could look at me and say, "You get no money, because I know you wouldn't have really given me the $100 if you'd lost. Your pre-commitment wasn't genuine."