Vladimir_Nesov comments on Counterfactual Mugging - Less Wrong
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Comments (257)
I don't see the difficulty. No, you don't win by giving Omega $100. Yes, it would have been a winning bet before the flip if, as you specify, the coin is fair. Your PS, in which you say to "assume that in the overwhelming measure of the MWI worlds it gives the same outcome", contradicts the assertion that the coin is fair, and so you have asked us for an answer to an incoherent question.
The difficulty comes from projecting the ideal decision theory on people. Look how many people are ready to pay up $100, so it must be a real difficulty.
The fairness of a coin is a property of your mind, not of the coin itself. The coin can be fair in a deterministic world, the same way you can have free will in deterministic world.