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cousin_it comments on Counterfactual Mugging and Logical Uncertainty - Less Wrong
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Omega could have known the 10000th digit of pi beforehand, so now it has a strategy for reliably extracting money from you. Or do you place some other restriction on Omega's behavior that I'm not seeing?
Like in the original problem, Omega's decision to run the game is independent on the game's parameters. Omega is not trying to win, it just implements the thought experiment.