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Counterfactual mugging is a limiting case of Psy-kosh's non-anthropic problem
Counterfactual mugging is the typical problem used to motivate updateless decision theory: Omega flips a coin. If Heads, it asks you for $1. If Tails, it offers you $5 only if it predicts you would have given it the $1 had the coin come up Heads. Counterfactuals are confusing though, so let us re-phrase it this way: Om