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Eliezer_Yudkowsky comments on Counterfactual Mugging - Less Wrong
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This requires though that Omega have decided to make the bet in a fashion which exhibited no dependency on its advance knowledge of the coin.
This is a big issue which I unsucessfully tried to address in my non-existing 6+ paragraph explanation. Why the heck is Omega making bets if he can already predict everything anyway?
That said, it's not clear that when Omega offers you a bet, you should automatically refuse it under the assumption that Omega is trying to "beat" you. It seems like Omega doesn't really mind giving away money (pretty reasonable for an omniscient entity), since he seems to be willing to leave boxes with millions of dollars in them just lying around.
What is Omega's purpose is entirely unknown. Maybe he wants you to win these bets. If you're a rational person who "wants to win", I think you can just "not worry" about what Omega's intents are, and figure out what sequence of actions maximizes your utility (which in these examples always seems to directly translate into maximizing the amount of money you get).
Quantum Coins. seriously. they're easy enough to predict if you accept many worlds.
as for the rest... entertainment? Could be a case of "even though I can predict these humans so well, it's fascinating as to just how many of them two-box no matter how obvious i make it."
It's not impossible-we know that we exist, it is not impossible that some race resembling our own figured out a sufficient solution to the lob problem and became a race of omegas...