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Nick_Tarleton comments on Newcomb's Problem and Regret of Rationality - Less Wrong
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I'd love to say I'd find some way of picking randomly just to piss Omega off, but I'd probably just one-box it. A million bucks is a lot of money.
It's often stipulated that if Omega predicts you'll use some randomizer it can't predict, it'll punish you by acting as if it predicted two-boxing.
(And the most favourable plausible outcome for randomizing would be scaling the payoff appropriately to the probability assigned.)
Newcomb's problem doesn't specify how Omega chooses the 'customers'. It's a quite realistic possibility that it simply has not offered the choice to anyone that would use a randomizer, and cherrypicked only the people which have at least 99.9% 'prediction strength'.