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Normal_Anomaly comments on Newcomb's Problem and Regret of Rationality - Less Wrong
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Would that make you a supersuperintelligence? Since I presume by "picking randomly" you mean randomly to Omega, in other words Omega cannot find and process enough information to predict you well.
Otherwise what does "picking randomly" mean?
The definition of omega as something that can predict your actions leads it to have some weird powers. You could pick a box based on the outcome of a quantum event with a 50% chance, then omega would have to vanish in a puff of physical implausibility.
I suspect Omega would know you were going to do that, and would be able to put the box in a superposition dependent on the same quantum event, so that in the branches where you 1-box, box B contains $1million, and where you 2-box it's empty.
Exactly what I was thinking.