[Cerril]

Well basically if this person is a reliable predictor, then it seems more likely that what we understand as the normal laws of causality don't apply. Knowing ahead of time that if we choose box B alone we're greater than 99% to get 100k, less than 1% to get 0; and if we open both we're greater than 99% to get 1k and less than 1% to get 101k, then the EV of box B alone is greater than $99k while the EV of both boxes is less than $2k, there's no real way to justify opening both boxes unless you have information that the predictor doesn't.

Of course if he's 99% likely to be correct it's far more likely that he has information that I don't, and so if he can somehow predict my actions I might as well choose the action with the best outcome (that is, if I pick A&B AND he is right >99% of the time, is is >99% likely that he had information leading him to believe that I would pick A&B. Ditto with just B).

It seems paradoxical, but only because such things cannot be done in the real world. For the sake of this experiment though, the only laws are those of the assumptions, and it's by those we're bound.