Two boxes is the only choice that makes sense. It is always better than one box.
No matter what you do after you enter the room, the predictor has already made their move, nothing you do now will change it. The only logical thing to do is to take both boxes because whatever the value in the second box is it will be added to the first box. If you only take the second box you are objectively always giving up $1,000 and getting no value in exchange for doing so (since not taking the first box doesn't change what's in the second)
And for you, of course, that's true! Because you are the sort of being who two-boxes, and this fact is visible to the predictor. Other types of being can do better.
This is the best reply in this thread, as it irrefutably demonstrates this so-called paradox is a religious question and has nothing to do with logic or probability.
The question is do you believe in an omniscient god or not.
The fact that they dress up god as a supercomputer and that attracts all sorts of math and tech nerds is hilarious.
Too late to edit my original comment now, but my intent was actually to make the argument for picking one, hence my comment on not caring much about the $1000.
If the predictor is indeed flawless, or almost flawless, if I were to be the type of person likely to pick both boxes, the opaque box would almost certainly be empty. So the winning strategy is not just picking the opaque box, but being the kind of person likely to pick the opaque box only.
You're right that what I do after I enter the room is irrelevant if it is somehow independent of what I have done before. But it can't be independent of what I did before if the predictor is flawless. If the predictor is flawless, then either my actions needs to be deterministic so that it can in fact know what I will do when in the room, or the predictor is supernatural and can know or cause me to act in a certain way for that reason.
Either way, giving any indication that you'd pick both boxes would be a bad idea (so I guess my typo above might screw me over if ever presented with this choice).
But the predictor would need to be almost as bad as pure chance for the odds to tilt away from one box. Unless you think it is materially worse than chance, it's a bad bet.
No matter what you do after you enter the room, the predictor has already made their move, nothing you do now will change it. The only logical thing to do is to take both boxes because whatever the value in the second box is it will be added to the first box. If you only take the second box you are objectively always giving up $1,000 and getting no value in exchange for doing so (since not taking the first box doesn't change what's in the second)