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).