alt Hacker NewsAssuming I have no way of testing the predictor, my decision would be to pick both boxes on the basis that $1000 is not a lot of money to me, but $1000000 is, and I wouldn't worry about the odds, because without knowing the nature of the specific predictor we're down to Pascal's Wager married to the Halting Problem:
We don't know whether or how our actions and thought processes processes might affect the outcome, and so any speculation over odds is meaningless and devolves to making assumptions we can't test, without even knowing whether that speculation itself might alter the outcome, or how.
But I don't need to speculate about the relative value of $1000 and $1000000 to me. Others might opt for the safe $1000 for the same reason.
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)