Well, the idea is that in order to predict which box you will pick, the predictor is basically running a perfect simulation of you. Depending on what the simula

Well, the idea is that in order to predict which box you will pick, the predictor is basically running a perfect simulation of you. Depending on what the simulated version of you does, then the predictor will either put nothing or a million dollars in the second box. So the problem is this: you are given the choice to pick one or both boxes, but you don't know whether you are playing for real or whether you are a simulation who will unwittingly tell the predictor what the real "you" will do. If your mind is deterministic and the predictor is perfect then you will necessarily choose the same in both simulation and reality. Alas, you need your simulated self to "tell" the predictor to put a million in the box, which is why it is preferable to only pick up that one box. It's not that causality runs backwards, it's that unbeknownst to you, you're actually choosing twice. Of course, that whole thought experiment is a bit silly. Even under determinism it would be borderline impossible to do this with a physical system, and agents generally have an incentive to be unpredictable when it benefits them, so I don't think it is massively important to decide correctly in such contrived scenarios.