If the Predictor is accurate or omniscient, then the game is rigged and it becomes a different problem. If the Predictor is making guesses then box predicting and box selecting are both interesting to figure out.

WTF? Who creates a system in which they can offer either some help now, or significantly more later, unless they are malicious or running an experiment?

Or you live in a system nobody in particular created (capitalism) and work at a social service with limited resources with a clientele who have no background experience with adults who can be trusted. An employer telling hem "work now and I'll pay you later" is not convincing, while a peanut butter sandwich right now is.