The standard "solution" (that isn't really a solution, but an explanation) is that the predictor has decided to reward the kind of person who one-boxes, and is

The standard "solution" (that isn't really a solution, but an explanation) is that the predictor has decided to reward the kind of person who one-boxes, and is extremely good at predicting whether you are that kind of person (perhaps even better than you yourself are). So, if you can "decide to be the kind of person" who one-boxes (and perhaps by induction "decide to be the kind of person who decides to be a certain kind of person"), you can make out pretty well.