In my scenario, there is a probability pN that the predictor leaves a note, regardless of what prediction the predictor makes. The note (when present) is always of the form “I predicted that you will pick the <right|left> box, and therefore <did|did not> put a bomb in the left box.” That is, the note is about what the predictor thinks you will do, which more closely matches your second paragraph. Your first paragraph concerns a prediction about what you counterfactually would have done in some other situations and is not relevant in this scenario.
However, your decision process should consider the probability 1-pT that the note is lying about the predictor’s actual prediction (and therefore bomb-placing).
In my scenario, there is a probability pN that the predictor leaves a note, regardless of what prediction the predictor makes. The note (when present) is always of the form “I predicted that you will pick the <right|left> box, and therefore <did|did not> put a bomb in the left box.” That is, the note is about what the predictor thinks you will do, which more closely matches your second paragraph. Your first paragraph concerns a prediction about what you counterfactually would have done in some other situations and is not relevant in this scenario.
However, your decision process should consider the probability 1-pT that the note is lying about the predictor’s actual prediction (and therefore bomb-placing).