In this scenario (the one where you always press the red button), any misprediction is actually guaranteed to go against you. The only way to win is for the prediction to correctly predict that you will press the red button (even if you lose).
I don’t think your statement “the reason the room can predict so well is because of some learning mechanism that’s been active for some time already” is more general. It’s much more specific, and contradicts the scenario premise that the predictor can predict with 98% accuracy anyone going in. That includes regardless of whether they’ve been in the room before.
In this scenario (the one where you always press the red button), any misprediction is actually guaranteed to go against you. The only way to win is for the prediction to correctly predict that you will press the red button (even if you lose).
I don’t think your statement “the reason the room can predict so well is because of some learning mechanism that’s been active for some time already” is more general. It’s much more specific, and contradicts the scenario premise that the predictor can predict with 98% accuracy anyone going in. That includes regardless of whether they’ve been in the room before.