I have to be a bit of a buzzkill and say that this is all placebo.

Your prompt might give the model context that gives it better token quality much in the same way that asking “How to swim?” is worse than “I’d like to learn the proper technique for the freestyle swimming stroke, and you’re an expert swimming coach.”

There’s no guarantee your prompt isn’t giving less factual answers to be honest. I wouldn’t go about telling the model that it’s often wrong, as it’s not useful context and might skew results.