We clearly disagree strongly on the probabilities here. I agree that all things being equal you have a better shot at convincing him than I do, but I think it is small. We both do the same thing in the Defector case. In the co-operator course, he believes you with probability P+Q and me with probability P. Assuming you know if he trusts you in this case (we count anything else as deceivers) you save (P+Q) * 2 +(1-P-Q) *1, I save (P) * 3+(1-P) * 1, both times the percentage of co-operators R. So you have to be at least twice as successful as I am even if there are no deceivers on the other side. Meanwhile, there's some percentage A who are decievers and some probability B that you'll believe a deceiver, or just A and 1 if you count anyone you don't believe as a simple Defector.

You think that R * (P+Q) * 2 + R * (1-P-Q) * 1 > R * P * 3 + R * (1-P) * 1 + A * B * 1. I strongly disagree. But if you convinced me otherwise, I would change my opinion.