Jamie's being overconfident. Just because a bullet can be traced back to a gun doesn't mean it can be traced back to a specific person (who knows if Richard didn't steal his gun). Besides, he talks too much, and arguably, Richard is still being too curious for his own good. In real life, the mug would punch you in the face at the first attempt to negotiate.
As for Jamie, we know he can pull some basic self defense moves, and he's putting himself in danger by refusing to give up his wallet while not using them against Richard.
Typhon

