Movies where the good guy and the bad guy never see each other

But Frodo and “the Eye” see each other several times. Frodo even hears a voice say “I see you” in the tavern.

Not sure how it worked in the movie, but in the book I think if Sauron actually did see Frodo at any point–not just being vaguely aware of him–Frodo would have been toast.

How about The Duel?

Actually, it depends on the version:

But in none of them does Feversham meet or face the Mahdi.