What if Sauron had a lazy eye?

You remember Sauron, right? From Lord of the Rings?  The really bad guy that had a giant eye in his tower?

Aragorn: “Is…is he looking at us?”

Gandalf: “Shit, I can never tell.”

Gandalf: “Frodo, as you cross into Mordor, be careful to not let the gaze of Sauron fall upon you!”

Frodo: “Dammit Gandalf, I can’t ever tell what he’s looking at anyway, how am I supposed to know?”

Sauron: “Hello little hobbits, I see yo-…damn, wait…great.  Now I’m looking at France.”

Sauron: “Is there anything I can do?”

Eye doctor: “Well I can put a patch over your good eye so the weak one becomes stronger.”

Sauron: “I…only have the one eye.”

Eye doctor: “Oh, well in that case do you at least have an army of orcs to do your bidding for you?”

Sauron: “Yes!”

Eye doctor: “Really? Wow, that’s impressive. You must get up very early in the morning.”