He deals out of both ends of his mouth

This is a real beauty from “the master”.   He combined “deals from the bottom of the deck” (cheating) together with “he talks out of both sides of his mouth,” (saying different things to different people) to create a saying that describes both cheating and lying.  He could also have been thinking of the idiom “playing both ends against the middle” (pretending to have a different position to different audiences while really supporting something else), again invoking the lying or cheating theme.  He isn’t called “the master” for nothing.