Suppose you're on a game show, and you're given the choice of N doors: Behind X doors is a car; behind the others, goats. You pick a door, and the host, who knows what's behind the doors, opens M other doors, revealing Y cars, and Z goats. He then says to you, "Do you want to pick this door instead?" -- pointing to one of the remaining closed doors. Is it to your advantage to switch your choice?