An old paradox, named after a game show host, the emcee of "Let's Make a Deal" continuously from 1963 to 1976, and intermittently as revived thereafter. Monty Hall presented contestants with three curtains, often labeled A,B, and C, and asked them to make a choice. They would get whatever gift was behind the curtain they chose. In the story/paradox, Monty tells you that behind one of the curtains is a magnificent new car, the car of your dreams. Behind the other two curtains, not-so-desirable gifts. You tell him: "I pick A, Monty." Monty: "Not so fast! I will now reveal what is behind curtain C." The curtain opens, and there is some worthless gag gift, say a pile of shaving cream. Monty: "Now, you can stay with your choice of A, or you can switch to B." What should you do? The usual first response, and for many people a very powerful intuitive response, is that it doesn't matter what you do. You now have just two curtai...