Let's Make a Deal

You're on the famous game show, and Monty Hall, the host, presents you with 3 closed doors. Behind one of the doors is a new Rolls Royce, but behind the other two are gag prizes.

You choose one door, but before it is opened, Monty opens one of the unchosen doors, revealing a pile of manure. He invites you to choose again: either keep the door you have already chosen, or switch to the other, unknown door.

What do you do, and why?

Answer