
You're on a game show, and you're given the choice of three doors. Behind one door is a car; behind the other two are goats. You pick a door, and the host (Monty Hall), who knows what's behind the doors, opens one of the other two doors, revealing a goat. He ALWAYS picks the door which has a goat. He then asks you, 'Do you want to switch or stick?'
Question: Is it to your advantage to switch your initial choice? Or keep the same door? Or does it not matter?