The Monty-Hall-Problem is an old mathematical riddle
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
The answer - even though it might seem strange - is yes, you should change.
For the full mathematical proof you can read wikipedia, but to visualize the problem you can use this little program and test it by yourself.
You can even automate a few hundred tests and see whats right on average.