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?
Surprisingly it does matter, if you choose the other door.Oscar Bonilla explains this result on his web page .
For all those that do not trust math (i.e. me), I wrote a small programm and put it on github .
The programm simulates Monties gameshow and tests three players: The math unaware player, the math aware player and the cheating player. Enjoy.