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?
In search of a new car, the player picks a door, say 1. The game host then opens one of the other doors, say 3, to reveal a goat and offers to let the player pick door 2 instead of door 1.
Game Play Instructions -
The Monty Hall problem is a counter-intuitive statistics puzzle:
There are 3 doors, behind which are two goats and a car.
You pick a door (call it door A). Youre hoping for the car of course.
Monty Hall, the game show host, examines the other doors (B & C) and always opens one of them with a goat (Both doors might have goats; hell randomly pick one to open)
Heres the game: Do you stick with door A (original guess) or switch to the other unopened door? Does it matter?
Surprisingly, the odds arent 50-50. If you switch doors youll win 2/3 of the time!
Today lets get an intuition for why a simple game could be so baffling. The game is really about re-evaluating your decisions as new information emerges.