Let's make a deal

And let's face it... I'm an engineer.

Wikipedia's topic of the day is the Monty Hall problem. This is the problem, as stated in the article:

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 is yes... You double your chances of winning if you switch to the other door. If you think that sounds totally wrong, you're in good company. When this problem appeared in Marilyn vos Savant's column in 1990, even mathematicians wrote to "correct" her, according to Ms. vos Savant.

But it does make me wonder about the quality of mathematicians these days. It's pretty simple to create a Monte Carlo simulation to verify beyond any doubt that the solution is correct. And since I'm an engineer, I thought it would be fun to make a web page where you can play the game yourself...


(click the image to navigate to the page)

Try it a couple dozen times. Remember, always change your selection when asked, and you should win the car 2 times out of 3.