Tuesday, October 13, 2009

I Love Monty Hall

OK, so I don't really love Monty. What I love is the problem that is named for him, which can be stated as follows:
You are a contestant on Let's Make a Deal. Monty has given you a choice of three doors. Behind two doors are goats, but one door has a nice, shiny new red car with a radio! You choose a door. Monty (who knows what is behind each door) then reveals that behind one of the other doors is a goat. He then he asks you: Do you want to switch to the other door, or do you want to stay with your original choice?

The question for you is: Should you stay with your original choice, switch doors, or does it not matter?
If you haven't before, stop and think about the problem before reading on.

Coding Horror has an article: Monty Hall, Monty Fall, Monty Crawl that a friend from work sent to me recently. I agree with the Jeff Atwood, who says:
What's interesting about this problem, to me at least, is not the solution, but the vehemence with which people react to the solution....
Here is a nice, simple explanation of the correct answer courtesy of Antonio Cangiano at Zen and the Art of Programming:
When you make your first choice your probability of winning the car is only 1/3. If you decide to switch, you will win only if the first choice you made was wrong. And since your first choice came with a 2 out of 3 chance of picking a goat, switching will then (logically) give you 2/3 chance of winning.
But don't believe me. Check out these sites:
Anyway, this is a great problem.

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