Sometimes even I’m amazed at the things I find myself occupied with instead of sleeping. Things such as,Â __The Monty Hall Problem__. The Monty Hall Problem is arguably the most famous math/probability questions of recent times. And, I don’t think you have to be a probability or math nerd to appreciate it — I’m not, and I do.

Do you remember a tv game show called __Let’s Make a Deal?__ Oh well, that’s ok. The idea of the game show sets up the problem thusly:

This really became a big deal when addressed by __Marilyn vos Savant __(famous for holding the “Guinness Book of World Records distinction for Highest IQ”) in Parade magazine’s “__Ask Marilyn__” column. Needless to say, she’s pretty smart. Her answer was: “Yes; you should switch. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance.”

A diagram helps to visualize it:

Now, think about that for a second. And then,Â __read some of the flurry responses that this generated__. Â What’s so tantalizing about this, of course, is that it’s so goddamn counter intuitive until you really think about it and, if you carefully read through theÂ __explanation__Â (still confused? an explanation really does help to make all of this much clearer). John Tierney, who also wrote about this at length back in 1991 (“__Behind Monty Hall’s Doors: Puzzle, Debate and Answer?__“), writes __more recently__:

*“This answer goes against our intuition that, with two unopened doors left, the odds are 50-50 that the car is behind one of them. But when you stick with Door 1, youâ€™ll win only if your original choice was correct, which happens only 1 in 3 times on average. If you switch, youâ€™ll win whenever your original choice was wrong, which happens 2 out of 3 times.”Â *

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More Monty Hall Problem-related links!

The Monty Hall Problem is also treated at length in Leonard Mlodinow’s excellent and interesting book,Â

__Drunkard’s Walk: How Randomness Rules Our Lives__.There is

*a lot*to be said about this topic (enough to fill an entire book,Â__The Monty Hall Problem: The Remarkable Story of Math’s Most Contentious Brain Teaser__, Oxford University Press, 2008).The official

__Let’s Make a Deal website__has a brief chronology of how that problem has appeared and reappeared in recent years.A close relative of this is also called

__The Three Prisoners Problem__.And check out this cool interactive version from The New York Times: “

__Interactive Feature: The Monty Hall Problem__” (click on the image below to play the game at nytimes.com): “Play enough rounds and the best strategy will become clear: You should switch doors.”