The Monty Hall Problem

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Some months ago, I had the honor of interviewing Monty Hall for a story I was writing. If you don't know, Monty created and hosted one of TV's longest-running game shows, Let's Make a Deal. (non sequitur: I'm once again reminded of that hilarious exchange in Airplane II: Lloyd Bridges's character: "If anyone has any ideas - anything at all - now is the time to speak up." Jacob: "How about a game show like Hollywood Squares, but with kids? Gary Coleman could host.")

So Monty Hall. He was one of those figures I remember from growing up "“ always on TV, someone you could trust to make you smile, an affable host with a pretty interesting game show in his command. The interview went fantastically well, and I learned a lot about not only the origins of the show (the network pulled the plug after seeing the pilot, but later threw it on the schedule as a last-minute replacement for another show that had bombed), but Mr. Hall, too.
mh-1975.jpg What I didn't know when I was a kid growing up watching the show, but only discovered in doing research for the interview, was something known as the "Monty Hall Paradox." (AKA "Monty Hall Problem") In a nutshell, the paradox asks the question: Do the player's chances of getting the car (behind door number 1, 2, or 3) increase by switching doors once a guess has been made (so technically it's down to two doors at that point).

I'll post the answer after the jump, but I'd be interested to know what you think before you click through.

theorum.pngInterestingly, the answer is always YES. From Wiki:

Once the host has opened a door, the car must be behind one of the two remaining doors. The player has no way to know which of these doors is the winning door, leading many people to assume that each door has an equal probability and to conclude that switching does not matter (Mueser and Granberg, 1999). This "equal probability" assumption, while being intuitively seductive, is incorrect. The player's chances of winning the car actually double by switching to the door the host offers.

For a very complex answer to WHY this is so, check out the full Wiki article, including a discussion of Bayes' theorem. If any of you recall my post on Mark Haddon's novel, the curious incident of the dog in the night-time, and have read the novel, you'll also find a pretty cool discussion of the Monty Hall Problem there.

July 11, 2007 - 11:54pm
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