Monty Hall Problem

by JT McGee

On Tuesday I proposed a question of probability. The correct answer to the problem is to swap, since it does net out a better possible outcome by a marginal, but measurable degree. As Mark said in a comment, this is a derivative of the Monty Hall problem.

This question is used by interviewers for jobs on trading desks, too.

Monty Hall

The Monty Hall problem is named after the man who hosted the TV show “Let’s Make a Deal.” At the end of the show, the contestant was asked to pick from one of three doors. Behind one door is a car, behind the others are two goats.

After the contestant makes their choice, the door is opened to one of two doors that were not selected. The goat appears. Now the contestant has to make a choice, he or she can swap their door for the remaining unopened door or keep the door originally picked. The contestant should choose to switch, as it would improve their odds dramatically. In fact, the door originally chosen has a 1/3 probability of winning, whereas the remaining unopened door has a 2/3 probability.

Wikipedia explains this best with this drawing:

PhDs Disagree

According to the Wikipedia page from which I’m stealing the majority of the content here, the magazine Parade ran an article showcasing the mathematics behind the decision. More than 10,000 people wrote in to disagree, thinking that it didn’t matter. It does. Interestingly, more than 1,000 of the 10,000 people had PhDs.

In just one week, we’ve already beat MBAs at retirement planning and PhDs at basic algebra. Next week, we’ll talk about methods to walk on water.

{ 6 comments… read them below or add one }

Buck Inspire August 4, 2011 at 20:32

Never thought I would read a Monty Hall post! Initially I thought it wouldn’t matter either, but that Wikipedia drawing does logically spell it out. Did you take probability or statistics in college?

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JT August 5, 2011 at 07:28

I should have known that a TV personality would draw you in. 😉

In answer to your question, yes and no. I understand practical statistics, most of which I learned from using Excel. But if you asked me a question in statistics jargon, I’d be lost.

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Hunter @Mapblog August 4, 2011 at 21:55

This issue was presented in the movie “21”. I didn’t get how it made a difference and I can see how it could stump some smart people out there.

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JT August 5, 2011 at 07:29

Oh yeah, I forgot about 21! There’s a really good History Channel documentary about the 21 team from MIT that’s worth the time to watch. It came out before the movie, and is probably more accurate to the real story.

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retirebyforty August 5, 2011 at 16:13

It doesn’t matter because you have 50% chance to win the car no matter which door you pick originally.
Since the host will always open a door with a goat in it, you can’t count that door in the probability equation. If they randomly open any door, then it will affect your choice. IMO.

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Car Negotiation Coach August 7, 2011 at 21:22

I think I’m probably one of the few people in the US that actually seriously factors in how much the goat is worth when I watch stuff like this.

JT- Do you know how much a healthy goat goes for on the open market? My guess is probably $300-$400 if not more. Shouldn’t that factor in?????

p.s. Of course you’ll still have to pay taxes on the goat so it’s more like $200-300….but if you’re into goat milk or goat cheese that should also be factored in.

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