Nice 1991 article re the Monty Hall Problem -"Behind Monty Hall's Doors: Puzzle, Debate and Answer?"

[astro]

[Article here](Behind Monty Hall’s Doors: Puzzle, Debate and Answer?)

Perhaps it was only an illusion, but for a moment here it seemed that an end might be in sight to the debate raging among mathematicians, readers of Parade magazine and fans of the television game show “Let’s Make a Deal.”

They began arguing last September after Marilyn vos Savant published a puzzle in Parade. As readers of her “Ask Marilyn” column are reminded each week, Ms. vos Savant is listed in the Guinness Book of World Records Hall of Fame for “Highest I.Q.,” but that credential did not impress the public when she answered this question from a reader:

"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 other 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 take the switch.

[Dewey_Finn]

Your URL is broken.

[Dewey_Finn]

I think this is the article you meant:

Behind Monty Hall's Doors: Puzzle, Debate and Answer? (Published 1991)

[Hari_Seldon]

I really really cannot understand the confusion. Think of it as trying to pick the wrong door. Two chances in three, right. Then always switch. If you chose the wrong door the first time, you win. If you chose the “right” door the first time, you lose. Too bad, but you will succeed two times in three.

It is said that even Paul Erdos could not be convinced of this. Astonishing! The math/computer science editor for American Scientist admits he didn’t believe and ran a Monte Carlo simulation which convinced him.

[Frylock]

I’m with you Hari. Though I was surprised by the solution at first, a single simple explanation along the lines of the one you gave was all it took. Now it seems almost obvious.

[Half_Man_Half_Wit]

@Hari_Seldon

I really really cannot understand the confusion. Think of it as trying to pick the wrong door. Two chances in three, right. Then always switch. If you chose the wrong door the first time, you win. If you chose the “right” door the first time, you lose. Too bad, but you will succeed two times in three.

It is said that even Paul Erdos could not be convinced of this. Astonishing! The math/computer science editor for American Scientist admits he didn’t believe and ran a Monte Carlo simulation which convinced him.

I actually did the same thing, though nowadays (through prolonged exposure) I too find the usual explanations intuitive, and can’t really fathom my reasons for resisting them anymore. It’s been a useful lesson in intellectual humility for me: whenever I find myself to be dead certain about something, consider it obvious and any dissenter to be misguided, I try and remind myself about how I was dead wrong on such a simple question.

[Learjeff]

This particular dead horse has been pretty thoroughly beaten already:

Let's make a deal (about a really, really beaten dead horse)

[ftg]

Again, not a very good article. MvS didn’t clearly state the conditions of the problem. (She did at least say that Mr. Hall knew what was behind each door.) E.g., if you leave out the condition that Hall makes the offer regardless of what door you picked, then many people think that the offer might be a tactic to get you to switch from the big prize. Etc.

I was always disgusted by her slam on people coming up with other answers when she didn’t state the problem clearly, as she does all too often.

[BigT]

@ftg

Again, not a very good article. MvS didn’t clearly state the conditions of the problem. (She did at least say that Mr. Hall knew what was behind each door.) E.g., if you leave out the condition that Hall makes the offer regardless of what door you picked, then many people think that the offer might be a tactic to get you to switch from the big prize. Etc.

I was always disgusted by her slam on people coming up with other answers when she didn’t state the problem clearly, as she does all too often.

But, according to her, most people did not argue based on the wording of the problem, and in fact seemed to have interpreted the problem the same way.

I know for sure that Cecil, when he got it wrong, did not argue based on the lack of clarity in the premise.

When even “the Perfect Master” gets it wrong, I do think you have the right to gloat.