Marilyn vos Savant and the history of the Montel Hall question

I vaguely remember the controversy. The Monty Hall Problem is pretty counter-intuitive and, in fairness (it was touched upon in the article) in "real life" it works a little different than it was presented in the original hypo.

Still, a resounding victory for the genius and proof that the Internet didn't invent the shrill response crowd, it just perfected it.

Enjoyed the read.

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Marilyn vos Savant

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She was pretty good-looking back in the day.
I've always had a thing for really smart chicks.





Dumb ones too, come to think of it.

Doesn't it matter more whether the opened door was chosen at random or picked specifically because it did NOT have the car? This issue confuses me even after reading the details.

Assuming the game host would never open a door containing the car, there are 12 possible scenarios here (4 separate ones for each door containing the car):

If Door 1 contains the car:

1) Guest picks Door 1, host opens Door 2. If guest switches, lose. If guest stays, win.

2) Guest picks Door 1, host opens Door 3. Switch: lose. Stay: win.

3) Guest picks Door 2, host opens Door 3. Switch: win. Stay: lose.

4) Guest picks Door 3, host opens Door 2. Switch: win. Stay: lose.

Theoretically there would be 2 more scenarios for Door 1 containing the car, but those would involve opening Door 1 which we've already ruled out for purposes of the contest. So far, switching is 50/50.

If Door 2 contains the car:

1) Guest picks Door 1, host opens Door 3. Switch: win. Stay: lose.

2) Guest picks Door 2, host opens Door 1. Switch: lose. Stay: win.

3) Guest picks Door 2, host opens Door 3. Switch: lose. Stay: win.

4) Guest picks Door 3, host opens Door 1. Switch: win. Stay: lose.

Still 50/50 by switching vs. staying.

If Door 3 contains the car:

1) Guest picks Door 1, host opens Door 2. Switch: win. Stay: lose.

2) Guest picks Door 2, host opens Door 1. Switch: win. Stay: lose.

3) Guest picks Door 3, host opens Door 1. Switch: lose. Stay: win.

4) Guest picks Door 3, host opens Door 2. Switch: lose. Stay: win.

Once again, 50/50.

What am I missing here?

I don’t follow her logic. We’re ultimately presented with information that a prize is behind one of two doors. Why should it matter which one is called door number 1, 2, or 3? Why should it matter that the original question was posed as if the odds were 1 in 3?

Let’s work it backwards. There are two doors. A prize is behind one. The odds of correctly guessing which door the prize is behind is 50/50, right? You choose one. I ask you if you want to change your mind. If you do and choose the other door, did the odds of correctly guessing suddenly change? Or is it still 50/50 odds? If so, explain. What about if I suddenly say, “Would you change your mind if I told you there was another door that did NOT have a prize behind it, would you change your mind?” Would that additional question and fact suddenly change the odds to 1 out of 3? What if I said there were 100 additional doors that a prize was NOT behind? Does that make the original question anything different than a 50/50 chance?

I still don’t understand how her answer is regarded as correct.

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I'm with you since I"m not a math/probability guy AT ALL, but how someone explained it to me was this.

At the start when you pick a door, you have a 33% chance of guessing correctly. After 1 door is revealed to be nothing, now your chances of picking the correct door are 50/50 between car and goat, so you're "supposed" to switch. I don't really get it, but that's how it was told to me.

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Look at it this way:

There are 3 doors. You pick door 1. The host says, "You can either keep door 1 or have BOTH of the the other doors."

You know for sure that at least one of these other two doors have a goat behind it, but you will still make the switch because two doors are better than one.

The actual problem follows the same logic.
You pick a door, and then are given the option of keeping your door or switching to the other 2 doors. The only difference is that this time they show you that one of the other two doors has a goat behind it...but you already knew with certainty that one of these two doors had a goat behind it, so him showing it to you doesn't change anything.

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I thought you were going to reference the time that she stated that there is a 50/50 chance of flipping heads even after 9 heads in a row.

I recall that caused a stir.

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Are you saying you disagree with that?

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You are the goat!
Glenn Calkins
Western State College

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