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Marilyn vos Savant and the Monty Hall Problem (2015)

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Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#101

Post by ghaff »

dekhn wrote: post #93

There's the Monty Hall Problem and then there's the Second Order Monty Hall Problem Problem. That is, did the wording as it was originally printed unambiguously define the problem to be solved, or was it ambiguous enough that some people who got it wrong got it wrong for the right reason? Like many others, I completely missed that when Monty opens a door to show you a goat, he always shows you a goat. I think under c…

I think this is the original "Ask Marilyn":

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 #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat. He says to you, "Do you want to pick door #2?" Is it to your advantage to switch your choice of doors? Craig F. Whitaker Columbia, Maryland

Yes; you should switch. The first door has a 1/3 chance of winning, but the second door has a 2/3 chance. Here’s a good way to visualize what happened. Suppose there are a million doors, and you pick door #1. Then the host, who knows what’s behind the doors and will always avoid the one with the prize, opens them all except door #777,777. You’d switch to that door pretty fast, wouldn’t you?

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Yes, the question as posed by a reader was ambiguous but Marilyn made a very reasonable interpretation based on what someone at that time would probably tend to know about game shows. And she even gave an explanation (using more doors) that I find tends to work with folks combined with the explicit assumption that the host will always pick goats.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#102

Post by jncfhnb »

kergonath wrote: post #71
niklasbuschmann wrote: post #42

> 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 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 switch your choice? Without additional assumptions this original wording is not cle…

> it could be that the host always shows a goat That’s what the sentence says: “and the host, who knows what's behind the doors, opens another door […] which has a goat”. > or the host shows something at random and we just look at the cases where he shows a goat Nothing says that the host opens a door at random. Quite the contrary, we know that the host has a perfect knowledge of the situation.

Incorrect. The host doesn’t need to choose randomly. His purposeful behavior could also be random. The only way you know the switching to be optimal is if it specifically says he picks a goat door to open.

If it says he opens a door, and it has a goat, then you’ve learned nothing about the remaining two.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#103

Post by lelanthran »

paulcole wrote: post #55
bemusedthrow75 wrote: post #22

Earlier quoted context omitted.

You don't need to know whether he does or does not do that all the time. Because he did it this time? Amazed this nitpicking is still going on; it's illustrative.

I once had somebody claim the answer was wrong because we weren't sure if the contestant wanted the car or the goat. This puzzle is like a shibboleth for nitpickers.

> This puzzle is like a shibboleth for nitpickers

More like a shibboleth for sore losers.

Just look at this thread, filled with people who got the wrong answer and want to prove that either the smartest person in the world was wrong or that the question is ambiguous.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#104

Post by jncfhnb »

bemusedthrow75 wrote: post #59
niklasbuschmann wrote: post #42

> 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 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 switch your choice? Without additional assumptions this original wording is not cle…

> Without additional assumptions this original wording is not clear The only problem you are being asked to solve is the one described only in the words of the problem. That's actually what this is all about. This is a learning exercise, not just about probability, but about comprehension of what the problem as described exactly says. That's what makes it so enormously valuable.

If you’re literally following the words then you cannot solve the problem. There is no information gain.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#105

Post by Scarblac »

dekhn wrote: post #93

There's the Monty Hall Problem and then there's the Second Order Monty Hall Problem Problem. That is, did the wording as it was originally printed unambiguously define the problem to be solved, or was it ambiguous enough that some people who got it wrong got it wrong for the right reason? Like many others, I completely missed that when Monty opens a door to show you a goat, he always shows you a goat. I think under c…

I assume that at the time of writing, most readers would have been familiar with the actual game show and the fact that the host always opens a door with a goat?

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#106

Post by ghaff »

topaz0 wrote: post #95

The explanation in the article is fine as far as it goes, but I think it's much more helpful to emphasize one key fact, which is that MH has to show a goat, and can't open your first choice door, even if it's a goat. That means that if you did pick a goat the first time around, he can only have revealed the other goat, in which case switching will necessarily give you the car. That happens with probability 2/3. This…

There are probably a lot of people at this point who have never watched one of these types of game shows. Maybe if they thought about it, they'd realize that MH probably will always show a goat but it wasn't explicit in the initial question that Marilyn answered.

Certainly, that constraint is important to the final solution.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#107

Post by jncfhnb »

bemusedthrow75 wrote: post #22
tromp wrote: post #12

Earlier quoted context omitted.

It might be that he only does the reveal-and-switch offer if your original pick was the car.

You don't need to know whether he does or does not do that all the time. Because he did it this time? Amazed this nitpicking is still going on; it's illustrative.

If he only opens a door when you picked the car, then you will lose 100% of the time by switching when he shows a goat.

I instead love when people get uppity about others being wrong about Monty hall while still being wrong about Monty hall!

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#108

Post by saalweachter »

orblivion wrote: post #85
saalweachter wrote: post #81

Earlier quoted context omitted.

_Let's Make A Deal_ was on the air for twenty (thirty?) years at the time of this controversy. There was sufficient evidence for Savant's Monty -- the car was revealed 0% of the time, not 33 or 66% of the time.

I've never seen the show; I'm curious, did he always open one of the doors?

I mean, the original run ended and the first revival also went bankrupt before I was born, but my understanding of the show is that the host always presented the three doors [at the end, to the show's winner, similar to the prize puzzle at the end of Wheel of Fortune] and always eliminated one of the losers.

Fun Facts which I think I'm remembering correctly: it wasn't always a goat, they would have other random animals behind the doors as well and because of the laws regulating game shows, the goats were actually a prize, for which you would receive "the cash equivalent" of the goat, if you picked that door. But because the goat was the prize, they couldn't force you to take the cash-equivalent of the goat, if you really wanted to keep the goat. Which was a big headache the handful of times it happened, because the goats were a rental.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#109

Post by ajross »

Workaccount2 wrote: post #46

Total aside here, but this article is a good example of the problem, so I just want to point it out. People go digging, usually pretty hard, to find insults to use as capital in whatever point they are trying to make. In this case, yes, she received a lot of criticism and ad-hominem attacks for her correct answer. But she wasn't really criticized for being a woman, despite it being repeated multiple times in the arti…

> Who the fuck is Don Rivers from the town of 1,400 people in central Oregon?

FWIW, Sunriver is a resort community outside of Bend. It's not the middle of nowhere, it's filled with tech industry vacationers and wealthy retirees.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#110

Post by full_monty »

bilsbie wrote: post #73

Has anyone else spent hours on understanding this and just accepted they’ll never accept it? I completely get all the explanations but it just feels too weird.

I think I have a simple explanation. There's 1/3 chance of picking the car. 1/3 of the time you pick the car, switch and lose. 2/3 of the time you pick a goat, switch and win. Why? Because 2/3 of the time you picked a goat, Monty shows you the other goat, so if you switch you definitely get the car.
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