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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)

#151

Post by topaz0 »

fortran77 wrote: post #70
gerad wrote: post #39

The intuitive way for me to understand the Monte Hall problem is to pretended there are 1000 doors. You pick 1. There’s a 1 in 1000 chance you get it right. The host then opens 998 doors that don’t have the prize. Do you keep your original or do you switch? Are the odds 50:50?

But this is wrong. The odds become 2/3 in the original problem, not 50:50. Your "intuition" isn't helping you.

I think GP is implying that you would reject 50:50 as absurd in this case (answer that rhetorical question with a "no"), and therefore should also reject it in the original. I agree that was not clear, though.

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

#152

Post by michaelcampbell »

Karellen wrote: post #50
gerad wrote: post #39

The intuitive way for me to understand the Monte Hall problem is to pretended there are 1000 doors. You pick 1. There’s a 1 in 1000 chance you get it right. The host then opens 998 doors that don’t have the prize. Do you keep your original or do you switch? Are the odds 50:50?

What improvement does your 1000-door variant have over the 100-door variant described in the article?

Bigger numbers make it easier to convince yourself if skeptical.

The problem stated with 3 doors is hard, with 5 is still not quite there for many. 100, 100, 10_000_000... becomes almost absurd.

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

#153

Post by TotempaaltJ »

I've read through this thread, and for anyone criticising the Monty Hall problem, the article, or Vos Savant herself, I recommend reading the original responses by Vos Savant, available on her website on te Internet Archive: https://web.archive.org/web/20181118225305/http://marilynvos...

They address every single (meta) concern I've read here.

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

#154

Post by empyrrhicist »

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…

Your re-framing is actually not quite right either (or at least, not complete). Key point: if the host picks the car, the game essentially re-sets.

Imagine the extreme scenario with 999 goats and 1 car. You select the first door, the host opens 998 doors at random, leaving your selected door and one other. Two scenarios are now possible:

1. There was a car in the 998 doors that got opened. Tough luck, you lose the game automatically now (game resets).

2. There was not a car in the 998 doors. In this scenario, you are still advised to switch.

Edit - I guess I misremembered a simulation I once did about it.

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

#155

Post by jncfhnb »

bemusedthrow75 wrote: post #147
jncfhnb wrote: post #145

Earlier quoted context omitted.

I have not restated the problem. You’ve incorrectly assumed that I would be showing you a goat in every case. But that is not included in the prompt. All you know is that you were shown a goat on one play. This is possible in the setup I’ve listed. You landed in that 33% case where you chose a car. There is nothing in the prompt that says we are not playing my variant of the game. Being told that you SAW a goat does…

> You’ve incorrectly assumed that I would be showing you a goat in every case. But that is not included in the prompt. Yes. It is. It is a fixed part of the scenario. Monty opens a door and shows you a goat. He knows it is going to be a goat (he is "well-aware of what is going on behind the scenes"). He's showing you a goat as part of the problem which is: should you switch? Again: think through what the problem actu…

No! Read the prompt very carefully.

> Imagine that you’re on a television game show and the host presents you with three closed doors. Behind one of them, sits a sparkling, brand-new Lincoln Continental; behind the other two, are smelly old goats. The host implores you to pick a door, and you select door #1. Then, the host, who is well-aware of what’s going on behind the scenes, opens door #3, revealing one of the goats.

You know nothing except you picked door 1 and then he decided to show door 3.

You do not know if he would have shown door 3 had you picked door 2! This is NOT in the prompt. You cannot assume that.

The experience of this contestant is fully and equally possible within my version of the game too!

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

#157

Post by empyrrhicist »

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…

nvm

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

#158

Post by TotempaaltJ »

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…

Vos Savant mentions this, and she's kept track of who did and didn't understand the conditions:

> And a very small percentage of readers feel convinced that the furor is resulting from people not realizing that the host is opening a losing door on purpose. (But they haven’t read my mail! The great majority of people understand the conditions perfectly.)

https://web.archive.org/web/20181118225305/http://marilynvos...

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

#159

Post by neverartful »

The following visualization helps to understand the answer:

https://imgur.com/a/hkme8jG

For the 3 different scenarios, switching is the correct choice in 2 instances. Not switching is the correct choice in 1 instance. 2/3 chance that switching will help you to win.

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

#160

Post by kragen »

dekhn wrote: post #112
ghaff wrote: post #101

Earlier quoted context omitted.

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…

Yes, I'm literally talking about this sentence: "host, who knows what’s behind the doors, opens another door, say #3, which has a goat." I parsed that as "50% of the time, monty opens another door and it has a car and you win immediately, and 50% of the time, monty opens another door and it has a goat". In retrospect I think my brain just sort of pictured that and proceeded to assume there was no reason to switch, an…

counterintuitively, it doesn't actually matter whether monty knew there was a goat before he opened the door; what matters is that you observed the goat, so you know you're not in one of the possible worlds where he opened the car door

edit: this is wrong, dekhn was right, see below

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