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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)

#251

Post by default-kramer »

city41 wrote: post #143
JackFr wrote: post #125

Earlier quoted context omitted.

> 50% of the time, monty opens another door and it has a car and you win immediately Why would you think you won? You didn't choose that one with the car and you aren't offered the opportunity to switch to the open one, only the closed one. The only interpretation which makes sense is that he always shows you a goat.

Not to mention Monty always showing a goat is what adds the tension and interest a game show needs.

I disagree. If Monty always reveals a goat, there is no tension. You know exactly what is going to happen. Maybe it could be used a way to pad the running time of the show, but it would not add tension. "Coming up next: Monty reveals what's behind one of the other doors!" seems like something a game show would do. Whereas "Coming up next: Monty reveals a goat!" does not.

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

#252

Post by kristjansson »

svantana wrote: post #247
kristjansson wrote: post #121

Earlier quoted context omitted.

As someone who misunderstood the problem as you describe, I'm much more invested in this version of the problem :) The problem statement is just a mess: > 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. even tiny edits like: > You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door which has a goat, say #3. or…

That's much better, but still not enough. We also need to add that the host will open a door regardless of which door I initially choose.

Ah yeah, good point:

> You pick a door and the host, who knows what’s behind the doors, opens exactly one of the two remaining doors according to the following algorithm: if both doors contain goats, he picks a door at random, else he picks the door he knows to contain the goat.

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

#253

Post by DerekL »

apetresc wrote: post #192
bazoom42 wrote: post #186

Earlier quoted context omitted.

> it just wouldn't make sense in the context of the game show for the presenter (who knows where the goats are) to ever open a door to reveal the car and give you the option to switch. None of it makes sense because it is not a real game show, it is a thought experiment.

Apropos the topic of being confidently incorrect, it was indeed a real show: https://en.wikipedia.org/wiki/Let%27s_Make_a_Deal Hosted by a real Monty Hall: https://en.wikipedia.org/wiki/Monty_Hall It even had the gag prizes like goats (or, as in the photo from the wiki page, a llama)

Yes, the actual show was mentioned in the article.

Also, Let's Make a Deal has been revived and canceled many times, and has been on the air since 2009.

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

#254

Post by czzr »

mihaic wrote: post #89
dynm wrote: post #75

Earlier quoted context omitted.

I actually like to back up even further and start with this problem: There are 1000 doors. You pick one. There's a 1 in 1000 chance you get it right. Now, do you want what's behind your door, or what's behind the other 999 doors? https://dynomight.net/2020/09/17/making-the-monty-hall-probl...

I think this is the clearest explanation I've heard of the principle, kudos!

Ironically this is exactly the explanation vos Savant gave in her original column.

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

#255

Post by DerekL »

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?

*Monty Hall

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

#256

Post by bhk »

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…

> the problem doesn't actually allow you to interpret otherwise

How so? The problem is typically presented as a single trial, with nothing that clarifies the intent of the host.

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

#257

Post by [deleted] »

rspeele wrote: post #241
bemusedthrow75 wrote: post #238

Earlier quoted context omitted.

It doesn't make a difference what causes Monty to reveal a goat. A goat behind a door the contestant did not choose is eliminated. That is all that matters. It could have been done by a Heath-Robinson machine, or a passing lonely shrubber, or elves. Monty isn't a floating variable in the puzzle who makes choices. His choice is fixed. Which I imagine is why vos Savant adds the actually extraneous information that Mont…

> It doesn't make a difference what causes Monty to reveal a goat. Oh, but it does! See the "Monty Fall" version of the problem, in which Monty accidentally trips and opens a door, which just happens to reveal a goat. In this variant there is no advantage gained by switching, because no more information was revealed about the remaining unopened door. The information gain only happens in the original game because we k…

[deleted]

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

#259

Post by munificent »

Lendal wrote: post #184
lamontcg wrote: post #167

The asymmetry is that if you pick the one with the car first (only 1/3rd chance) then Monty Hall can show you either of the other doors. If you pick one without a car first (2/3rd chance) then Monty Hall must show you the door that doesn't have a car and the remaining door always has the car. So 2/3rd of the time you have a 100% chance of a car if you switch, 1/3rd of the time you have 0% chance of a car if you switc…

Aha! This is the first explanation that reveals the most common error. The fact that the reveal isn't just a random door. The host must not reveal the car. That changes everything. I believe that's what most people are missing. But if you actually stated that explicitly, you would give away the answer and the problem wouldn't be fun anymore. The fun is in not explicitly stating every unconscious assumption you have a…

You would be surprised how many people do correctly understand the problem (that the host must open a door and must not reveal the car) but still get the resulting probability wrong.

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

#260

Post by bemusedthrow75 »

rspeele wrote: post #241
bemusedthrow75 wrote: post #238

Earlier quoted context omitted.

It doesn't make a difference what causes Monty to reveal a goat. A goat behind a door the contestant did not choose is eliminated. That is all that matters. It could have been done by a Heath-Robinson machine, or a passing lonely shrubber, or elves. Monty isn't a floating variable in the puzzle who makes choices. His choice is fixed. Which I imagine is why vos Savant adds the actually extraneous information that Mont…

> It doesn't make a difference what causes Monty to reveal a goat. Oh, but it does! See the "Monty Fall" version of the problem, in which Monty accidentally trips and opens a door, which just happens to reveal a goat. In this variant there is no advantage gained by switching, because no more information was revealed about the remaining unopened door. The information gain only happens in the original game because we k…

Nope.

But I am going to leave this to someone else to explain. I'm tired out now.

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