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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)

#261

Post by jncfhnb »

bemusedthrow75 wrote: post #238
rspeele wrote: post #234

Earlier quoted context omitted.

I am curious how you feel about the "Monty Fall"/"Monty Crawl" problems linked elsewhere in the thread.[0] For my part I am somewhat sympathetic to jncfhnb's point. The exact phrasing that Vos Savant was asked did not specify the rules that the host was required to open a door, nor that it always must be a goat door. It simply says that the host has knowledge of what's behind the doors, and in this particular iterati…

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…

Noooo

It is not the fact that a goat is behind the door. It is the fact that a goat door would always have been opened! These two facts are not the same!

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

#262

Post by esafak »

swayvil wrote: post #244
wslh wrote: post #235

Earlier quoted context omitted.

On this topic, please watch what I think is one of the greatest scenes in movies: Kaspar Hauser directed by Warner Herzog [1]. [1] https://youtu.be/C9uqPeIYMik?si=ZjJIH1RhQFTN_ARR

Hey that riddle was in Labyrinth (with David Bowie as the goblin king!)

https://www.youtube.com/watch?v=grOpvXBmTx8

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

#263

Post by [deleted] »

jncfhnb wrote: post #261
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…

Noooo It is not the fact that a goat is behind the door. It is the fact that a goat door would always have been opened! These two facts are not the same!

[deleted]

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

#264

Post by andrewla »

grraaaaahhh wrote: post #237
andrewla wrote: post #206

The reason the scenario is kind of twisted is that in the iterated game of "you pick door, he shows goat, switch or no", vos Savant's answer is clearly correct. But in the iterated game of "you pick door, and host chooses whether to show a goat or to let you open the door you initially chose" I don't think you (or he) can get better than 50-50. If you chose the correct door initially, then he can try to trick you int…

>I don't think you (or he) can get better than 50-50. Doesn't Monty reduce your win chances to 33% just by never opening a goat door?

That's an excellent point.

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

#265

Post by jncfhnb »

bemusedthrow75 wrote: post #260
rspeele wrote: post #241

Earlier quoted context omitted.

> 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.

Suppose Car is C.

The only possible options are (equally likely)

You choose A and get shown B You choose B and get shown A You choose C and get shown A You choose C and get shown B

4 options. You lose 50% of the time.

The 2 options where you would normally get the 2/3 odds are explicitly ignored when you are told Monty chosen randomly and randomly got a goat.

You choose A and get shown C or you choose B and get shown C are forbidden.

50/50 probability on the dot.

If Monty chooses with intention then the options where you choose goat and are shown goat double in probability so you get back to 2/3

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

#266

Post by bemusedthrow75 »

jncfhnb wrote: post #261
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…

Noooo It is not the fact that a goat is behind the door. It is the fact that a goat door would always have been opened! These two facts are not the same!

I'm sorry what now? Stop second guessing the puzzle which is clearly stated.

I'm so, so done with this now that I am actually going to render inoperable my only HN account so I cannot possibly come back to this, or any other thread.

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

#267

Post by jncfhnb »

zachm0 wrote: post #248
jncfhnb wrote: post #198

Earlier quoted context omitted.

Cite where it is stated then

There is a link in the article to the first appearance of the Monte Hall problem. https://www.jstor.org/stable/2683689 On the last line of the problem he opens an empty box.

It’s still wrong. He needs to declare (or at least he needs to consistently) open an empty box; not any random box or a box of his choosing at his whim. If he opens a random box; you have not learned anything about the keys GIVEN he opened an empty box

This paper adds that in as an assumption after the prompt, which I’m pretty sure is not the original prompt

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

#268

Post by city41 »

default-kramer wrote: post #251
city41 wrote: post #143

Earlier quoted context omitted.

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.

Yeah, you make a good point. I can sort of see it both ways, I think it would depend on how the show handled it. Leaving it across a commercial break then yeah it probably does make more sense the door is random.

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

#269

Post by Verdex »

topaz0 wrote: post #168
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…

What astonishes me is not that people interpret the scenario differently, but that they are so quick to conclude that others are doing the math wrong and feel superior or even angry, rather than thinking about whether you might be talking at cross purposes about different scenarios. So I see the second order problem a bit differently: it's not "was the statement unambiguous", it's about what you do with the (possibil…

It's kind of like the xkcd airplane on a treadmill blogpost:

https://blog.xkcd.com/2008/09/09/the-goddamn-airplane-on-the...

There appears to be problems that make it easy for people to assume the worst of others.

And on a side note, I discovered about 6 months ago that mythbusters actually did this experiment. At the end of the day, few things work better than seeing something happen in real time.

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

#270

Post by kragen »

hgomersall wrote: post #236
kragen wrote: post #170

Earlier quoted context omitted.

nope, do the math edit: i ran a monty carlo simulation¹ and i was doing the math wrong. it really does matter if monty knows or not. here's the simulation where he knows: In [15]: non_censored_trials = got_car_trials = 0 In [16]: for trial in range(100_000): ...: car_door = random.randrange(3) # the other two doors have goats ...: your_door = random.randrange(3) ...: monty_door = random.choice(list({0, 1, 2} - {your_…

But if the car door is picked, there's no further game to play. Surely the only interesting thing to ask is, conditioned on seeing a goat, what's the probability the third door contains a car. The cases of observing a car are irrelevant since that's not the scenario. I'm still not convinced it's any different whether Monty Hall knows or not so long as the goat door is opened. Edit: having written this, thinking about…

your first paragraph is what i thought before running the simulation, but it turned out to be wrong. if my simulation isn't convincing to you, try writing one that is
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