Marilyn vos Savant and the Monty Hall Problem (2015) • Hacker News Board

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

#241

Post by rspeele » Mon, Feb 26, 2024, 9:09 PM UTC

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…

> 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 know that Monty was forced to avoid the winning door in the (66% likely) case where we didn't already pick it.

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

#242

Post by city41 » Mon, Feb 26, 2024, 9:09 PM UTC

tialaramex wrote: post #185

NoboruWataya wrote: post #161

Wow, I knew about the problem and was vaguely aware that it had generated some controversy amongst statisticians but I had no idea about the insanely arrogant and obnoxious (not to mention wrong) abuse Marilyn had received from the "intellectual elite". I have little sympathy for the "ambiguous question" defence. Not only is Marilyn's interpretation grammatically valid, it just wouldn't make sense in the context of t…

Also regardless of whether she's a woman or she's known for intelligence, a response in which you say "You're wrong" needs an extra second's thought to consider whether, in fact, they are wrong, or maybe just their understanding is different from yours and you need to reconsider with their context. Some time back in an HN thread about programming languages I read a response in a thread about inference which said that…

I almost never say "you're wrong", no matter how confident I am. Because I can be, and often am, wrong myself. If there is a disagreement, a miscommunication, etc, why not instead work with the person to find where you two differ and look for common ground? If the other person really is wrong, it's almost always naturally revealed that way.

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

#243

Post by failrate » Mon, Feb 26, 2024, 9:11 PM UTC

The great thing about the apparent paradox is that you can write up a quick script in your favorite language and test it. I did not (quite) jive with this answer until I simulated it myself and golly gee!

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

#244

Post by swayvil » Mon, Feb 26, 2024, 9:13 PM UTC

wslh wrote: post #235

NoboruWataya wrote: post #161

Wow, I knew about the problem and was vaguely aware that it had generated some controversy amongst statisticians but I had no idea about the insanely arrogant and obnoxious (not to mention wrong) abuse Marilyn had received from the "intellectual elite". I have little sympathy for the "ambiguous question" defence. Not only is Marilyn's interpretation grammatically valid, it just wouldn't make sense in the context of t…

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!)

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

#245

Post by jncfhnb » Mon, Feb 26, 2024, 9:13 PM UTC

LegibleCrimson wrote: post #228

jncfhnb wrote: post #221

Earlier quoted context omitted.

You confused yourself. There are four possible outcomes at the end, but they are not equally likely. So not 50/50. If Monty always shows a goat, it is undeniably a 2/3 chance to win on switch. The nuance here being discussed is whether you can assume Monty would have shown you the goat had you chosen a different initial door just because he showed you one this time. If you don’t know that, then you don’t learn anythi…

I'm covering the problem statement. I'm ignoring the cases where Monty revealed a car because it didn't happen. You can't chalk it up as a win or a loss, because it didn't happen. It's always "You choose a door, the host reveals a goat behind another door. Do you switch?" The scenario does not include him revealing the car. If he intentionally chooses a goat, switching gets the car 2 times out of 3. If he chose rando…

Yes you’re correct. You’re just the first person I’ve ever seen cover the true random Monty variety who doesn’t force the situation where he shows a car in as a win or loss.

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

#246

Post by jncfhnb » Mon, Feb 26, 2024, 9:15 PM UTC

habinero wrote: post #230

jncfhnb wrote: post #178

Earlier quoted context omitted.

> Monty isn't a contestant. Monty's action and outcome is part of the fixed description of the problem. He opens one of the doors and reveals a goat. Full stop. Incorrect and I invite you to cite the line of the prompt that says otherwise. This is the critical missing piece of information that makes it the commonly understood “Monty hall problem” and not the improperly stated prompt that we actually have. “Monty did…

No, you're solving the wrong thing. This is a thought experiment, not a real life scenario with ambiguity. In this thought experiment, MH will always open a door to a goat on purpose and always ask if you want to switch, because the entire point of the thought experiment is that people find the 2/3 odds if you switch unintuitive and baffling, leading to extremely long thread chains. You're doing the equivalent of say…

With all due respect, no. Please don’t jump in at the end of a long thread and bring it back to the beginning. We are not discussing “The Monty Hall Problem”. We are discussing the specifics of the actual original prompt with its failure to document all assumptions.

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

#247

Post by svantana » Mon, Feb 26, 2024, 9:17 PM UTC

kristjansson wrote: post #121

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…

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.

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

#248

Post by zachm0 » Mon, Feb 26, 2024, 9:23 PM UTC

jncfhnb wrote: post #198

KrazyButTrue wrote: post #193

Earlier quoted context omitted.

> If you don’t have a guarantee that he will always open a goat door... Well you do have that guarantee -- as it is stated in the problem. It's clear that no matter what door you open, you will be shown a goat.

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.

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

#249

Post by harshreality » Mon, Feb 26, 2024, 9:24 PM UTC

lucas_membrane wrote: post #226

NoboruWataya wrote: post #161

Wow, I knew about the problem and was vaguely aware that it had generated some controversy amongst statisticians but I had no idea about the insanely arrogant and obnoxious (not to mention wrong) abuse Marilyn had received from the "intellectual elite". I have little sympathy for the "ambiguous question" defence. Not only is Marilyn's interpretation grammatically valid, it just wouldn't make sense in the context of t…

>> The game would be reduced to "does Monty feel like gifting you a car or a goat today". But, in fact, that is the way the real show worked. He was more likely to give you a car when he hadn't given away any cars for a while. And Marilyn's description of the problem included no information about whether or not Monty offered to swap doors rarely, frequently, or always, or about the previously observed outcomes depend…

If you're playing the game as stated, and if the host opens a door revealing a goat, you must switch for the best odds.

The offer to switch doors is part of the problem statement. You can't justify your decision based on the possibility in the real game that you might not get the offer to switch (which would mean that when you do it might be an intentional red herring).

Even if there's a 50% chance there are all goats, or a 75% chance, you still switch. That reduces the overall probability of a win, but it doesn't affect the relative probability from switching. The only reason you might not want to switch is if the first choice had been forced, such that there was an above-random chance that your first pick was the car.

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

#250

Post by jcl » Mon, Feb 26, 2024, 9:24 PM UTC

Scarblac wrote: post #105

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?

As Monty Hall pointed out in interviews, he was not obligated to offer the opportunity to switch and sometimes did not. So in this case knowledge of the actual show may have contributed to confusion.

https://en.wikipedia.org/wiki/Monty_Hall#Monty_Hall_Problem

(But vos Savant stated in later columns that most of the critical responses she received assumed that the host was obligated to offer the switch, so they were genuinely confused by the paradox.)