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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)

#231

Post by paulcole »

dekhn wrote: post #225
paulcole wrote: post #223

Earlier quoted context omitted.

Do you think that given the context of the puzzle – about a US game show, printed in a US paper that the question is being asked in many developing countries? Or are you looking to find fault with something for the sake of finding fault?

No, I'm making the pooint that in many parts of the world, a goat is more valuable than a car because of the lack of car infrastructure.

Incredible point. Thank you for your service.

The shibboleth for nitpickers title is locked up.

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

#232

Post by habinero »

Jimmc414 wrote: post #35

I never understood this one. Not choosing a new door seems like an implied 50/50 choice to keep your original selection. edit: I know it works out on paper, but if I put myself in the situation, I know that if I decided not to choose again that is a choice and I am re-choosing the same door.

The difference is MH knows what's behind the doors and deliberately shows you a goat.

It's not 50/50 because the choice wasn't random.

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

#233

Post by digitalscribe »

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…

> Not only is Marilyn's interpretation grammatically valid

I would consider both interpretations equally valid. If anything, in law we have the "rule of the last antecedent" (phrase/clause modifies nearest antecedent noun) so that the hater's interpretation could be more correct if based only on this rule.

This language is ambiguous: "host ... opens another door, say #3, which has a goat."

The two options are Marilyn's interpretation of the door always containing a goat (invariant version), or that one door he opens (say #3) just happens to contain a goat (hater's version) but it could have contained a car.

As suggested by someone below, a much clearer formation could have said "host opens a door with a goat, say door #3" to avoid this particular ambiguity.

There's also the issue of usage of "which" signifying a non-restrictive non-essential clause.

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

#234

Post by rspeele »

bemusedthrow75 wrote: post #140
jncfhnb wrote: post #132

Earlier quoted context omitted.

Ok let’s play! We play this game 1000 times. 33% of the time you pick the car and I show you a goat. You switch and lose 100% of the time. 66% of the time you pick a goat and I don’t show you a goat. Assuming you don’t switch because you believe this means you have an equal odd on your current door, you lose 100% of the time. Congrats. You have lost every single round.

You've restated the problem (incorrectly) -- changed it. There's still a goat you could show me. And it is a fact that you show me a goat. Nowhere in the problem does it suggest there is a chance you show me a goat. I do honestly admire your dogged commitment, and I think the way you are committed shows up an important point about the article and the history of the problem. Which is that one can quite clearly fairly…

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 iteration of the game, he showed you a goat and asked you about switching.

That does not exclude a scenario where the host is a manipulative fellow, who chose to show you the goat only because he knows you are about to win, trying to convince you to lose. A contestant on the real show would surely worry about this possibility.

Of course, the people who wrote to disagree with Vos Savant almost never said "the problem is not fully stated", they said "it's 50/50 you fool", which isn't right. Additionally, since it wouldn't be a math problem at all if we let the host have agency, it is reasonable to assume the unspoken rule that he does not, leading to Marilyn's correct 2/3rds answer.

[0]https://web.archive.org/web/20230706235720/https://probabili...

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

#235

Post by wslh »

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

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

#236

Post by hgomersall »

kragen wrote: post #170
Chinjut wrote: post #165

Earlier quoted context omitted.

If you want the result where there is a lower conditional probability of your originally selected door having the prize versus the remaining unopened door, then it completely does matter to have the setup be "Monty always opens a door with a goat" instead of "Monty opens a door at random, and in this particular case, it happened to have a goat behind it".

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 the 100 door case. If 98 random doors open (that aren't the one I picked) then the fact they all contain goats is pretty suggestive that I have the car, or at least 50/50. I'm not convinced by the code example though.

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

#237

Post by grraaaaahhh »

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?

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

#238

Post by bemusedthrow75 »

rspeele wrote: post #234
bemusedthrow75 wrote: post #140

Earlier quoted context omitted.

You've restated the problem (incorrectly) -- changed it. There's still a goat you could show me. And it is a fact that you show me a goat. Nowhere in the problem does it suggest there is a chance you show me a goat. I do honestly admire your dogged commitment, and I think the way you are committed shows up an important point about the article and the history of the problem. Which is that one can quite clearly fairly…

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 Monty is fully aware what is going on behind the scenes -- to underscore the concept that Monty isn't a variable.

The fact that a goat behind an unchosen door was revealed is what is crucial to the setup of the entire puzzle.

And that -- despite jncfhnb's protestations -- is information that makes the puzzle determinate.

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

#239

Post by HarHarVeryFunny »

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…

I think the problem statement is clear, and is independent of how the TV show actually operated.

The problem posed is that you have three closed doors, behind one of which is a car, and behind the other two are goats. You get to pick one of the closed doors, and will win whatever is behind it (you want the car).

One of the doors you did not pick is now opened, revealing a goat. You therefore now know the car is either behind the door you picked or behind the other closed door.

In this setup, the question is: if offered the chance to switch your selection from the door you initially picked to the other closed door, should you switch? Does it make a difference?

Mariyln Vos Savant said switch. The peanut gallery (some statisticians who should have known better) said it makes no difference - with two doors left you've got a 50/50 chance of winning the car whether you switch or not.

First off, you can run multiple simulations of the game (with random positions of the goats and car), and prove for yourself that always switching is a better strategy, so it's sad that anyone would insist that it's not, even if that seems logical.

The simplest way to explain why switching is the correct strategy is this:

When you make your initial selection, you have:

a) A 1/3 chance of selecting the car, and

b) A 2/3 chance of selecting one of the two goats

So, 1/3 of the time you selected the car and will therefore lose if you switch, and 2/3 of the time you selected a goat and will therefore win if you switch. Switching will therefore be a winning strategy 2/3 of the time.

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

#240

Post by [deleted] »

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

[deleted]
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