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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)

#271

Post by jncfhnb »

bemusedthrow75 wrote: post #266
jncfhnb wrote: post #261

Earlier quoted context omitted.

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.

It is NOT STATED in THIS VERSION OF THE PROMPT that monte will always open a door and that it will always be a goat door.

It is simply stated that on one play of the game, Monte CHOSE to open a door and it was a goat. If this is truly all you know, you have learned nothing.

It is only useful information if monte explicitly opens a goat door for you. If he opens a door at random and gets goat your information gain goes away even if it’s the same door!

I’ve literally mapped it out for you else where. There’s only 4 outcomes. You can check yourself.

2:2

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

#272

Post by mhb »

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?

Yes. Just like in TFA.

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

#273

Post by petesergeant »

HarHarVeryFunny wrote: post #239
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 eithe…

> The simplest way to explain why switching is the correct strategy

In my experience the most _intuitive_ explanation is to simply ramp it up to 100 doors, with Monty opening 98 of them, to make it clear that switching offers you the benefit of all unopened doors.

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

#275

Post by SeanLuke »

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…

> 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.

The second part I agree with, but not the first part; because it sounds like you're saying MH is required by the rules to reveal a goat. But the problem works fine if he always opens a remaining door at random and it happens to be a goat.

I'd say it as: once you had chosen a door, Monte was required to open some other door. And the door he happened to open, for whatever reason, had a goat.

Wouldn't that work?

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

#276

Post by kragen »

calderknight wrote: post #220
kragen wrote: post #210

Earlier quoted context omitted.

it's pretty counterintuitive that his personality enters into it, isn't it?

If the format of the game allows him to show the car to the player, how could his personality not enter into it? In every case where the player picks a goat-door, the host will be presented the option to either reveal the car or the goat. I mean, one can imagine various complicated scenarios in which the host might reveal the car exactly 50% of the time in such cases, but none seem like they can be reasonably arrived…

it turns out that there is in fact no way that his personality could not enter into it, but that was not obvious to me until i did the simulation. even if he chose to reveal the car exactly 50% of the time in such cases, that would be a result of his personality, wouldn't it?

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

#277

Post by topaz0 »

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…

Yes, it's exactly 50/50. It's not hard to work out the details, as I did in another thread elsewhere on this article. Here goes:

-There's a 1/100 chance my door is a car, in which case it doesn't matter which of the others stays closed, it will always be a goat. The game will proceed, and switching will lose.

-There's a 99/100 chance my door is a goat, in which case the car is behind some other door. Choosing 98 out of 99 doors to open at random is the same as choosing 1 out of 99 doors to leave closed at random. So the chance that the car stays hidden in this case (so that switching will win) is 1/99, and 98/99 that the game ends early because the car is revealed.

-Adding it up, the game ends without the chance to make a choice 99/100 * 98/99 = 98/100 of the time. Of the remaining 2%, 1/100 comes from the first case (switching loses) and 99/100 * 1/99 = 1/100 comes from the second case (switching wins). The strategies are equally effective.

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

#278

Post by tsimionescu »

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…

> the fact they all contain goats is pretty suggestive that I have the car, or at least 50/50

That's exactly the point. If he doesn't know, then it's exactly 50/50 and there is no reason to switch. If he does know, then it's 1/NUM_DOORS versus NUM_DOORS-1/NUM_DOORS, so you'd be crazy not to switch.

The point is, if he picks at random, in the 100 door case, the vast majority of the time he will open the car door while opening those 98 doors. The case where you get to pick again would be exceedingly rare. Conversely, if he only opens goat doors, you will get your second pick 100% of the time.

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

#279

Post by petesergeant »

city41 wrote: post #242
tialaramex wrote: post #185

Earlier quoted context omitted.

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.

Also it’s a lot more fun to simply shout “FALSE”

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

#280

Post by zachm0 »

jncfhnb wrote: post #267
zachm0 wrote: post #248

Earlier quoted context omitted.

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

If I understand correctly, you’re saying Monte’s intention (randomly picking an empty box vs purposely picking an empty box) is effecting the odds that the box in hand has keys?

Also, do you have any evidence that this isn’t the original?

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