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The Time Everyone “Corrected” the World’s Smartest Woman (2015)

priceonomics.com

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Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#221

Post by megablast »

6gvONxR4sf7o wrote: post #121
lachstar-x wrote: post #102

Earlier quoted context omitted.

Can you help me understand - in my view the choice to switch doors or keep the same door is irrelevant, because even if you keep the same door you're making a choice that is now 2/3 of the right answer. If you switch or keep, you're still choosing from two doors that contain a car and a goat. The other door is no longer relevant and doesn't affect the new state at all. It's your perspective (narrowing the choice down…

I wrote out a hopefully helpful intution down below [0]. Here's a terse part of it: > Or just imagine monty hall with infinite doors. I'm thinking of a number between 1 and infinity (secretly, it's 19083412039102388171230123). You pick a number, and then I'll narrow down your choice to two options. Do you think you just happened to pick my number, or do you switch? You're right that it's absolutely the narrowing down…

Ok. But you picked a very very very very small number between 1 and infinity. That can’t be random.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#222

Post by galaxyLogic »

mkl wrote: post #185
listenallyall wrote: post #166

Earlier quoted context omitted.

You're quoting Priceonomic's 2021 description of the problem. This is NOT the 1990 Parade Magazine description of the problem that generated all the responses.

The 1990 Parade Magazine description is almost identical (and actually more explicit, since "say #3" is a removable parenthetical): "the host, who knows what’s behind the doors, opens another door, say #3, which has a goat" -- https://web.archive.org/web/20130121183432/http://marilynvos... The host's knowledge is explicitly mentioned, and the only purpose this could have is that so he can use it to avoid giving the g…

Yes.

The probability that car is behind the door NOT selected by the host is 1/2 - because the host had only two choices which are equally good for him.

Probability that car is behind the door initially selected by the user is 1/3 because that is what happens when you randomly choose one out of three.

We have to think in terms of two different probabilities: a) That user selects the correct door initially and b) That door not selected by the host has the car.

But yes it is counter-intuitive. I can't quite point out which step in the flawed reasoning of no benefit from switching occurs. How do people come up with the incorrect result, and what are the flawed assumptions they make that cause them to arrive at the wrong answer? Where exactly does the logical error happen?

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#223

Post by flomo »

hn_throwaway_99 wrote: post #116
6gvONxR4sf7o wrote: post #13

There are a number of things I like about the monty hall problem. There's the history, the unintuitiveness, the subtle easy-to-screw-up nature of probability problems, the calculation, the sociology, and the overconfidence of wrong experts. Most of all, it's the calculation vs intuition that I like. You can do the calculation, or run simulations and prove correctness. In fact, it would be much harder to be so widely…

In this case, though, I don't believe it's just calculation vs. intuition. The reason the 100 or million door problem helped me understand was because it clarified an implicit rule of the game: that the door the host chooses to open is not random . If it were random, it would make for a very boring game ("Uhh, there's the prize, you win, I guess that's game over.") Once I understood that the host would only ever open…

One of the sources of confusion with this is Monty Hall did not always behave the way the problem dictates. He sometimes would open the prize door right away, or he would reveal a goat that was not behind a door or etcetera.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#224

Post by listenallyall »

leephillips wrote: post #179
failwhaleshark wrote: post #128

Earlier quoted context omitted.

Lol. I worked at a biomedical informatics shop with IITians and other folks who were MD + PhD CS. No one referred to anyone as doctor and no one there took a MENSA test. I think it's safe to say the only "doctors" are clinical MDs, podunk colleges to seem elitist, and Spies Like Us during the surgery scene.

Only losers take Mensa tests and talk about their IQs. But plenty of PhDs use the Dr title in the right context. It's just the height of jerkdom to insist on people addressing you with it.

> the height of jerkdom to insist on people addressing you with it

Tell that to Dr. Jill Biden. Who doesn't even have a Ph.D.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#225

Post by casefields »

tmule wrote: post #141

There’s a bit of historical revisionism at play in the article. Here’s an accurate representation by Aaron Brown of what transpired: https://www.quora.com/Why-do-some-PhDs-argue-against-Marilyn... Quoting for those who don’t want to go off-site: “You have to have lived through this ancient travesty to care about it. It’s probably best forgotten. Marilyn Vos Savant published an incorrect answer to the Monte Hall probl…

Wait, if she did get the original wrong and only presented the correct answer on her third solution, where's the proof? This whole thing would be a waste of time if that's true.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#226

Post by flomo »

hn_throwaway_99 wrote: post #116
6gvONxR4sf7o wrote: post #13

There are a number of things I like about the monty hall problem. There's the history, the unintuitiveness, the subtle easy-to-screw-up nature of probability problems, the calculation, the sociology, and the overconfidence of wrong experts. Most of all, it's the calculation vs intuition that I like. You can do the calculation, or run simulations and prove correctness. In fact, it would be much harder to be so widely…

In this case, though, I don't believe it's just calculation vs. intuition. The reason the 100 or million door problem helped me understand was because it clarified an implicit rule of the game: that the door the host chooses to open is not random . If it were random, it would make for a very boring game ("Uhh, there's the prize, you win, I guess that's game over.") Once I understood that the host would only ever open…

One of the sources of confusion with this was Monty Hall did not always behave the way the problem dictates. He sometimes would open the prize door right away, or he would reveal a goat that was not behind a door or etcetera.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#227

Post by megablast »

gonehome wrote: post #69
dllthomas wrote: post #34

Earlier quoted context omitted.

Interestingly, if the host picks randomly (and if he reveals the car, you... start over, or you get the car, or you get nothing, or ... it doesn't matter because it happens not to have happened in the time we're considering) then you are faced with a 50/50 chance.

Yeah - and at least for me this was part of the confusion. The problem is often stated incorrectly. Critically the host always removes a goat. If the person presenting the problem just says “the host opens one of the doors”, but doesn’t specify he’s always revealing a bad door then it’s not clear why that matters. The many door example makes it easy to intuit as well.

That’s obvious. If he reveals the car, he isn’t going to ask you if you want to switch. A goat is a goat. It doesn’t matter to you which goat you get.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#228

Post by tomerv »

spenczar5 wrote: post #111
TchoBeer wrote: post #64

Earlier quoted context omitted.

I don't understand how this could be. If you start over when the host picks the car, then isn't that the same as the host picking the goat every time, i.e. the same as the host knowing.

This is a small enough situation that we can do complete enumeration of the states. Let's say you pick door 1. Let's go through all the possibilities: the states of the 3 doors, which one monty reveals, and what do we do, and what is the result? 1 | 2 | 3 || Monty Reveals | You switch | Result --------------------------------------------------- G | G | C || 2 | Yes | Win G | G | C || 2 | No | Lose G | G | C || 3 | N/…

You are not enumerating the options correctly. You have 3 rows for the GGC and GCG options but 4 for the CGG option, which is assigning the CGG option higher probability. In reality, they have equal weight.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#229

Post by hoten »

“The winning odds of 1/3 on the first choice can’t go up to 1/2 just because the host opens a losing door,”

Wow. I've never seen it phrased so simply. _of course_ it doesn't change–if you picked the door with a goat, the host has no choice but to open the door he does. If you pick the door with the prize, whatever door he picks simply doesn't matter. There's no new information to learn about your own pick from that.

Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)

#230

Post by wildermuthn »

6gvONxR4sf7o wrote: post #13

There are a number of things I like about the monty hall problem. There's the history, the unintuitiveness, the subtle easy-to-screw-up nature of probability problems, the calculation, the sociology, and the overconfidence of wrong experts. Most of all, it's the calculation vs intuition that I like. You can do the calculation, or run simulations and prove correctness. In fact, it would be much harder to be so widely…

I was trying to think this through and realized it would be faster and more accurate to just write up a little script. Pretty sure this is accurate:

https://replit.com/@NateWildermuth/Monty-Hall-Problem

Thinking about this was a lot easier once I could look at the code. It seems like what's happening is that when changing doors, you are actually changing to two doors rather than one, giving you 2/3 odds?

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