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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)

#181

Post by listenallyall »

atdrummond wrote: post #163
hellbannedguy wrote: post #143

I still don't get it. 1. Three doors. 2. Two doors have a goat, and one has a car. 3. The contestant has a 1/3 chance of winning the car? 4. The contestant loses. 5. New game, and odds? 6. There's a 50/50 chance of winning? (I'm assuming Monte Hall has no clue to where the car is. He is just opening doors.) 7. Could someone explain it to me, and thanks in advance. (Off topic but a fawn had two babes in my back yard.…

You have three doors. As you note, you have a 1/3 chance of winning. Monty now reveals a losing door. At this point, your door has a 1/3 chance of still winning - the probability of that choice can’t change. However, as we now know one door has a 0/3 chance of winning (it’s been revealed) the remaining door must have (1-1/3) chance of winning. Thus, the remaining door has a 2/3 chance of winning.

I'm going to disagree with your framing here. Probabilities DO change as more information becomes available. For example, prior to rolling a pair of dice, you have a 1/36 chance of rolling a 12. However as sooner as you see the value of the first die, the probability changes to either 0 (most likely) or 1/6. In your description, if Monte opens a door randomly -- which you don't make clear whether he does or doesn't -- then the presence of the goat DOES change your P(winning a car).

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

#182

Post by visarga »

kingsuper20 wrote: post #21

I'm familiar with the problem and my intuition is still wrong. I wonder if you couldn't design a gambling machine that has a variant of the Monty Hall problem built-in favoring the house (naturally).

Looks close to the one armed bandit problem which is fundamental in Reinforcement Learning.

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

#183

Post by asciimov »

Reading "Ask Marilyn" in the paper was one of those Sunday rituals that I miss from my childhood. Along with the puzzler from Will Shortz on NPR on the way to church and reading the Sunday funnies.

I kinda miss the newspaper, the way it was back then.

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

#184

Post by stordoff »

lachstar-x wrote: post #167
zeroimpl wrote: post #122

Earlier quoted context omitted.

The other door is not irrelevant. When you first picked a door, there was a 33% chance it was right, and a 67% chance one of the other two doors was right. Once the other door got opened, it is still a 67% chance that the other two doors is right, but you now know which one of those two it would be - the one which wasn’t opened.

Thats what I'm stuck on, I suppose. Imagine the entire situation is reversed. The Reverse Monty Hall problem. I'm given a choice between two doors, once of which contains a car and one contains a goat. I have to choose, 1 or 2. Then the game show host reveals that there was also a third door, which contained a goat, which is no longer relevant and never was relevant. I'm then also asked to choose a door (which is als…

In your reverse problem, I don't see how the new door can ever be relevant, as you know the car is behind 1 or 2, so you're only ever interested in picking between those 2.

In the original problem, its presence _is_ relevant, as the car could be behind doors 1, 2, or 3. Say you pick door 1 - there's a 1/3 chance you are right.

The host is then left with doors 2 and 3. We know there is a 2/3 chance the car is behind _one_ of these doors. When the presenter reveals a goat (say in door 2), he is reveling information about this set of doors - there is still a 2/3 chance that the car is behind one of the doors in this set, but there's only one door left we don't know anything about (3). There is therefore a 2/3 chance that it is behind _this_ door.

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

#185

Post by mkl »

listenallyall wrote: post #166
mkl wrote: post #151

Earlier quoted context omitted.

I think it's made pretty explicit. In this version: "Then, the host, who is well-aware of what’s going on behind the scenes, opens door #3, revealing one of the goats." The host has to open a door that doesn't show the car.

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 game away.

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

#186

Post by the__alchemist »

listenallyall wrote: post #152
hellbannedguy wrote: post #143

I still don't get it. 1. Three doors. 2. Two doors have a goat, and one has a car. 3. The contestant has a 1/3 chance of winning the car? 4. The contestant loses. 5. New game, and odds? 6. There's a 50/50 chance of winning? (I'm assuming Monte Hall has no clue to where the car is. He is just opening doors.) 7. Could someone explain it to me, and thanks in advance. (Off topic but a fawn had two babes in my back yard.…

Monte Hall DOES have a clue where the car is, and is NOT "just opening doors" With the full knowledge of where the car is, Mr Hall opens a door that is NOT the door the contestant chose, and is also NOT the door containing the car.

This is the crux of it!

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

#187

Post by LanceH »

mypalmike wrote: post #165
2muchcoffeeman wrote: post #126

Earlier quoted context omitted.

* Most of all, it's the calculation vs intuition that I like. You can do the calculation, or run simulations and prove correctness.* It puzzles me that so many smart people got it wrong. It’s so easy to check your working. When I first heard of this problem, I got it wrong too. Then I was told the answer, and to prove it to myself, it’s trivial to list the scenarios and simulate on paper. It’s still uncomfortable to…

I think people didn't check because the answer of 50% is so strikingly obvious (despite being wrong) that it seems like there's no work to check.

It's right depending on your assumptions. If the host has rules of only picking the right most door the contestant doesn't pick, and it happens to be a goat then the answer is 50%. Basically if the host is just as willing to show a car as show a goat and it is a goat which is shown, the answer is 50%.

There is a confirmation bias that people expect people who are aware of the Monty Hall Problem expect others to be wrong about it and attribute it to people not understanding. I think it's perfectly acceptable for someone to read the vague "the host, who is well-aware of what’s going on behind the scenes" and not assume that means he chooses to pick a goat. They're probably right, and the people saying 50% are reasoning along the lines of "there are two doors so 50/50".

For rigor, I think the host's rules need to be more strict: "The host knows what is behind the doors and will never reveal the car".

Or a 50% answer is correct if you lay out the principles of how the host acts given his knowledge.

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

#188

Post by elliekelly »

I’m disappointed that this entire thread is focused only on discussing the Monty Hall problem and conveniently pretends her gender, and how she was treated, is unworthy of discussion. Come on!

If we can’t even mention how STEM women are often treated as default-incompetent in this, _very_ egregious case then we have no hope of being able to have the discussion at all.

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

#189

Post by Winsaucerer »

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…

That was exactly what happened with me. I hadn't understood in the original proposal that the host's choice is not random. At some point during someone's offer of the '100 door' version, I realised they were operating with this extra piece of information I lacked.

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

#190

Post by Mountain_Skies »

Interesting that they chose to identify Marilyn vos Savant in the headline as "Woman" instead of by her name. Also interesting that in doing so, they qualified her then believed to be world's highest IQ, male or female. Looks like they were attempting to be woke but ended up being misogynistic instead. It's also worth noting that many people did agree with her so it wasn't "everyone" correcting her.
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