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

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

#211

Post by kstenerud »

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).

I think stordoff's answer would be helpful:

When you first pick a door, you have a 1/3 chance of it being the right door. There's a 2/3 chance of it being behind a door you didn't pick.

When the host then opens a door, there's still a 2/3 chance that it is behind one of the doors you didn't pick. However, there's now only one door in this set, so there's 2/3 chance that it's behind _that_ door.

To look at another way, imagine if the host didn't reveal the content of the door, but gave you the option to switch to BOTH of the other doors instead of your door. Your odds of winning clearly go up, as you now have two chances to win (and all are of equal probability). That's equivalent to what's happening here. By showing you the losing door of those two, he doesn't change anything - there's still twice the chance it was behind one of the doors you didn't pick compared to the one you did, and by switching you win if it was behind either of them.

https://news.ycombinator.com/item?id=27093045

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

#212

Post by acomjean »

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…

Can’t it be random if there are two goat doors the host has to choose from? But I see your point about it clarifying the problem.

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

#213

Post by [deleted] »

kbelder wrote: post #207
mcphage wrote: post #106

Earlier quoted context omitted.

Why would talking that test convince me of the usefulness of IQ tests?

How they're useful is debatable. But if you had a hundred people take an IQ test, and divided them into quartiles, you would notice some clear and strong differences between the groups, in a lot of different aspects. What to do about the differences is an exercise left for the reader.

[deleted]

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

#214

Post by snitzr »

I wanted to prove this to myself programmatically so I made this Python script: https://gist.github.com/snitzr/7ecf0abaacce610893e9364b13bce...

It’s better to switch.

One way to think about it is in an exaggerated way. If there was a googolplex number of choices and you chose one and then all but your choice and another door were taken away, you’d have almost a 100% chance of being correct if you switch.

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

#215

Post by lnl »

mathrando wrote: post #113
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…

Whether Monte Hall is counter intuitive is a function of how the question is phrased. When you phrase it in a way that underlines the mechanical nature of the host's decision, people get it right. When you phrase it in a way that suggests the host's choice is itself random, people get it wrong. I think the first formulation primes people to think of it from the perspective of the host, which is the right perspective…

> When you phrase it in a way that suggests the host's choice is itself random, people get it wrong.

In other words, they still get it right; they get it right for the separate question that that phrasing implies.

If the host's choice is random, so that when you initially picked wrong it's equally probable that the host open the door with the car and then say "sorry, looks like you lost" (which is what I assumed when I first heard this problem, not being familiar with the show), then even if the host happened to open the door with a goat and give you a chance to switch, it doesn't matter if you take it or not. People are correct that, for that question, the probabilities are one in two for both of the remaining doors.

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

#216

Post by robocat »

CyberRabbi wrote: post #72

Smart lady but IQ tests are definitely not useless, if you disagree try this test: https://test.mensa.no

IQ tests apparently have a very wide standard deviation, and regression to the mean would also be an issue (if you select for high IQ, you are also selecting for medium IQ with large positive error).

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

#217

Post by fourthark »

LanceH wrote: post #187
mypalmike wrote: post #165

Earlier quoted context omitted.

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 wr…

Intention doesn’t matter. The problem states that the host opens another door and reveals a goat.

It doesn’t matter that the host meant to do that. Now that the information is revealed, the probabilities have changed.

Obviously if the host revealed the car, that would also affect the probabilities!

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

#218

Post by inopinatus »

dec0dedab0de wrote: post #199

The problem with the Monty Hall problem is that it's based on implicit rules. Every explanation I've ever hear never says that no matter what they will never remove the winning choice.

There is a written rule: it's illegal. The Communications Act was amended in 1960 making it a federal offense for game shows to rig the outcome. Surreptitiously and intentionally removing the main prize on offer easily qualifies as just such a deceptive practice.

https://www.visitthecapitol.gov/exhibitions/artifact/communi... if you need that in ink & vellum.

Unlawful behavior can be reasonably excluded from both the construction and the answers to logic puzzles, except when noted otherwise (or otherwise reasonable in context), which is why taking Monty hostage, busting through all three doors, jacking the car, snatching the goat, and driving off into the sunset, is not a reasonable response to the problem either, no matter how great TV it might make for.

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

#219

Post by casefields »

macintux wrote: post #25
pmiller2 wrote: post #17

Earlier quoted context omitted.

I'm willing to forgive pretty much anyone who's fooled by something that also fooled Paul Erdos: https://www.wired.com/2014/11/monty-hall-erdos-limited-minds...

Being wrong isn’t a crime. Harshly lambasting a woman for, largely, being a woman and disagreeing with you is the problem.

I don't see the problem. We are still doing this today. Pick a hot button topic that has some "consensus" then watch how outliers get treated. For example, COVID and climate change. I'm not saying people going completely against the narrative but professionals publicizing concerns or data that just doesn't fit the current narrative.

This is more of meritocracy run amok. I've got the fancy credentials which shows I'm brilliant, and I know it.

World renowned Harvard Philosopher Michael Sandel on The Tyranny of Merit: https://youtu.be/Qewckuxa9hw

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

#220

Post by [deleted] »

peteretep wrote: post #41
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).

The best intuitive explanation I know modifies the problem to have 100 doors, and after you choose one, the host opens 98 doors that don’t have the prize.

[deleted]
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