The Time Everyone “Corrected” the World’s Smartest Woman (2015) • Hacker News Board

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

#201

Post by [deleted] » Sun, May 09, 2021, 4:36 AM UTC

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…

[deleted]

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

#202

Post by listenallyall » Sun, May 09, 2021, 4:37 AM UTC

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…

It's a tv show - a valid purpose is that he needs to stretch by 30 seconds before going to commercial. Another purpose is that the audience thinks seeing a goat is funny. Another purpose is to prove the show uses two different goats and doesn't do a switcheroo behind the scenes.

What the Parade article does NOT say is that the first door opened is ALWAYS not the contestant's choice and ALWAYS reveals a goat.

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

#203

Post by Dylan16807 » Sun, May 09, 2021, 4:41 AM UTC

justsee wrote: post #177

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…

This seems the most interesting aspect of the problem: "However, the probability of winning by always switching is a logically distinct concept from the probability of winning by switching given that the player has picked door 1 and the host has opened door 3." [1] [1] https://en.wikipedia.org/wiki/Monty_Hall_problem#Criticism_o...

Probability of an outcome always depends on what pool you're sampling from.

People pretty much always understand what the options are, but still get the analysis wrong. That is what I find interesting. Not the idea that there's some secret mechanism at play that alters the odds of a specific case. Even in that wonky "open the door on the right when possible" world, a contestant that always switches will still win 2/3 of the time.

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

#204

Post by kbelder » Sun, May 09, 2021, 4:42 AM UTC

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…

No, the experts didn't get it wrong because they got hung up on a (fairly ridiculous) misinterpretation of the rules. They got it wrong because they didn't bother doing the math.

And yes, this is deservedly a strong cultural memory, because it's so easy to fall into that error without realizing it. There are some PHDs who got it wrong, and are _still_ making frankly ridiculous arguments about how the rules were vaguely defined, rather than simply admitting that they made basic mathematical errors.

Be careful that you're actually fighting against revisionism, and not falling for revisionism.

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

#205

Post by saeranv » Sun, May 09, 2021, 4:43 AM UTC

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…

This is the best explanation I've read thus far.

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

#206

Post by jdashg » Sun, May 09, 2021, 4:43 AM UTC

someguydave wrote: post #162

haberman wrote: post #76

Earlier quoted context omitted.

When you choose the first door, you are partitioning the "board" into two parts: the door you chose, and "everything else". By opening a door, Monty lets you cover 100% of the "everything else" partition using only one guess. So now you get to choose between partition 1, which covers 1/3 of the board, and partition 2, which covers 2/3 of the board.

I think the confusing part for many people is the unstated fact that the host takes all prizes into account when revealing a door, and that the host is forbidden from revealing the car. If the host chooses randomly then his pick adds no information (other than the extra revealed prize)

I don't think people are confused by this in their initial solutions, but rather this after-the-fact problem modification happens to match the incorrect intuition people have.

The instinct is strong that "I am right" so "I must have just solved the wrong problem", thus "the problem was confusing".

Rather, I think you will find that most people don't expect the host will ever pick a door with a car until after you tell them that switching is better, and rationalization begins.

Additionally, it's on the solver to realize that a problem is under-constrained, and to ask for more constraints. That means that even if you were earnestly confused by the question, you presented a solution to an under-constrained problem. This is like answering "what is the square-root of four" with "it's negative two".

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

#207

Post by kbelder » Sun, May 09, 2021, 4:45 AM UTC

mcphage wrote: post #106

CyberRabbi wrote: post #72

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

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.

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

#208

Post by kstenerud » Sun, May 09, 2021, 4:48 AM UTC

the__alchemist wrote: post #4

The hubris of some of the her critics - especially ones with titles - is remarkable.

When someone famous with a reputation of always being right is suddenly wrong, there's a scramble to be the one who corrects them. It's a point of pride and fame.

The Monty Hall problem is particularly troublesome because the statistical connection is for some reason counterintuitive and difficult to grasp unaided, even for experts. Being that rare person who just gets it right away means that you'll have a lot of people thinking it's you who have misunderstood.

So in this case I'd say that this kind of reaction was rather normal (albeit with a sexist bent in a number of the responses).

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

#209

Post by b0afc375b5 » Sun, May 09, 2021, 4:50 AM UTC

My intuition keeps betraying me, but a truth table finally convinced me:

  | Car | Goat | Goat | Switch? | Win? |

  |-----+------+------+---------+------|

  | T   | F    | F    | F       | T    |

  | T   | F    | F    | T       | F    |

  | F   | T    | F    | F       | F    |

  | F   | T    | F    | T       | T    |

  | F   | F    | T    | F       | F    |

  | F   | F    | T    | T       | T    |

Number of wins when not switching: 1

Number of wins when switching: 2

EDIT: Woops, hackernews does not like an org-mode table. Found out you can indent by 2 spaces to preserve format.

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

#210

Post by billforsternz » Sun, May 09, 2021, 4:53 AM UTC

rfrey wrote: post #191

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…

The trick is that the host does not pick a door to open at random... If they did there would be a 1/3 probability they opened your door. If they didn't open yours under that circumstance, there would be a 50/50 chance you already picked the good door. But it's not random... Monty will never open the door you chose. That's what messes up the intuitive probabilities.

Not only will he not open the door you choose, he won't open the door in front of the car either. I think that's the key point that confuses people. He knows where the car is and he always exposes a goat instead.