Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

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

priceonomics.com

Post reply on HN
Print view View original

171–180 of 331 posts

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

#171

Post by visarga »

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…

This shows how much of our intelligence is crystalized (external). We look intelligent because we're reusing the solutions found by others. As soon as we can't do that it becomes apparent that the intelligence of a single person is not so great. It took us millennia to get where we are.

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

#172

Post by stordoff »

lachstar-x wrote: post #102
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…

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…

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.

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

#173

Post by salamanderman »

shkkmo wrote: post #57
salamanderman wrote: post #26

Earlier quoted context omitted.

The fact that the host never shows the car is critical to the solution. You choose a door. There's a 2/3rd chance that the car is behind one of the other doors. Monty is kindly going to show which of the other two doors not to choose. ... The other way to think of it is, you choose a door, and then you're asked "would you like to keep what's behind your door, or would you like to have the sum of the other two doors?"

Not at all. Once the door is opened, it doesn't matter if the host knew there was a goat behind it or not. Edit: The host's knowledge only matter if the host can choose not to open a door.

If the host opens the door with car, and asks you if you'd prefer to switch to the unopened door, then you have a 100% chance of being wrong, as the door with the car isn't one of the choices. But, sure, my second point still stands, that it's effectively asking if you want your door or the sum of the other two doors.

But, to be clear, the question states that Monty opens the door with the goat. If you were to write a monte Carlo to test this empirically, you'd have to have your "Monty" choose the door with the goat.

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

#174

Post by utopcell »

You pick the car with 1/3 probability and a goat with 2/3. If you picked the car and switch, you lost. If you picked a goat and switch, you win because the only other door left has the car.

The problem is simple to reason through. The hard part is convincing yourself that you need to think through it given what seems "obviously correct".

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

#175

Post by hypertele-Xii »

ecdavis wrote: post #88
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.

Years ago I challenged you on this and you suggested I write a simulation to check. I did just that and my understanding of the problem improved dramatically. That exchange made a pretty big impact on me and is something I think about fairly often, so thanks. :) https://news.ycombinator.com/item?id=9079260

I also wrote a simulation, in PHP, when I first encountered this problem.

  ";
  // switch
  $wins = 0;
  for ($i = 0; $i

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

#176

Post by stale2002 »

TchoBeer wrote: post #87
jVinc wrote: post #61

Earlier quoted context omitted.

> vs "the treadmill moves backwards to keep plane airspeed at 0". You might be correct in thinking people misunderstand it as that, but that's physically impossible, so I don't think you can argue that people have some sort of alternate understanding under which they are actually correct. That's just one type of wrong reasoning people might apply to the problem. Add to that, in your hypothetical understanding of Mont…

It's great that you're so sure of yourself, just a shame that you're wrong. If the host picks randomly, your chances are in fact 50-50. Think of it this way: imagine every time the hosts picks the car the universe resets. Now imagine you see the host picking a goat. There's a 2/3rds chance in your universe you picked the car, and a 1/3rds chance you picked a goat, and so switching would seem like the bad option. This…

> imagine every time the hosts picks the car the universe resets

Do you believe that we live in a universe that is reseting, every time Mr Monty hall opens a car?

As in literally Mr Monty Hall. From the game show. In real life.

Because the purpose of the question is to mimic the show.

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

#177

Post by justsee »

2muchcoffeeman wrote: post #126
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…

* 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...

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

#178

Post by freeopinion »

tebou wrote: post #47
crooked-v wrote: post #32

Earlier quoted context omitted.

From what I understand, that would just be overcomplicating the matter, because most modern video gambling machines just use a set number of wins per time interval.

That is incorrect, and most likely illegal anywhere gambling is legalized. The machines are random, with no enforcement on wins per time interval. Source: I work in the industry.

I have a Ph.D. in slot machines and you blew it big time. In Nevada they are very much controlled, just not by time interval.

Oh, and fwiw, I know several people who always win when they come to Las Vegas. I know because they've told me so. This proves that you don't actually work in the industry.

(I really hate that I have to disclose that I don't really have a Ph.D. is slot machines.)

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

#179

Post by leephillips »

failwhaleshark wrote: post #128
fastball wrote: post #66

Earlier quoted context omitted.

This is why I no longer call people Dr.

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.

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

#180

Post by [deleted] »

2muchcoffeeman wrote: post #126
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…

* 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…

[deleted]
Post reply on HN