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

Marilyn vos Savant and the Monty Hall Problem (2015)

priceonomics.com

Post reply on HN
Print view View original

71–80 of 331 posts

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#71

Post by kergonath »

niklasbuschmann wrote: post #42

> Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice? Without additional assumptions this original wording is not cle…

> it could be that the host always shows a goat

That’s what the sentence says: “and the host, who knows what's behind the doors, opens another door […] which has a goat”.

> or the host shows something at random and we just look at the cases where he shows a goat

Nothing says that the host opens a door at random. Quite the contrary, we know that the host has a perfect knowledge of the situation.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#72

Post by paulcole »

wizerdrobe wrote: post #11
paulcole wrote: post #7

Earlier quoted context omitted.

What part of the scenario is poorly written in your opinion?

TFA is very well written, but in almost every reproduction of the Monty Hall problem you’ll find it very poorly written such that one would reasonably be led to believe the question is “if I have two doors what is the probability.” Don’t believe me, go search for memes presenting the problem. It’s been on the internet for decades at this point. The setup is near always to send a poor rewrite then link you to a story…

> how people on the internet love tricking others to feel “right.”

I guess it all depends on your perspective. I see a lot more people on the internet piling on with nitpicks to avoid feeling "wrong."

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#75

Post by dynm »

gerad wrote: post #39

The intuitive way for me to understand the Monte Hall problem is to pretended there are 1000 doors. You pick 1. There’s a 1 in 1000 chance you get it right. The host then opens 998 doors that don’t have the prize. Do you keep your original or do you switch? Are the odds 50:50?

I actually like to back up even further and start with this problem: There are 1000 doors. You pick one. There's a 1 in 1000 chance you get it right. Now, do you want what's behind your door, or what's behind the other 999 doors? https://dynomight.net/2020/09/17/making-the-monty-hall-probl...

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#76

Post by HumblyTossed »

I recall reading a lot of the replies and one always struck me - a (I believe) teenager wrote a program that proved her right.

That person wrote a program and proved her right, while all these stuffy old men got just downright testy with her - one even getting misogynistic with here. It was gross to read about.

But good on the teenager for actually sciencing it.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#77

Post by mathstuf »

tromp wrote: post #66
gerad wrote: post #39

The intuitive way for me to understand the Monte Hall problem is to pretended there are 1000 doors. You pick 1. There’s a 1 in 1000 chance you get it right. The host then opens 998 doors that don’t have the prize. Do you keep your original or do you switch? Are the odds 50:50?

Your formulation is once again ambiguous. Instead of clearly stating that Monty had to open 998 empty doors, you state that he did that. Which could mean he happened to do that. Had to vs happened to makes a big difference. Had he opened them at random and by (extremely small) chance they happened to be empty, the odds are quite different.

There's a variant where Monty trips and opens one of the doors by accident. Then it is 50/50 again (because he could have tripped into the car door). See also this video where cutting off a question in the middle changes the probability because of the information it provides: https://www.youtube.com/watch?v=bDZieLmya_I

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#78

Post by bemusedthrow75 »

bilsbie wrote: post #73

Has anyone else spent hours on understanding this and just accepted they’ll never accept it? I completely get all the explanations but it just feels too weird.

No. I am not a mathematician but I got it once I understood that this is not drawing coloured balls randomly from a bag (which is how all my school probability problems seemed to go).

That is:

- the setup of the system matters.

- The state of the system at the point of the decision to switch matters.

- The choices don’t get re-randomised.

So the probabilities assigned to the original choice (and the remaining alternative) still count.

If the host had closed a curtain over the stage and randomised the remaining doors, then it would be 50:50.

But he didn’t. So you’re still in the probabilities of the original choice.

One of the goats has been removed. The car and one goat remain: you know this for sure.

You are being offered a door knowing that behind it must, necessarily, be the opposite of your original choice, and the probabilities have not been reset.

If you originally picked the goat, that door absolutely has a car behind it. And there's a 2/3 chance you picked the goat originally. So by inference there's a 2/3 chance the door has a car behind it. You should switch.

I didn’t get it until I had written a simulation to see it for myself though!

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#79

Post by mithr »

rspeele wrote: post #65
gerad wrote: post #39

The intuitive way for me to understand the Monte Hall problem is to pretended there are 1000 doors. You pick 1. There’s a 1 in 1000 chance you get it right. The host then opens 998 doors that don’t have the prize. Do you keep your original or do you switch? Are the odds 50:50?

The explanation that worked for me was: Suppose after you make your initial choice, instead of opening a door, Monty simply asks if you'd like to switch to BOTH the other two doors, such that you win if the prize is behind EITHER of them. That switch is intuitively a great deal, giving you 2/3 odds. The only way you can lose is in the 1/3rd case where you already picked a winner. The original scenario is equivalent t…

I do think this modified scenario makes the solution much clearer. At the same time, I also think that it feels like a significantly-enough different scenario from the original that saying the two scenarios have the same probability then becomes the non-intuitive part. The act of revealing what's behind the second door seems like it should change the probability from 1/3 (one door) vs. 2/3 (one of two doors) to 1/2 (one door of the remaining unopened two) vs. 1/2 (one door of the remaining unopened two, since one was "eliminated").

It's amazing how even seeing the probabilities written out, or running simulations, doesn't really make it easier to truly understand the result.

Re: Marilyn vos Savant and the Monty Hall Problem (2015)

#80

Post by paulpauper »

Jimmc414 wrote: post #19
swayvil wrote: post #5

Am I the only person who wonders how "Marilyn Vos Savant" also happens to be the smartest person? If you didn't notice, "Savant" means smart. So is it just a coincidence? Karma? The pressure of carrying such a name drove her to smartness?

Perhaps Bill Ackman was right about impact of a person’s name. I doubt it, but it’s an interesting observation.

like the surname "mason" or "farmer"
Post reply on HN