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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)

#71

Post by astrange »

crooked-v wrote: post #29
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...

Something tells me Erdős didn't resort immediately to personal insults when faced with the problem, though.

I'm not sure about that since Erdos had the typical pre-GenZ-wokeness vocabulary of a nerd, where everything they said was worded as an insult to people less smart or with different hobbies than him. To the point where it's in his Wikipedia article:

> Women were "bosses" who "captured" men as "slaves" by marrying them. Divorced men were "liberated".

> People who stopped doing mathematics had "died", while people who died had "left".

> Music (except classical music) was "noise".

(Did boomers ever notice all their wife-based humor was about how much they hated theirs?)

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

#73

Post by astrange »

BelenusMordred wrote: post #30
crooked-v wrote: post #5

Earlier quoted context omitted.

It actually is the family name on her mother's side, though she changed it to that back from her mother's married name (Mach).

> Mach Amusing that her alternate name still exudes intellect. https://en.wikipedia.org/wiki/Ernst_Mach

Or that she's very good at IPC.

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

#74

Post by [deleted] »

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…

[deleted]

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

#75

Post by paxys »

Cpoll wrote: post #44

Another statistically unintuitive problem (which I've witnessed a lecture hall enter a state of uproar over): There are 2 red and 2 blue balls in a box. One ball is removed at random, what are the odds that the ball is blue? Now we repeat the problem, but before examining the ball, we remove a second ball. We observe that the second ball is blue. In this case, what are the odds that the first ball is blue?

Probability of draws:

B then R -> 1/3

B then B -> 1/6

R then B -> 1/3

R then R -> 1/6

Removing the cases where the second draw was R:

B then B -> 1/3

R then B -> 2/3

Therefore the first ball being blue has a 1/3 chance.

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

#76

Post by haberman »

javajosh wrote: post #23

So this is at least in part about the "Monty Hall Problem" and why it's solution not intuitive. The article missed an important angle: when the host opens a door, he's giving you more information , which explains why it's better to switch. If you're the host, you need to know which door the car is behind to do your job 2/3 of the time, to avoid revealing it. It's this quality of unexpected information exchange that I…

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.

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

#77

Post by dfxm12 »

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 don't think you could. In most jurisdictions, gambling machines are tightly regulated to be random, and definitely not skill based.

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

#78

Post by npinsker »

jVinc wrote: post #61
jml7c5 wrote: post #20

From reading the problem as posed in the article, the confusion seems similar to the "plane on a treadmill" thing, where people are interpreting the premise of the problem differently. (In plane on a treadmill: "the treadmill moves backwards @ -1 * plane airspeed" vs "the treadmill moves backwards to keep plane airspeed at 0". In this: "the host will open the door at random and in this example it happen to have a goa…

> 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 does change your odds -- you're now living in a world in which the car didn't get revealed, and by Bayesian reasoning that means it's more likely that you live in a world where you picked the correct door.

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

#79

Post by saeranv »

GlenTheMachine wrote: post #38
saeranv wrote: post #9

I guess Monte Carlo simulations weren't well-known or easily accessible back then? It would have been the perfect way to shut up her critics.

This particular one isn’t that hard to just do by hand. Which I did at the time, was surprised at the result, and stared at the column long enough to convince myself why she was right.

Using Bayes theorem? But if you know to use Bayes theorem, then you're already formulating the problem correctly, which is the problem all the critics are running into.

Edit: Someone mentioned you could manually "simulate" it with a pen and paper, which I think is what you meant. If so, very good point.

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

#80

Post by listenallyall »

crooked-v wrote: post #32
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).

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.

This is absolutely false in virtually all commercial regulated gambling casinos in the United States.
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