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 Time Everyone “Corrected” the World’s Smartest Woman (2015)
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Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)
#22I 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.
You could do it in Excel in probably 20 minutes.
Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)
#23So 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 find most fascinating about this particular puzzle!
Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)
#24I may be missing something (not a mathematician, probabilist) but doesn’t the fact that the host would never reveal the car change the calculation? In the table shown in the article game 3 & 6 are nonsensical so with the remaining 4 games the odds are even between switch & stay.
No, it's correct. The easiest explanation, IMHO, is:
1. If you already selected the correct door, you should not switch, obviously. Equally obviously, the odds of being in this state are 1/3, because your initial choice was random.
2. If you did not select the right door, then the host clearly revealed the only one of the two remaining doors without a prize. In this state, you clearly should switch to the only door remaining, which contains the prize.
That is, the likelihood that switching will get you the prize is 2/3, because it corresponds to the states where you initially guessed wrong.
Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)
#25The hubris of some of the her critics - especially ones with titles - is remarkable.
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.
Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)
#26I may be missing something (not a mathematician, probabilist) but doesn’t the fact that the host would never reveal the car change the calculation? In the table shown in the article game 3 & 6 are nonsensical so with the remaining 4 games the odds are even between switch & stay.
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?"
Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)
#27There 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…
When I first heard of it in high school, I immediately coded a simulation and had an answer in less than 5 minutes that I could be confident about. I would have sat second-guessing myself for 5 minutes had I not done that.
Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)
#28The hubris of some of the her critics - especially ones with titles - is remarkable.
Hubris of title and its correlation to being dead-ass wrong is a time-honored tradition.
Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)
#29The hubris of some of the her critics - especially ones with titles - is remarkable.
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.
Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)
#30Is "Vos Savant" her real name? It's kind of a giveaway.
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.