I 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 Time Everyone “Corrected” the World’s Smartest Woman (2015)
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Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)
#12I 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.
i was about 15 when this went down and immediately wrote one that confirmed she was right. formative experience in my life.
Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)
#13There 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 wrong now that any statistician can so easily just code up a computer to run it a zillion times and get an empirical answer. But despite that, your intuition might still say otherwise.
I'm fascinated by the gap between intuition and logic particularly because it can be closed as soon as you find the right lens to take to a problem. I like the example in the article about 100 doors, or even a million doors, where it really helps drive it home in your gut.
That moment when you find the right intuition for a thing is a magical one that makes me love math.
Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)
#14"You made a mistake, but look at the positive side. If all those Ph.D.’s were wrong, the country would be in some very serious trouble."
Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)
#15I 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.
they were. the critics didn't use them. she told them to "try it" in one or two columns before she had to explain it very slowly and methodically in a third, as I recall. I'm old. I read each of these as they arrived in the paper.
Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)
#16I 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.
This is the missed portion of the explanation. If one were watching the show for the first time, and unaware that the host ALWAYS revealed a goat, and that the door that they revealed was not random, then they could reasonably think that it is a 1/2 coin flip decision. This is almost always statisticians doing a poor job of explaining the problem, and then thinking themselves clever when people "get it wrong."
Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)
#17The 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...
Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)
#18Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)
#19I 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 table is for the host revealing one door that you didn't pick and that has a goat behind it, not for the host revealing door #3.
Re: The Time Everyone “Corrected” the World’s Smartest Woman (2015)
#20From 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 goat" vs "the host will never open a door with a car behind it".)