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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)

#141
There’s a bit of historical revisionism at play in the article.

Here’s an accurate representation by Aaron Brown of what transpired: https://www.quora.com/Why-do-some-PhDs-argue-against-Marilyn...

Quoting for those who don’t want to go off-site:

“You have to have lived through this ancient travesty to care about it. It’s probably best forgotten.

Marilyn Vos Savant published an incorrect answer to the Monte Hall problem. She got the correct answer from a lot of readers, including me. She then published a second incorrect answer claiming that all the letters she got—including from math PhDs were wrong. Finally she got the answer right—the one she undoubtedly got from any math PhD or intelligent person who wrote her—but continued to claim (a) that her previous answers were correct and (b) that all the letters were wrong.

As a result, the public is mostly misinformed about this simple problem.

The set-up is simple. There are three doors, one of which has a valuable prize behind it, and two of which have worthless prizes. You select one door. The host opens one of the other two doors to show you a worthless prize, and offers you the opportunity to switch your choice.

The key to this problem, which Marilyn finally saw in her third solution, is the knowledge and intentions of the host. If the host doesn’t know which door has the prize, there’s no reason to switch or not switch, it’s the same either way. If the host knows the door and is trying to hurt you, don’t switch. If the host knows the door and is trying to help you, switch.

Marilyn’s first answer was to always switch, regardless of the host’s intentions. This is also the answer that most people now believe. It’s a common error that people make all the time. That’s why people wrote in to correct her.

In order to justify her incorrect first answer, she claimed it was obvious that the host used the strategy of always opening a non-prize door and offering you the chance to switch. This does indeed justify switching. But that assumption was missing from her first and second answers, along with any discussion of the host’s knowledge and intentions mattering.

Her justification that the assumptions were too obvious to need stating was the actual television program Let’s Make a Deal, hosted by Monte Hall, which eventually gave the name to the problem. But anyone who watched the show knew that was not Monte’s strategy. Sometimes he opened another door and gave a chance to switch, sometimes he didn’t. He was well aware of the problem if he followed Marilyn’s assumed strategy, and was scrupulous about not giving any advantage to the contestant. You can tell this from statistics on the show—on average it didn’t pay to switch—and his published statements.

Clearly there are much bigger problems in the world, and it doesn’t pay to get upset about misinformation put out by popular vain people. If was very frustrating at the time, but it seems quaint that such things upset us in the 90s when there is so much worse information put out today by even more popular and more vain people.“

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

#142
post #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."

This is why I no longer call people Dr.

I have a relative with a PhD in Economics. His personality leads me to believe that he would totally be one of the people to write in to Marilyn. He does sign things with Dr. Drives me up the wall.

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

#143
I still don't get it.

1. Three doors.

2. Two doors have a goat, and one has a car.

3. The contestant has a 1/3 chance of winning the car?

4. The contestant loses.

5. New game, and odds?

6. There's a 50/50 chance of winning?

(I'm assuming Monte Hall has no clue to where the car is. He is just opening doors.)

7. Could someone explain it to me, and thanks in advance.

(Off topic but a fawn had two babes in my back yard. It was pretty amazing. At first, it looked like the mother abandoned her babies, but she didn't. The babies stayed in the same spot for two day. By the third day, I thought she abandoned them. I looked into care. I was informed to leave them alone. They said, if you knew for sure the mom was killed, you could bottle feed them Goat's milk. Cow's milk is not good for baby deer. I didn't overreact, and mom was there all along. She now just visits with her healthy kids. This has been my best spring in memory. Happy Mother's day to the moms out there.)

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

#144
post #79

Earlier quoted context omitted.

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.

You can brute force this without knowing Bayes’ theorem (see the grids in the article as an example of iterating through every possible solution then counting to arrive at the right probability).

Ah! I see, I thought the commentator was saying to solve it mathematically. Manually "simulating" it makes sense.

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

#145
I find that the phrasing of the Monty Hall problem makes the solution less certain than stated.

> "You pick a door, say #1, and the host, who knows what’s behind the doors, opens another door, say #3, which has a goat."

That's what the gameshow host did in this one trial, but why do we assume that the host would do the same thing every time? Perhaps the host only tries this other-door-goat diversion tactic when the contestant first selected the door with the car!

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

#146
post #95

> Whereas only 8% of readers had previously believed her logic to be true, this number had risen to 56% by the end of 1992, writes vos Savant; among academics, 35% initial support rose to 71%. that 71% leaves 29% of _academics_ not getting the elementary math of the problem. I'm baffled this is _that_ hard?

That 29% is probably made up of men that honestly think she should be pumping out babies instead of doing men's work. I wish I was being sarcastic or otherwise kidding.

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

#147
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…

The presentation of the problem included the phrase "the host, who knows what's behind the doors, opens another door", so I think in that case the interpretation that Monty deliberately reveals a goat is more appropriate (in addition, obviously, to being what was intended), although I agree there is wiggle room enough to admit both possibilities and clarity about which case you are discussing is important as it chang…

> as it changes the answer.

It doesn't. If the host randomly reveals a car, then you have 0% chance to win. If he doesn't you have 66% chance to win by switching.

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

#148

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…

The day this was published in Parade magazine, I was sure that she was wrong.

Even though I was a computer programmer then (1990), I didn't own a computer. I drove across town to my parent's house to use my father's computer to prover her wrong.

I didn't even have to run the program. Just the act of writing the program made me realize that she was right. When I was writing the part where the host picks which door to open, I had a revelation.

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

#149

Earlier quoted context omitted.

I don't understand how this could be. If you start over when the host picks the car, then isn't that the same as the host picking the goat every time, i.e. the same as the host knowing.

This is a small enough situation that we can do complete enumeration of the states. Let's say you pick door 1. Let's go through all the possibilities: the states of the 3 doors, which one monty reveals, and what do we do, and what is the result? 1 | 2 | 3 || Monty Reveals | You switch | Result --------------------------------------------------- G | G | C || 2 | Yes | Win G | G | C || 2 | No | Lose G | G | C || 3 | N/…

What would this table look like if Monty always revealed a goat? Would any win or lose row be added or removed?

I know the result is right, but I don't think this table illustrates the reason.

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

#150
post #88

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

This made my week :)
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