Welcome to the Mrs. Auntie SciBabe Gameshow, where there is always a mathematically correct answer to my games. I have three doors and behind those doors are two goats and a car. I understand with these gas prices you may be hoping for a goat, but humor me, and choose door 1, 2, or 3.
From the remaining two doors you didn’t pick, I’m going to eliminate one option by opening a door to reveal one of the goats. We now have two doors, one with a car behind it, one with a goat.
Would you like to switch doors?
Today’s Moment of Science… The Smartest Woman in the World and the Monty Hall Problem.
The show Let’s Make A Deal was co–created by Monty Hall and has enjoyed several TV runs since its debut in 1963. Contestants would swap briefcases or sealed envelopes or artisanal dogfood recipes until either winning something amazing or something amazingly tragic.
The show inspired mathematician Steve Selvin to write into the journal The American Statistician regarding, what he called for the first time in print, the Monty Hall problem. That being the ‘do you switch doors’ conundrum, specifically after one option has been revealed and eliminated by the host.
Selvin said yes and offered a solution for the problem. Though he received some initial criticism, he sent in a follow-up letter with a more in-depth explanation for why it was advantageous to switch, and the whole thing was more or less forgotten about.
Until someone asked Marilyn vos Savant the same question.
(I told you that story to tell you this story.)
If you ask some of the internet’s finest skull measurers, IQ scores are absolute assessments of brain power, or worse, a yardstick for self-worth. Marilyn vos Savant would be the first to tell you that IQ tests are “useless.” Which may seem like an unlikely opinion from a person with one of the world’s highest measured IQs. With so many factors to intelligence though, IQ tests mostly tell us if someone can provide the correct answers to a particular IQ test.
That said, if someone never tests below “mother of fuck this kid’s a genius,” they can probably convert a pdf.
Marilyn vos Savant, whose last name is mere coincidence, scores between 186 and 228 depending on the test, not that she gives a stray pube about it. She didn’t do a lot of the typical genius career stuff. She went into finance just long enough to make a tidy fortune and support herself as a writer. In 1986, she was interviewed for a piece in Parade magazine which featured her answering questions from readers. This led to her long-running column, Ask Marilyn.
In 1990, reader Craig F. Whitaker wrote into the column to ask Savant “is it to your advantage to switch your choice” in the Monty Hall problem. To which she accurately answered “yes.”
Y’all, this was a pile-on before there were pile-ons.
Savant received something like 10,000 pieces of mail in the style of ‘fuck you you fucking fuck,’ about a thousand of which were from people who claimed to have PhDs.
If it’s still a little unclear why switching doors gives you an advantage, you’re not alone. Accomplished mathematicians have needed this one proven to them.
Say instead of three doors at the Mrs. Auntie SciBabe Gameshow, we start with a hundred because we’re doing math and we need to prove a point. You start with a 1/100 chance, all the other doors combined have a 99/100 chance of having the prize. Then the reveal starts and it’s all goats behind one door after another. Eventually, I’ve eliminated 98 doors, and just two remain closed, one with a car behind it, and one with a goat.
It’s possible your original selection has the car. But that choice only came with a 1% chance, which didn’t change when a herd of goats was released into the studio audience. The right choice is to switch every time, because there’s still a 99% chance the car is behind the other door.
With just three doors, the problem can seem trickier. But it’s the same principle; you start with a ⅓ chance, and the other two doors have a ⅔ chance. After eliminating a door with a goat behind it, switching still offers a ⅔ chance at the car. It won’t win every time of course, but simulations show that it works.
Marilyn vos Savant dedicated three further columns to the issue, eventually collecting a small mountain of apologies. She’s continued to publish books and write her column at Parade, whereas plenty of people who sent her “corrections” are mostly only remembered for that time they tried- and failed- to correct the smartest woman in the world.
This has been your Moment of Science, still wondering how often people accepted their consolation goats.
Addendum, because this visual seemed to help quite a bit:
I posted this in the comments yesterday with the Monty Hall Problem post, a lot of people said the visual really helped explain why switching doors works.
Our brains are not wired to understand probability intuitively, so don’t panic if this is taking your highly capable brain a few tries.
The Monty Hall Problem:
You’re a contestant on the show Let’s Make A Deal and you’re presented with three doors, behind which there are two giant framed oil paintings of cats assholes and a car.
(Normally this game uses goats but we’re using oil paintings of cats assholes today).
You’re asked to choose door 1, 2, or 3.
After you choose, the host- who knows where the prize is- opens one of the two you didn’t choose to reveal a painting of a cat’s asshole.
You’re left with two doors, one with a car behind it, one with cat ass. Will switching doors give you any advantage?
It seems super counterintuitive, but it is always the right decision to switch doors. Because you only had a 1/3 chance of guessing correctly on that first door, and that didn’t retroactively change when one majestic cat tuchus was revealed.
To clarify a few comments I saw-
-The host never reveals the car. It’s cat’s assholes for days.
-The host doesn’t open one at random, the problem is approached under the assumption that the host knows what’s behind all doors.
-I saw a few comments to the effect of “because there are two blank doors that could be eliminated when you chose the right door, it’s actually a 1/2 chance after all.” Which is at least creative in how it’s wrong.
And my personal favorite:
-“I still just don’t get it and you math people can say it’s right all you want but still I say it’s a 1 in 2 chance.”
Yeah go through life with that attitude. Miss everything cool and die mad. But switch doors, it’s just good math.
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I’d still go for the goat. Just nobody object to what I do with it, which would involve a freezer and cookware. Goat meat is tasty!
And due revenge on goats overall after my cousin’s goat and an incident with it.
My cousin had the dubious wisdom to acquire a pet goat. She had an acre of land, so why not I guess. At a family get together, I decided to make friends with the loose goat, so I got on the ground at eye level and petted it. Got along famously, forgetting that goats express affection by head butting.
(Clop!) Ow! While rubbing my forehead with a couple of fingers and looking at my life, who was in hysterics, literally doubled over. I then glanced back at the goat, which was splay legged, sitting and a bit wobbly.
Until they day she died, my wife swore that the goat’s eyes crossed on impact.
My cousin found a new home for the goat after it butted her thigh, giving her a dessert saucer sized bruise.
True story.
The moral, Sicilian-American heads are decidedly harder than a goat’s head – or cast iron, which is another story, for another day.
Hey, my commander even recognized that I have a built-in Kevlar helmet.
One thing I love about this last year (well, besides that we MAY be defeating the fuckAllHumans known as Covid) is the amazing advances in AI. And AI is especially when unleashed on games is finding some strategies and tactics that know human would ever have been ‘stupid’ enough to even try. Who needs maffs when ya can just unleash a few billion iterations of sumtin with just a bit more smarts than your average republican.