For some reason the internet still has weird arguments about the Monty Hall "paradox". I think it might be because sometimes the way it is explained is a bit confusing to some people? Idk, but I do remember that when I first heard about it the explanation was kinda weird to me until I rephrased it in simpler terms.
Here is the thing. You have 3 doors, one of them has a car train behind, the others have goats. You pick a door at random, the host doesn't open it, but he eliminates one of the other doors by showing it has a goat behind it, and asks you if you want to change your choice. So perhaps you picked door A first, he eliminated door B, and now your choice is between door A and door C. If you change your initial choice, it turns out that you will be correct 2/3 times, whereas if you don't you will only be correct 1/3 times. This confuses some people because they expect that since it becomes a choice between 2 doors it should be 50-50.
The simple explanation is that if you picked the door with the train the first time, then by changing you will always lose. If you didn't pick the correct door the first time, then changing always wins. But you will only get it right the first time 1/3 times, whereas you will get it wrong the first time 2/3 times, so changing is advantageous. That's it. That's all there is to it. There doesn't need any more mystification.
If it is still not intuitive, imagine if you had a million doors, you picked one, and the host eliminated all the others except one. There is (almost) no way you picked the right one the first time, it is literally a one in a million chance. So if it is not that one, and it almost certainly isn't, it must be the other which the host practically hand picked for you.
EDIT: For the reasoning to work, the important assumptions are two. One, the host always eliminates a goat, never a train. Two, the host always reveals one of the other two doors, not the one you picked. Both of these are significant, without the first one you have only a 1/3 chance of winning regardless of whether you change or not, and without the second one it becomes a regular 50-50 choice.
There's also the fact that the first person to famously solve the "paradox" was a woman. How is this possible? Am I truly being bested in logical reasoning by... a woman?
Edit: Marilyn vos Savant, her name sounds kinda badass, like a genius superhero or fantasy protagonist's name.
She wasn't the first person, it was an older problem which was restated in a few different forms, and it was solved basically the moment it was discovered, it's pretty trivial compared to what probability theorists and statisticians usually deal with. Vos Savant was a columnist who supposedly had a really high IQ and people sent her puzzles to solve. However, the puzzles usually already had known solutions. It is definitely true however that this is why a lot of people who read her got pissed, they were annoyed that she was a woman and were very intent on owning her.
Interestingly, she herself has gone against mathematical consensus for silly reasons a few times since.
deleted by creator
to be fair, you have to have a very high IQ to understand decision-making trees applied to hypothetical game show conundrums
Yeah pretty much.
True, true. I meant that she did it first in a very public way. You know, it must really suck to be famous for being a genius. How are you supposed to deliver on these expectations?
True.
deleted by creator