Nothing makes me want to call math fake as much as the Monty Hall problem. Not even 0.999999... equaling 1. Yes I understand the proof yes it technically makes sense but I just hate the Monty Hall problem so, so much.
Is that the game show one with the doors?
Correct. The basic scenario is that there is a car behind one door and a goat behind two doors, and you don't know which is which but the game show host does. If you pick the door with the car, you win the car. The host let's you pick a door, then opens one of the two doors you didn't pick, revealing a goat. The host then offers you one last chance to switch your pick from your original door to the other remaining closed door.
The Monty Hall problem states that you should always switch your pick, and that by doing so you will double your chances of winning the car.
Which, intuitively, that's nonsense. Your choice has no actual impact on the reality of the situation. You're guessing blindly the same as before, it's just now that you have a one-in-two chance of guessing the right door instead of a one-in-three chance.
EXCEPT
During your first round of choosing, you had a 1/3 chance of guessing the car vs a 2/3 chance of guessing a goat, if you were only allowed that one guess. But once it's narrowed down to two doors, one with a goat and one with a car, you're now guaranteed to get the exact opposite outcome of what your original guess would have been if you switch. So if you stick with your first choice, you still have a 1/3 chance of getting the car and 2/3 chance of getting a goat. But if you switch, then suddenly that becomes a 1/3 chance of getting a goat, and a 2/3 chance of getting the car.
It's bullshit and I hate it so much.
I understand it but i hate it, like the maths is right but logically it just doesn't click
See, you understand my pain.
#why doesn’t choosing the same door you already chose have the same effect? that’s what I want to know#like does math not agree with the sage advice of ya authors that not choosing is also a choice?
The trick to it is that you're technically playing two games in a row, and the second one is the only one that you actually have to win.
In the first game, you have two chances to lose (picking a goat) and once chance to win (picking a car). Worse-than-even odds. But the important thing is, you don't actually get a prize for winning this first game. It's just set-up for the second one.
In the second game, sticking with your door is basically saying "I think I made a lucky guess in the first game, I'm sticking with that decision." Switching doors is saying "I don't think I got lucky in the first round, so I'm going to change my decision." You are gambling on whether you won or lost the first game, and what wins or loses you the prize is guessing correctly whether you were lucky in the first game. And because the odds of the first game were worse-than-even, guessing that you lost the first game is the safer bet, because you probably weren't lucky.
The really painful part of it is that our brains want to interpret it all as one game, where you've basically got 50/50 odds no matter what you do. That's what our every instinct is screaming at us should be happening, because the physical endgame is two closed doors, only one of them with something we want behind it, which has been there from the start. But it isn't one game with 50/50 odds. It's two games in a trenchcoat, and their combined odds are skewed.
“You are gambling on whether you won or lost the first game” is in fact the only time the Monty Hall problem has ever made even a shadow of sense to me, and I think you should get an honorary PhD in math or maybe philosophy for writing it down.
That's actually very flattering, especially considering how long I've wrestled with this thing, thank you.
Ok but lets be honest id be happier with a goat
