alt Hacker NewsIt's kind of like me reading the wikipedia page on the Monty Hall problem.
I read an explanation about why it makes sense to change doors. But no, my gut tells me there's a 50/50 chance. I scroll down, repeat...
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1/3 chance you picked the door with the car, 2/3 chance it's behind one of the other two doors.
These probabilities don't change just because you subsequently open any of the doors.
So, Monty now opens one of the other 2 doors and car isn't there, but there is still a 2/3 chance that it's behind ONE of those 2 other doors, and having eliminated one of them this means there's a 2/3 chance it's behind the other one!!
So, do you stick with your initial 1/3 chance of being right, or go with the other closed door that you NOW know (new information!) has a 2/3 chance of being right ?!
it's easier to think about it with 100 doors.
if you get to pick one and he opens 98 of the remaining ones, obviously you would switch to the remaining one you didnt pick, since 99/100 times the winning door will be in his set.
Chasing this tangent a bit -- I have never been happy with the Monty Hall problem as posed.
To me the problem is that it is posed as a one-shot question. If you were in this actual situation, how do you know that Monty is not deliberately trying to make you lose? He could, for example, have just let you open the first door you picked, revealing the goat. But he chose to ask you to switch, then maybe that is a big hint that you picked the right door the first time?
If the game is just "you will pick a door, he will reveal another door, and then you can choose to switch" then clearly the "usual" answer is correct; always switch because the only way you lost is if you guessed correctly the first time (1/3).
But if the game is "try to find the car while the host tries to make you lose" then you should never switch. His ideal behavior is that if you pick the door with the goat then he gives you the goat; if you pick the door with the car then he tries to get you to switch.
Yeah I studies Statistics in graduate but still believes that it's wrong. It's mathematically correct but it's wrong! I refuse to believe it!
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That gut feeling approach is very human like. You have a bias and even when the facts say that you are wrong you think that there must be a mistake, because your original bias is so strong.
Maybe we need a dozen LLMs with different biases. Let them try to convince the main reasoning LLM that it’s wrong in various ways.
Or just have an LLM that is trained on some kind of critical thinking dataset where instead of focusing on facts it focuses on identifying assumptions.