>>11235242I am not sure if someone already posted this.
But this is the ultimate example of intellectualism fucking itself over.
People say: This case defies intuition!
But the thing is: It doesn't.
Your intuition of keeping your own door is correct.
Let's reformulate this problem:
Consider the monty hall problem as a 2 person game.
There is a player who chooses doors, and there is a game master who decides what happens in the game.
The game master wants to keep the car.
So how is the game master going to play?
If you pick a goat, he will just LET YOU LOOSE RIGHT THEN AND THERE.
If you pick a car, he will try to trick you into switching the door by showing one goat.
If this is the behavior of the game master, then your chance of winning by keeping your original door is 100%, and the chance of winning otherwise is 0%.
However, you can not be sure about that either. Maybe the plan was to open a door no matter what happens?
THEN, the chance is actually the famous 66%.
So the actual solution to the monty hall problem is actually the expected value of the set of algorithms the game master might have played times the estimated probability that he is playing them.
And here we leave the realm of mathematics and enter the realm of mass psychology and game show meta.
How do you estimate the behavior of the game show host?
Well, your INTUITION is telling you that he is trying to trick you. That is why it tells you to stay with the door you chose.
