It fundamentally doesn't make sense to me. After years of thinking about it and hearing every explanation of it, I still don't understand it.
It just makes no sense.
I numerically understand the mathematics behind it, I guess, but it doesn't make any real life sense except there is magic involved.
The classic Monty Hall problem says there are 3 doors (2 goat doors, 1 car door), I can choose one, then 1 goat door is being opened randomly, thereby eliminating a goat... and I increase my chances of winning a car from 1/3 to 1/2 by switching.
Now let's change the experimental setup:
1. There are 100 doors and 100 players, each choosing exactly one door.
2. Doors with goats get opened at random until 98 doors get eliminated.
3. There are now two doors with their two original players left, one is guaranteed to have a goat, the other is guaranteed to have a car.
4. One of the players is given the chance to switch their doors with the other player.
5. Alternatively: Both players can agree to change their doors.
I can't wrap my head around why there should be a difference in chances compared to the original setup. Neither for alternative 4 nor alternative 5. I don't understand why there isn't always just a 50/50 chance of me winning if I can choose between two doors.
With 100 doors without any other player, I can still choose only between two door in the end. Apparently, mathematically, I have a 1/100 chance of being right without switching and a 1/2 chance of being right when switching. But WHY? Why does it work in real life?
So, in my alternative set up, why are the chances magically different? Why does it matter how many doors were there in the beginning? Why does it matter how many players there are? If only I am given the chance to switch but choose not to, shouldn't I only have a 1/100 chance of winning and, thereby, basically guarantee that the other player has a car? Like, of course not, the chance is OBVIOUSLY 50/50 and switching means nothing. Why is it different in the original Monty Hall problem? My information is the exact same: False options were reduced, two doors are left, one has a car, one doesn't, and I don't know which is which. Why does anything that happened previously matter? lol wtf man my brain just can't.
Edit: Thanks for the answers, I have to think through some of them. I still don't get it, my brain refuses, but I already learned a lot so far.