It's because the host has knowledge of the situation. Each door has 1% chance. You lock one door closed that the host can't touch, goat or car. The other rule for the host is they have to open all of the doors except one and they also can't open the car.

The door they leave is all possibilities from all doors at the begining minus your door (since the host couldn't mess with it), which is 1%. Your original choice determined that door would stay closed by the host so the host can't effect it's odds with their knowledge. There is only a 1% chance you locked the car behind that door picking randomly. Either you got the 1% and locked the car door or you didn't. The host will remove 98 goats without random chance and which will leave a car or a goat left. There's a 99% chance you made them leave the car with your first choice being 1% and a 1% chance you made them leave a goat. It's still the original odds, but it flips because the host has knowledge and either was forced to removed all possible bad choices and leave the car or you managed to hit the 1/100 chance at the start. There's a 99% chance you didn't, so switching has a 99% chance the host left it there.

[–] [email protected] 2 points 1 year ago

I think this might have been the answer that helped me the most. Most of all, it's that the Monty Hall problem isn't about you, it's almost entirely about the host's action of revealing doors.

There's a 98/99 chance he left that door because it's the car, or 1/99 because it's the goat (assuming the one left out of calculation is your door which he can't choose). Your original choice, whether or not you picked the car, is largely irrelevant. His actions can't affect your door because he can't choose it

You're not betting on a new set of 1/2, you're not even betting on the door itself having a new probability. You're betting on the act of the host revealing doors.