alt Hacker News1/3 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 ?!
The other way to see it is by just looking at the different outcomes of car behind door A, B or C.
Let's call the door you initially pick A.
car initial monty stick swap
A A B A C -- or Monty picks C, and you swap to B
B A C A B
C A B A C
So, if you stick, get it right 1/3, but swap get it right 2/3.