1/3 chance prize is behind a given door. Pick a door, you've got a 1/3 chance it's behind it.
But there's a 2/3 chance it's behind one of the other doors.
So you've got two sets of outcomes at this point. Set A has 1/3 probability (the door you chose). Set B has a 2/3 probability (the two doors you didn't choose).
You then get this incredibly valuable information. The door in Set B that doesn't have the prize. So now Set B still has a 2/3 probability of having the prize. But you know that higher probability now applies to only the one door in Set B.
So you end up with:
Set A door = 1/3 chance |
Set B door = 2/3 chance
1/3 chance prize is behind a given door. Pick a door, you've got a 1/3 chance it's behind it.
But there's a 2/3 chance it's behind one of the other doors.
So you've got two sets of outcomes at this point. Set A has 1/3 probability (the door you chose). Set B has a 2/3 probability (the two doors you didn't choose).
You then get this incredibly valuable information. The door in Set B that doesn't have the prize. So now Set B still has a 2/3 probability of having the prize. But you know that higher probability now applies to only the one door in Set B.
So you end up with: Set A door = 1/3 chance | Set B door = 2/3 chance
Make the switch every time.