+23252 You should switch.
When the game starts, you get to choose one door, so you have a 1 in three chance to get the right door.
When the game starts, the host gets the other two doors, so he has a 2 in three chance of getting the right door.
Would you then trade your one door for his two doors? I would.
This is what the host is offering you: his 2 out of 3 chance of winning versus your 1 out of 3 chance of winning.
Because he shows you a losing door doesn't change the odds (he always has to have at least one losing door).
If you keep your first door, you have a one-in-three chance of winning; if you switch, you'll win (on average) two out of three times.
+23252 You should switch.
When the game starts, you get to choose one door, so you have a 1 in three chance to get the right door.
When the game starts, the host gets the other two doors, so he has a 2 in three chance of getting the right door.
Would you then trade your one door for his two doors? I would.
This is what the host is offering you: his 2 out of 3 chance of winning versus your 1 out of 3 chance of winning.
Because he shows you a losing door doesn't change the odds (he always has to have at least one losing door).
If you keep your first door, you have a one-in-three chance of winning; if you switch, you'll win (on average) two out of three times.
