Yes, of the host opens a door, it will always be a losing door. Nobody is disputing that. The part that is underspeified is: does the host always open a door a

Yes, of the host opens a door, it will always be a losing door. Nobody is disputing that. The part that is underspeified is: does the host always open a door and if not, does the player's choice of a door impact whether the host opens a door?