There's a third rule set where switching always makes you lose: Guest selects a door. If it has a goat behind it, the host opens that door and says "you lose".

There's a third rule set where switching always makes you lose: Guest selects a door. If it has a goat behind it, the host opens that door and says "you lose". If the guest initially picks the car, then the host opens a different door and asks the guest if they want to switch. For the player, if you've reached the point that the host is offering you to switch, there's no way to know whether you are in the case where switching improves your odds to 2/3, keeps them the same, or decreases them to zero.