Try thinking of it this way: The information is in which door the host does not open. 2/3rds of the time, your initial choice will be a goat. In those cases th

Try thinking of it this way: The information is in which door the host does not open. 2/3rds of the time, your initial choice will be a goat. In those cases the host deliberately avoids opening the remaining door with a car - thereby telling you where it is. If you chose the car door initially, then indeed you get no new information. But that only happens 1/3rd of the time. I am curious if that changes your opinion.