Monty Hall extended

#1
(My question requires knowledge of the Monty Hall problem, i'm assuming on a stats forum most of you will not only have heard it but be bored sick of it so i wont explain it here. If you don't know what it is here's a video:
)

Anyway, my question is; after your pick, does it matter if the host picks one of the remaining two doors at random instead of deliberately choosing the empty one?
Obviously sometimes he will pick the door with the car behind it and there would have to be some contingency for this for the sake of the game show. I however, am interested in the times when he picks a door without the car behind it. On these occasions should the contestant swap?

(The contestant knows the host himself doesn't know the location of the car.)
Thank you for any contributions.
 

Dason

Ambassador to the humans
#2
I think you would need to define what would happen in the situation that the door to the car is chosen