[mtlogstdo]

I don't really understand how you think the game could work if the host didn't know where the prize is? They'd keep accidentally revealing the prize, and then asking you whether you want to switch to the other remaining door, at which point... what's the point? The game is over.

I've not usually seen it explicitly stated like this that the host knows, but it's always seemed obvious to me that they must.

[seoaeu]

There's an alternative version where the host opens a door at random. If it is a goat, they proceed the same as the normal version. But if it reveals the car, the host says, "Sorry, the car was behind door C. You lose."

And a third version where the host only asks you to switch if you initially picked the car, and otherwise always ends the game early.

The best part is that during the game you can't actually tell which rule set you are playing with!