[antris]

Strictly speaking it's not the hosts knowledge that changes the problem, but the fact that as a contestant you know how the host operates. This makes you able to extract information about the choice the host makes.

Different ways of host operation changing the outcomes are listed here: https://en.wikipedia.org/wiki/Monty_Hall_problem#Other_host_...

>"Monty Fall" or "Ignorant Monty": The host does not know what lies behind the doors, and opens one at random that happens not to reveal the car. Switching wins the car half of the time.