If the host has knowledge what matter is whether the host has the freedom to not open a second door (which they often have in TV shows where time is of the esse

If the host has knowledge what matter is whether the host has the freedom to not open a second door (which they often have in TV shows where time is of the essence), and deprives you of a second round. If the host has this freedom, and he is adversarial and assumes you know the monty-hall paradox, then the only time where he will offer you to show a second door is if you have guessed right to make you change.