> Your intuition is wrong and it doesn't matter what the host knows before showing you the door that doesn't have the prize.

This is not correct and your source doesn't support your point

From your link:

> Monty helps us by “filtering” the bad choices on the other side

Monty knows which door holds the car and which holds the goat

How can they reliably show you the door that doesn't have the prize, if they don't know where the prize is? They can't, which means the host must know, which means it must matter what the host knows?

He's not reliably showing it. You're being presented with a situation in which the door shown doesn't have the prize.

An illuminating example uses a deck of cards. You're trying to get the ace of spades. You pick a card. I don't know anything but I turn over 50 of the 51 remaining cards and they're not the ace of spades. Do you want to switch your pick to the alternative unknown card?

To a casual observer it looks like they picked the door without price by chance.