Step 1: Take three cards face down, one of which is an ace. Step 2: Divide it into a pair of cards, and a single card. Step 3: Reveal one of the pairs of card

Step 1: Take three cards face down, one of which is an ace. Step 2: Divide it into a pair of cards, and a single card. Step 3: Reveal one of the pairs of cards. If you reveal and ace, return to step 1 since this history is eliminated from the story we've been told: we know this wasn't a possible path to our endgame. Otherwise continue to step 4. Step 4: Which of the remaining two cards is more likely to be an ace? Step 5: Realize that they're just as likely as each other to be the ace. Step 2 didn't magically imbue the card remaining in the pair with extra probability juice. Long story short, you definitely need Monty to make an intelligent selection, so Monty's knowledge is far from irrelevant. It matters whether he revealed a goat by luck or by knowledge, because he's 2x as likely to get "lucky" in the case where there are 2 goats behind the doors you didn't choose in your original guess.