[heleninboodler]

It's a lot easier to see the 2/3 nature if you imagine that instead of revealing the goat and then asking if you want to switch, Monty said "you've chosen this door that has a 1/3 chance. I'm offering you to switch to choosing both of these two remaining doors, at least one of which definitely has a goat by definition." This is functionally the same offer. It's 2/3 to switch because you're effectively choosing two doors and having Monty automatically grant you the car if it's behind one of them.

[listenallyall]

The initial door reveal is misdirection by an informed host, such that it has no effect on the odds, which are always, players choice of door is 1/3. Imagine instead:

After the player picks a door, the host states out loud, "we started with 2 zonks, you picked one door, so there must be at least one unchosen zonk... and I'm going to show you one behind door #X (door opens with zonk)... now, would you like to switch?"

Wouldn't make for good TV but it describes what is actually happening. Knowing that the host will always show an unchosen zonk is the key to realizing that opening that door has no impact on the player's odds (1/3 originally, 1/3 after the reveal, thus switching is 2/3).

[heleninboodler]

> The initial door reveal is misdirection by an informed host, such that it has no effect on the odds, which are always, players choice of door is 1/3

Yes, exactly. Which means when you switch, the host is effectively allowing you to choose both the other doors, which gives you 2/3 odds.