The twist is that you aren't picking 1 door if you switch. You are picking 2 doors because Monty has already eliminated one when you made your first pick. That's precisely the 2/3 odds.

When you first look at it, you break it down in your mind as a different problem:

There are only two doors. One of them has a prize. Which one do I pick.

It's not like flipping a coin. That's why it "seems" counterintuitive.

The 100 doors example does help because it makes the odds more obvious by using larger numbers (for me anyway - this is where it first clicked). 1/100 of guessing correctly. Or the other way, 99/100 to get it wrong. When 98 of the incorrect ones are eliminated, you know one of those two has the prize. Do you feel confident in that 1/100 shot? Well, better to feel confident in the 99/100 that you were wrong. Which means if you switch, you win.

Basically you can look at it as using the odds of which does not contain the prize. Because the winning door will never be the one to be revealed. So if the odds are 2/3 you'll get it wrong, play those odds by switching.

Of course this doesn't help if they're moving the car and goats around back stage. Then all bets are off.

Bruno