Quote:
That made it click for me for some reason. It's the forcing of Monty's choice bit that's key.

Yup.

Another way to re-word Ninti's explanation could be:

If you choose the first goat, he is forced to reveal the second goat, and the correct choice is to switch.
If you choose the second goat, he is forced to reveal the first goat, and the correct choice is to switch.
If you choose the car, he reveals either one of the goats, and the correct choice is not to switch.
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Tony Fabris