[ecdavis]

You're right.

That's really interesting and counter-intuitive.

https://gist.github.com/ecdavis/da8f67258860e9f35620

EDIT: After thinking about it for a while it seems obvious and I feel fairly stupid.

1/3rd of the time your initial choice was correct. The random host always reveals a goat, you take the opportunity to switch and lose as a result.

1/3rd of the time the random host reveals a car, the game ends without an opportunity to switch.

1/3rd of the time the random host reveals a goat, you take the opportunity to switch and win as a result.