[rsa25519]

> In this: "the host will open the door at random and in this example it happen to have a goat" vs "the host will never open a door with a car behind it".)

If the host opens a door with a goat, then it doesn't matter whether or not it was intentional.

[dllthomas]

Yes it does. Or more precisely, it matters whether the host could be counted on to do so reliably; the mechanism for that doesn't matter.

There's a difference here, that our language obscures, between procedure and hypothetical.

[tpush]

The intention of the host only matters if the contestant would have to choose the subsequent action (switching or not) before the hosts opens a door.

If the host has revealed a goat door, and the contestant then has to decide what to do, the intentions of the host for having chosen the door are irrelevant.