[spronkey]

This. However, the alternative scenarios aren't the "Monty Hall Problem" - - the host will never open/blast a car door.

I usually find this problem annoying, not because it's all that difficult, in fact it's quite intuitive - when you're told the exact parameters defining the Monty Hall Problem and systematically work through them.

In my experience though, it's used more often as an exercise in diminution, a sick wet dream of probability teachers, where the learning party isn't aware of the problem, and usually either hasn't been explained, or doesn't quite grasp, the exact circumstances around whether the host's choice is random or decided.

There are lots of "it depends" moments that can be applied to incomplete descriptions of the problem, including (amazingly) whether the host offers a choice at all - this is the one that seems to trip up most people, as they might start to question the "motives" of the host (which are irrelevant in the actual statistical problem).