The lack of specificity is not that the host might open a door with a car, but whether the host had to open a door at all. This is not clear from Savants formul

The lack of specificity is not that the host might open a door with a car, but whether the host had to open a door at all. This is not clear from Savants formulation, and indeed does not match the actual game show, where the host had discretion in every episode whether to open a door. If the host does not have to open a door for the candidate (which is quite likely, he's playing his own strategy of making the show exciting, not predictable), then the usual solution (always switch) is not correct. All this, and probably any variation and every solution of the problem that comes up in this thread (and probably every other Monty Hall forum thread in the post 3 decades) are discussed extensively in the Wikipedia entry (e.g. https://en.wikipedia.org/wiki/Monty_Hall_problem#Other_host_behaviors https://en.wikipedia.org/wiki/Monty_Hall_problem#Other_host_...). Maybe every time a new Monty Hall thread comes a mod should just stick the Wikipedia entry at the top. I've never seen anything in any of the following discussion that hasn't been covered in Wikipedia already.