alt Hacker NewsThe host might be selecting between two goats, or might be selecting between a goat and a car. Either way, it doesn't matter because we don't get any additional information about whether our original choice was correct. (To clarify, this applies to the original problem, not the Crawl variant, where we either sometimes get definitive information, or sometimes get no information)
Edit: Furthermore, I don't think that author's solution to the Crawl problem is correct. When the host eliminates a door, either you will get information that says you should switch, and you'll win 100% of the time; or you won't get information, and you should still always switch and win 2/3 of the time.
> it doesn't matter because we don't get any additional information about whether our original choice was correct
That's the missing assumption. I would say assuming that people are perfectly random falls into the "standardized test" category.
> you won't get information, and you should still always switch and win 2/3 of the time.
You always get some information, the set of possible results becomes narrower, so saying the probabilities don't change is not sufficient. Not a good idea to discuss the problem in informal language though.