Adding ad hoc hypotheses about the host's motivations turns this into a family of related problems, but not The Monty Hall problem.
For any given logic puzzle, you can safely assume anything not specified is outside the problem.
Here, what Monty had for lunch, whether he finds the contestant attractive, or some complex algorithm for his behavior is left unspecified and -- since this is a logic puzzle -- this must mean none of this matters!
Imagine if Monty opened a door with a goat only if he had had goat cheese for breakfast. Sounds ridiculous for the logic puzzle, right?
We can safely assume, like Savant, that Monty always picks a door with a goat, turning this into a logic puzzle about probability.
Anything else is going out of your way to find ambiguity.
Well sure, it doesn't appear that vos Savant was asked the Monty Hall problem. She seems to have been asked an ill formed alternative problem and answered that instead. Then the interpretation of the ill formed question with the most interesting assumptions about the host's behaviour became the Monty Hall Problem.
And the linked article (and by extension Mr. Diaconis & CrazyStat) was talking about the question that vos Savant was asked as opposed to the one where the assumptions to come to an answer are enumerated.
> We can safely assume, like Savant, that Monty always picks a door with a goat, turning this into a logic puzzle about probability.
No we can't. Otherwise we can safely assume any random axiom, like "The answer is always the 3rd door". You have to work with the problem as written.
For any given logic puzzle, you can safely assume anything not specified is outside the problem.
Here, what Monty had for lunch, whether he finds the contestant attractive, or some complex algorithm for his behavior is left unspecified and -- since this is a logic puzzle -- this must mean none of this matters!
Imagine if Monty opened a door with a goat only if he had had goat cheese for breakfast. Sounds ridiculous for the logic puzzle, right?
We can safely assume, like Savant, that Monty always picks a door with a goat, turning this into a logic puzzle about probability.
Anything else is going out of your way to find ambiguity.