[Cushman]

Sure, I see what you're saying. In a technical sense the information in the host's head does "matter". My comment is more along the lines that "information content in a system" is a sufficiently abstracted idea from "knowledge of a human being" that, especially if you equivocate them, it's not a useful metaphor for someone who doesn't already get why the right answer is right.

[dllthomas]

Yeah, it's not even strictly "does Monty know?" It's whether his action embodied that knowledge or not. Obviously (I hope) Monty knowing but still picking based on a coin flip is the same as Monty not knowing.