This starts by assuming humans are bad at coming up with unbiased numbers but then requires them to do so. I don’t get how this could work with biased inputs.
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As such, while randomness is best, the given method is quite sufficient for having fun, and both players can agree that it's fair: they each have equal influence over the result.
Perhaps it’s just the feeling of “I took a risk and it didn’t work” vs “I chose badly and was outsmarted by the dm” seem different to me in an important way.
You could reframe this all easily as well for “I’m thinking of a number between 1 and 100, guess it within Y distance to succeed”. That’s mathematically equivalent I think, if you allow it rolling around.