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I think Markov chains would be a bad idea for the use case of passwords because some words always follow certain words.

Ah, true — I was thinking more along the lines of "part of speech" Markov chains, if that's even possible. (As in, just an endless stream of "article noun verb adjective noun adverb conjunction adjective noun verb adjective noun conjunction adjective etc." that could then be mad-libbed by diceware.)

It is possible (and, I think, a rather clever idea).

You could, for example, use a part-of-speech tagged corpus (a large collection of text where each word was tagged with its PoS by a grad student). Just train a Markov model on the parts of speech instead of the words themselves, and you would be able to generate English-like mad-libs.

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