So they seem reasonably comparable... It would be nice to redo the calculation while accounting for how common each word is, and also that special characters ar

So they seem reasonably comparable... It would be nice to redo the calculation while accounting for how common each word is, and also that special characters are used less often in passwords. I know this was a rough estimate, but I think it is way, way off. Passphrases are not usually generated by random choice of English words but are instead a particular, meaningful English sentence. This means not only are you dealing with word distribution nonuniformity but word history correlations. Without doing any math in particular, let's pick a typical 4 word phrase (literally, I'm opening the book in front of me and looking for a 4 word sentence.) "This will be natural" In all honestly, this is closer to a combination of a subject (with a great deal less entropy since familiar subjects are common) a tense, and an adjective. I think you'd be lucky if there were 2^18 sentences of similar complexity, let alone 2^62. In comparison, four random words drawn from an English dictionary. "idiocy rammer stars cookshop" Passphrases of this class might have closer to 62 bits of entropy. So what does this mean? In all likelihood, if passphrases become more common, we'll see language model based cracking routines which generate billions of sensible English sentences to crack these passwords. Length is no protection ("abcedfghijklmnopqrstuvwxyz1234567890"). Anything with genuinely high entropy is by definition difficult to remember.