[om2]

It's not really meaningful to measure entropy of a single password, only of a distribution of passwords. You could assume a password comes from some distribution, but how would you know? Does "grefn" come from a distribution of "pick a 5 letter dictionary word and then randomly change one letter or a distribution of "pick 4-7 random ASCII characters"?

[Terretta]

> It's not really meaningful to measure entropy of a single password

Here’s a ‘not meaningful’ formula then: E = L × log₂(R)

• E is the entropy, in bits, representing how hard the password is to crack.

• L is the password length (number of characters).

• R is the size of the character set (e.g., 26 for lowercase letters, 52 for upper/lowercase, 62 if digits are included).

• log₂(R) is the number of bits needed to represent each character.

I hear your point: a single password might not actually use all character types, so the actual entropy could be less than its potential. Maybe they could have drawn from a wider range and didn’t.

But for everyday user feedback, assuming the fewest sets seems fine to nudge people toward picking stronger passwords.

[MathMonkeyMan]

One definition for the randomness of a finite string is the size of the smallest program that produces it. The definition is dependent on how programs are interpreted.

If my string is "aaaa", does that mean its entropy is zero? There is at least information about its length. And by your definition, how do we know that this password isn't from a 256 character set? Does "Aaab" have 26 times the entropy of "aaab"?

Topics like this make more sense to me when the strings are infinite, or when the population of strings is known.

[afiori]

A good password generator should check that the random generation did not give too many repeats or that the password is not easily guessed by a simple common password list