[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