What does "password strength" really mean?
If people used a textual representation of number obtained from a reliable hardware random number generator then the meaning would be unambiguous. It's the number of digits in that number. But most people don't do that (perhaps more should).
So what does it mean to say that a password has so many bits of entropy? Well, I guess it means how many truly random bits it would take to index their password from the universe of passwords the user considered. This is more an exercise in psychology than it is in mathematics. You have to figure out how users generate passwords or discount passwords. For example requiring a mix of upper and lower case letters doesn't add as much entropy as you'd think, because most users are mediocre typists who'll avoid using the shift key too often. Requiring digits means that many people will just "0" for "o" and "1" for "L".
So it's really easy to concoct passwords which you know are bad, because you know the methods used to select which passwords you'd consider; if the developers of the strength meter don't take your particular generation algorithm into account the meter will show the password to be stronger than you know it to be.