Earlier quoted context omitted.
Funnily enough I opened a new bank account the other day (Chase) and to my surprise they don't allow special characters to be used in the passwords. Special characters don't make as much of a difference as password length: http://xkcd.com/936/ (a comic that must appear on any password-related thread). According to the XKCD analysis, an 8 character password based mostly on letters with some numbers and symbols has ~28…
Do you know how they are calculating the approximate entropy score of the characters used in the passwords? I entered the password from the xkcd comic in this web site: http://rumkin.com/tools/password/passchk.php And got an entropy of 51.8 bits. Long passwords are great (especially if one is using a password manager), but not many places accept them.
I imagine the calculation goes something like this:
1/50000 Likelihood of a particular uncommon word
1/8 Substitute up to three letters for numbers
1/2 Initial capital or initial lowercase
1/32 Add a punctuation character at the end
1/10 Add a digit at the end
1/2 Possibly swap punctuation and digit at the end
----------------------------------------------------------
1/512000000 Resulting probability
-28.93157 log2(1/512000000) -- number of bits of entropy
So, if e.g. XKCD assumed only 25000 uncommon words to choose from, that would give ~28 bits of entropy.