Memorization and guessing

The easier a password is for the owner to remember generally means it will be easier for an attacker to guess.[1] Passwords which are difficult to remember will reduce the security of a system because (a) users might need to write down or electronically store the password, (b) users will need frequent password resets and (c) users are more likely to re-use the same password. Similarly, the more stringent requirements for password strength, e.g. "have a mix of uppercase and lowercase letters and digits" or "change it monthly", the greater the degree to which users will subvert the system.[2]
In The Memorability and Security of Passwords,[3] Jeff Yan et al. examine the effect of advice given to users about a good choice of password. They found that passwords based on thinking of a phrase and taking the first letter of each word are just as memorable as naively selected passwords, and just as hard to crack as randomly generated passwords. Combining two unrelated words is another good method. Having a personally designed "algorithm" for generating obscure passwords is another good method.
However, asking users to remember a password consisting of a “mix of uppercase and lowercase characters” is similar to asking them to remember a sequence of bits: hard to remember, and only a little bit harder to crack (e.g. only 128 times harder to crack for 7-letter passwords, less if the user simply capitalises one of the letters). Asking users to use "both letters and digits" will often lead to easy-to-guess substitutions such as 'E' --> '3' and 'I' --> '1', substitutions which are well known to attackers. Similarly typing the password one keyboard row higher is a common trick known to attackers.