I know the general math behind using character-based and dictionary-based passwords/passphrases and how to determine the entropy of the result. But I am unclear how adding uppercase letters, numbers and other characters or words to a dictionary-based passphrase changes the entropy.
For example, using Diceware, a six word passphrase gives me 77.4 bits of entropy. But if I now were to do simple changes to the phrase, such as use some uppercase letters, add numbers or other symbols, how does that affect the entropy? (I don't even know if uppercase letters matter since it's the same dictionary of words.) Could I achieve 77 bits of entropy by using just a five word passphrase and adding a few numbers and symbols?
Similarly, what happens if I add a word from outside the dictionary? Does that merely make the dictionary one word larger and therefore, not really change the entropy at all?