When creating a new password, people often recommend you use both uppercase and lowercase characters, numbers, and symbols. How does adding any of these increase the strength of a password?
Here's why I think it doesn't decrease the probability of a hacker finding out your password: Two people are asked to create a password of length
4. They are both allowed to use the full set of characters on a standard keyboard; let's pretend there's
100 such characters. Thus, the probability of a hacker guessing such a password would be
(1/100)^4. Person A creates the password
aaaa. Person B creates the so-called "more secure" password
aA$#. How does the fact that person A using "simpler" characters change the probability? The hacker has no idea who is using only "simple" characters or not, so it can't be used to increase the probability of guessing each character correctly.