We can implement password policies to attempt to mitigate this, but what we end up doing is frustrating our users, who will struggle to remember the 8 character

We can implement password policies to attempt to mitigate this, but what we end up doing is frustrating our users, who will struggle to remember the 8 character minimum, alphanumeric, at least one capital letter, at least one piece of punctuation password we have forced them to choose. >>> math.log((26+26+10+32) ** 8, 2) 52.4367108134211 So a "perfect" 8-character password has about 52 bits entropy. $ wc -l /usr/share/dict/american-english 99171 /usr/share/dict/american-english >>> math.log(99171,2) * 3 49.792892048685374 3 random dictionary words has almost 50 bits. 4 words would have about 66 bits. Couldn't average-user password strength be hugely improved by giving better password instructions (if your signup / passwork-change page is SSL as it should be, maybe even provide a few dozen random words as possibilities)?