If everyone in the world were using 100 passwords, you'd need space for 800 billion passwords, which is 39.5 bits of entropy. Assuming an alphabet of 74 charact

If everyone in the world were using 100 passwords, you'd need space for 800 billion passwords, which is 39.5 bits of entropy. Assuming an alphabet of 74 characters (lower + upper + digits + a few symbols), you'd need a little over 6 characters to make 800 billion unique passwords. A random password of 9 characters has a very low chance of overlapping any other password in the world: somewhere around Sqrt(74^9 / 74^6.2) ~= 0.2%. That's a 0.2% chance of overlapping any other password -- multiply that by the probability of having your password leaked for the chance that it's on the blacklist. Make it 10+ and you're fine.