Diceware, 6 words 2.2 x 10^23
Diceware, 5 words 2.8 x 10^19
Diceware, 4 words 3.6 x 10^15
a-zA-Z0-9, symbols, 10 4.3 x 10^19
a-zA-Z0-9, 10char 8.4 x 10^17
a-zA-Z0-9, 8char 2.2 x 10^15
A 6 word diceware phrase has 100 million more combinations than the 8 character alphanumeric. Diceware, 6 words 77 bits
Diceware, 5 words 64 bits
Diceware, 4 words 51 bits
a-zA-Z0-9, symbols, 10 65 bits
a-zA-Z0-9, 10char 59 bits
a-zA-Z0-9, 8char 50 bits
For any remote site, I recommend using 22 characters from [a-zA-Z0-9]; this is 128 bits, and is easily copy-pasteable.It's highly amusing when a site tells me that such a password is insufficiently complex, given that it will never in the lifetime of the universe be guessed.
The entropy calculations are probably generous. The wordlist isn't as long as it looks, because some of the words are strange and people tend to re-roll if they get something like that. It's probably better to assume there's only 1000-2000 "words" people will safely combine.
Also, the combinations list assumes that the attacker knows the method/word-list used to generate the password, which may not be foreknowledge the attacker has access to, especially in cases of giant many account password brute forcing attacks.
Just because your passphrase may essentially be a PIN look up into a lookup table doesn't mean the attacker knows that or has access to the same lookup table.
You can also add additional entropy via punctuation or casing.
The point to a random passphrase is to try to avoid "human" mistakes like over favoring a subset of words, and rerolling words you don't like potentially makes your collection of passphrases more susceptible to analysis or social engineering (word association) attacks.
Like I said, it's generally better to pick a word-list you are comfortable with all the possible words than to subset a word-list you aren't entirely comfortable with.
The goal of something like Diceware is to be easy for humans to memorize but also still true random (see: xkcd's battery horse comic). If you don't need to memorize it, then yes, why not entirely generate a random sequence of letters/numbers/symbols/emoji.
> Distributed_By: WalgreenCo. 200 Wilmont Rd.
And it would both be very strong, and be difficult for someone at my desk to guess by looking at things on my desk.
As XKCD famously pointed out[0], Diceware[1]-style pass phrases can be both secure and memorable. XKCD's four word example isn't secure when fast brute-force attacks are feasible, but eight words is still easily memorable and secure enough for anything. The important point here is that "random words" really does mean "random", i.e. not picked by a human.
[0] https://xkcd.com/936/
[1] https://en.wikipedia.org/wiki/Diceware