Are there password-cracking algorithms that attempt passwords from lowest-entropy-to-highest-entropy?
Is it even theoretically possible to sort passwords by "entropy" ? (seems like a hard thing to easily measure; password "a.b..c...d....e.....f" has low entropy, but would any password-cracking algorithm try it before 6 random characters?)
Is it even theoretically possible to sort passwords by "entropy" ? (seems like a hard thing to easily measure; password "a.b..c...d....e.....f" has low entropy, but would any password-cracking algorithm try it before 6 random characters?)
Yes, but there is no one useful definition of entropy— you don't know the prior.
E.g. http://openwall.info/wiki/john/markov assumes one kind of prior (that your password is the realization of a markov random walk with some measured transition probabilities— something that was shown to be a pretty good model of real passwords in the literature). You can even use it to sort pre-existing wordlists.
There is of course the zero information prior— e.g. the uniform one, where you'd conclude that "password" and "jxiesotm" are equally good passwords. But it's not very useful.
I calculated the entropy of my passphrase when I chose it, and it was good enough. It was less originally (but still over 5000 years to crack), anyway I altered the phrase a little (played with caps, special chars, and so on). I am pretty confident that my super-secret password is safe 
Perhaps your alterations are sufficient, I can't say— but you're making a fundamental error here by assuming an entropy measurement tool can tell you anything useful. All tools can really do reliably is give you upper bounds on the entropy (e.g. saying that 'password' and "jxiesotm" each could have as much as 49.3 bits of entropy (assuming a 72ch charset)).
You can try to guess a tighter bound than that, but you'll be wildly off depending on if you got the model right.
If choosing 16 word phrases verbatim from books were something people did often enough for an attacker to adopt that prior than your password would only have (assuming my really armwavy numbers of 80k books of 80k words) about 32.5 bits of entropy in that model. You can insist that some tool says that 16 words magically gives you 500 bits of entropy, but it simply isn't so if you picked those words out of a book. Even without ever having the actual book I can make much stronger predictions just by knowing that the words are comprehensible english.
[9, 9, 9, 9] < do these numbers have very low entropy? You can't say from just looking at them. What matters is how they were generated. How about [140, 166, 77, 233, 193, 177, 35, 167]? (It seems like it has high entropy but it's just a DES encryption of zeros with a key of zeros).
Ideally, what you want to do is to make the zero information prior the correct prior by choosing uniformly. This is removes the risk of the attacker beating the odds with better predictions of password choices because there is no way to beat the uniform prior if you're actually using the uniform prior and it's not easy for you to confuse yourself about how much entropy you actually have.
