Now my knowledge of this comes through watching The Imitation Game, a glance of a wiki article, and a couple of computerphile videos, so forgive me if it's obvious.
While watching the Imitation Game, I couldn't help but think that the Bombe that was being developed was just doing a naive search through all possible combinations, so there would be some days where you'd run through all 159 quintillion odd settings before you got to the right one. So why was it so good?
I understand that quite a few setting could be discounted, as the enigma machines couldn't map a letter to itself, but surely that's still quite a lot of settings to search through. And while it'll be faster than doing it by hand, it's still quite a lot.
So naturally, I'm guessing that one of my assumptions is wrong, and Turing and co. are in fact, smart cookies. What sort of algorithm are they using to break the cypher, or how are they filtering the possible iterations down?