The Bombe doesn't decrypt Enigma encrypted messages.
What it does is figure out which keys (initial rotor positions and plugboard settings) are logically consistent with the information you have, eliminating the bulk of possibilities and leaving humans to do the remaining work. In an actual Bombe (or the replica at Bletchley today) this results in a "stop" - the machine trying every possibility halts because the combination it's trying now isn't logically impossible. Humans then take the result of the "stop" and check whether they can decrypt the message, the Bombe can continue searching for other possibilities.
The logical inconsistency results from the fact that Enigma guarantees that any symbol X will encrypt to some different symbol. It will never encrypt to X. If that seems to happen it's an inconsistency and this can't be the correct key, try again.
This is a grave problem with designs like Enigma, and it's one reason why Enigma is the dying gasp of this approach, if you've got something like Lorenz you can't rule out any of the keys by logical contradiction like the Bombes, just as you can't with modern ciphers.
The attack this device implements requires you to have a run of known plaintext and its corresponding ciphertext, with correct alignment between the two.
The bombe searches for keying configurations that could have produced that encipherment. When you find one, you can go test if it decrypts the rest of the message into german or gibberish.
Excellent summary and explanation. Just to add; imagine you know the start of a message is the weather forecast for the day, or the date, or fixed greeting (or for something more modern - a known file header).
The "known plaintext" might be something you can observe/predict.
IIRC one cryptanalyst realised that the first 4 characters in ciphers from one particular operator never included the letter 'L'. They deduced that that operator always sent 4 Ls as an initial test, since L was on the right hand side of the keyboard and therefore the easiest key to hit for a right-hander. With LLLL as your known plaintext, decoding that operator's messages became a lot easier!
Well there were no spaces in enigma messages, but you can use the aforementioned property that no letter encrypts to itself to look for possible plain-texts and figure out their alignment.
e.g. "?E????????" is not HEILHITLER, at least not with that alignment.
Let's not forget one German message, one time, was undecoded to this very day. A paranoid conspiracy theorist of course, how could anyone doubt the security of the Enigma? How could anybody be onto Blechley Park's shit? A troll, if you will, in the forties.
This is of course a very short message, and almost certainly "broken" in some sense, e.g. perhaps part of it is missing or the operator mistakenly changed something part way through. It was sent towards the end of the war, the U-boat which sent it is being chased at the time and will be sunk before Germany surrenders a few days later.
Dice-rolling seems unlikely as humans think repetitions like "KKZZ" or "VVBB" seen in this message are "wrong" and "don't look random enough" which is why you can't let humans do this work. Also the radio operators probably have better things to do than risk getting executed for wasting resources on such games at a point where Germany has definitely lost the war.
On the other hand, screw-ups due to being stressed by people trying to kill you in a war you're probably aware you've lost already are very likely. I'd be a complete wreck if I was that operator.
