these rules was that the key-maker had his possible wheel orders listed in groups or columns by left hand wheels and that he tended to hop from column to column from a desire to "mix them up" and to avoid "crashers" - a totally fatuous ambition but one very understandable in a person without cryptographic knowledge. That he should always have tended to hop in the same way was a natural human failing.
One part of the new system consisted of listing on a combined table for all keys the number of occasions on which each left hand wheel had been followed by the other wheels. The table brought up to date looks like this:
This produced a most impressive result and led to a heavy saving of bombe time - overall perhaps a 30 or 40% saving. Assume it had been 1 on the left the day before; a fairly good crib (60%) would only be run for 6, 7, and 8 on the left and, if it went down, it would still be more likely that the crib was wrong than that it was wheel 2, 3, 4, or 5 on the left and another crib would be run before these were considered; in the same way, if a certain crib were available, the best wheel orders could be run first thus increasing the likelihood of an early break and saving bombe time. When a bad wheel order did happen, one tended to be badly caught, but taken all in all the amount of time saved was very great indeed.
The second important rule, and one which became extremely powerful towards the end of the month, was the rule of 'Threes'. There were 15 wheel orders a month and it was extremely rare for any left hand wheel to be used 3 times so that when a left hand wheel had been used twice it could be ignored for the rest of the month. For the last pair of the month normally only 2 left hand wheels remained and probably one of these was preferred on the basis of the table given above. The effect of this was that at the end of the month not more than perhaps 25 or 50, sometimes even 10 or 15, wheel orders need be run instead of the normal 276. With much less effort a limitation comparable to that of Banburismus was obtained.