# Captain Walter Fried's Fish Notes Annex to #F 71, Screed on Delta D Counts and Colossus runs

### Page 2

Tony Sale's
Codes and Ciphers

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We are liable to get fantastic counts on / or 5 (Doodlers):
or to messages with a lot both of 5 and U (Punctuation): or to get
messages with 3, J, F as the highest letters (plain German).

Linear combinations of the factors, of course, give linear
combinations of the effects; it is however important to keep in mind
the constituent parts.

2. Details of Techniques.

We normally get the first four X (Chi) - settings in pairs, - from
a run for X1 and X2 followed by a run for X3 and X4 or for
X4 and X5. Any run in which two X's are to be set is called a long
run : any run for only one X is called a short run.

Long runs. A long run is liable to produce a purely random score in
the neighbourhood of 3.2 sigma ; scores of 3.5 to 4 sigma are far from
being rarities. It is important to improve judgment by scoring the
best scores of runs; a chart exists, making use of the second best
competitor, giving the decibanage in favour of the best score. As a
rough rule of thumb, it has not in the past been our practice to accept
as a basis for further runs a X1 X2 result below 3.5 sigma.

If a X1 X2 result of probability p is accepted. it can
be much improved if a good result is obtained on a run using these
settings as a basis. Suppose that, on the (3+4)x/1x2x run, a result is
obtained whose probability (lusing the chart) works out to be q. We can
assume that the probability of the X34 settings being right and the
X12 wrong is negligible. (This can be checked by doing the (3+4)x
count at the place in question).

we now compare 4 theories (a) X1234 all right.
(b) X12 right 34 wrong.
(c) X12 wrong 34 right.
(d) X1234 all wrong.

The odds of these are pq : p(1-q) : 0 : (1-p) (1-q) [ see Appendix]
In fact the odds in favour of (a) are pq : 1-q - or, the odds on the