# Captain Walter Fried's Fish Notes March 1944 to January 1945

### Page 6

Tony Sale's
Codes and Ciphers

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TOP SECRET CX/MSS

SUBJECT: Fish Notes Report #F 14
TO : CO, SSA, War Dept. 3 April 1944

1. The formalae used for setting X patterns can be developed
in a number of different ways. The following exposition is in some
respects a simplification but in others and amplification. I have
tried to translate from British terminology to our own and to fill
in gaps which appeared in the development. These gaps could, no doubt,
be easily bridged by a professional mathematician but I have atterpted
to set the matter forth in a wiy that can be understood by anyone with
a knowledge of algebra and the elements of probability theory. I have,
however, omitted some steps in the argument which might be necessary
for a complete and formal derivation from the theorams of inverse
probability. The use ot Delta Dij is purely illustrative. The formulae
are applicable to any relation in which lambda has an appreciable value.
The symbol lambda, incidentally, is frequently used here to indicate the
"bulge", or excess over random, of any variable. It has a different
meaning in this report, for example than in my report #F 5.

2.
n = message length
p = probability of dot in Delta Dij
1/2 = random probability of dot

If, at a given Delta Xij setting, s dots are yielded in Delta Dij arid if, a
priori, this setting is just as likely to be right as wrong, the odds
that it is right, or the factor in favor of its being right,

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