# The Special Fish Report

## Albert W. Small (December 1944)

### Page 60

Tony Sale's
Codes and Ciphers

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CX/MSS
TOP SECRET Special Fish Report Page 60

In the motor runs shown, "slants" were counted because they

showed the greatest bulge from the 32-letter count.

Total letters in message: 3,652. Total slants, 214.

Average score expected at wrong settings, 138. Sigma, 7.3 Set total,

156. Expected score right position, 174.

This last deserves explanation. If there are "d" dots in

M37 then "a'" = (37-d)/37 and total number of Mb = x positions in a

message "T" long = T(37-d)/37. Average score for any given character

run opposite Mb = x positions (assuming Delta-D characters to be perfectly

random at such positions) = (T/32)*(37-d)/37 . Assume that the character

being run has a total of "r" as shown in the 32 letter count. Since r

= sum of counts at Mb = x and Mb = . position (at right settings), we have

Mb = . position count should equal r - ((T/32)*(37-d)/37), provided the motor is

set correctly. If the motor is set incorrectly, Mb = . positions should

give a score of r*(d)/37.

Psi runs give terrifically high bulges. Motor runs are done

first; and then the chi's and motor are both known. The undeltaed Z text

is then run on Colossus against psi1 and psi2, with the chi's and motor

being added in correctly, so that at the right settings of psi1 and psi2

the resultant text is P(1 plus 2). P(1 plus 2) has a great advantage in

scoring: out of 2,000 letters a score of 1400 or more can be expected.

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