The Special Fish Report
Albert W. Small (December 1944)
Codes and Ciphers
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.