# The Special Fish Report

## Albert W. Small (December 1944)

### Page 82

Tony Sale's
Codes and Ciphers

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CX/MSS
TOP SECRET Special Fish Report Page 82

This scoring is quite clearly derived: If ther is one dot, the

odds that the unknown is also a dot are:

which equals 2 if b is 2/3, and thus 10Log10 = 3. Similarly if there are

three and four dots, given no crosses.

In the example shown, the score values are given for crosses

without dots, as are given for dots without crosses. This is justified

in practice where it is not known whether or not the dots are really

dots, and the crosses crosses, there being a possibility that the signs

are reversed, but actually it is not correct. A complete and correct table

for scoring, assuming b = 2/3, follows:

SCORES IN DECIBANS FAVORING HYPOTHESIS THAT
THE UNKNOWN IMPULSE IS A DOT (Relatively a dot)

Probability that
signs are the
right way round  .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 GIVEN: SCORES: .... 3 4 4 5 6 7 8 9 10 12 16 ... 3 3 4 5 5 6 7 8 10 10 11 .. 3 3 4 4 4 5 5 6 6 6 7 . 3 3 3 3 3 3 3 3 3 3 3 xxxx -16 -12 -10 -9 -8 -7 -6 -5 -4 -4 -3 xxx -11 -10 -10 -8 -7 -6 -5 -5 -4 -3 -3 xx -7 -6 -6 -6 -5 -5 -4 -4 -4 -3 -3 x -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 any mixture of dots and crosses 3 2 2 1 1 0 -1 -1 -2 -2 -3

In the sample given, the ???? ".5" should have been employed if ignorance

was assumed.

The above table is derived from the following formula:

Let "p" equal probability that our signs are the right way round, then the

probability of another dot given "n" dots in a ??? of Delta-PSI'

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