General Report on Tunny
25X Page 192
What is required is q as a function x, R, ω and this can theoretically be obtained by eliminating ζ from W12, W16.
It is more convenient to replace W16 by the pessimistic approximation W17. Then by taking a series of values of ζ, it is easy to construct a table of q as a function of 
. This is given in 25B(c).
(f) Decibanning from a letter count.
On the correct wheel the expected score is the expected value of |Z + Rδ|, so that it can be calculated from W11 by putting ω = 1, and the table of 25B(c) is applicable (R5 p 109). Inspection of the table shows that when ω = 1, and the total decibannage, roughly 
, is sufficient to make the run worth while, q = 1 i.e. crude decibanning is adequate.
It follows that if the wheel is independent of the run, but not necessarily correct, crude decibanning will tend, in practice inappreciably, to be too pessimistic, except for very feeble runs. This remark applies to decibanning , from a letter count, any run not used in making the letter count wheels, including all runs on a newly set message.
If the run is used, but not alone, in making the wheel, some value of ω between 1 and the actual wheel-length is required, but it has not been found necessary to investigate this more precisely.
(R3 pp 6,7. Premonitions R2 pp 57, 72. Non-linearity R3 p 132. Triviality R5 p 70. Further references under methods for Χ2 limitation.)
25X THE NUMBER OF LEGAL WHEELS.
In order that Χ6 shall generate a ΔΧ5 with 12 crosses, it must consist of 6 blocks of crosses and 6 blocks of dots. Each block must contain at least one character, and, for legality, not more than four. There must be in all 12 (or 11) crosses and 11 (or 12) dots.
The number of ways in which such blocks can be chosen is
| {coefft. of x2 in (x + x2 + x3 + x4)6} | .{coefft. of x4 in (x + x2 + x3 + x4)6} | |
| = | {coefft. of x6 in  } |
.{coefft. of x5 in } |
To find the number of legal wheels this must be multiplied by 2, to allow for 11 crosses and 12 dots; divided by 6 because the first block of crosses may be any one of six; and if different settings of the same wheel
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