Nack58 and Trice62
Posted By: Nack Ballard In Response To: Nack58 and Trice62 (christian munk-christensen)
Date: Tuesday, 1 February 2011, at 1:55 a.m.
In Response To: Nack58 and Trice62 (christian munk-christensen)
Is Nack 58 an improvement of Nack 57?
Or is Nack 58 used in certain length races and Nack 57 in certain length races? (this has probably been discussed earlier but I couldn't find it)
Nack58 is the same as Nack57 (link kindly provided by Stick in nearby post) except in one detail. You subtract 32 instead of 33 in the initial step. This was an adjustment I made after NeilKaz posted some rollouts at certain changeover counts. (Neil and I are not sure but we suspect the best number might be 31.7 or so if one wants to put that fine a point on it.)
The Nack58 formula states that from the leader's pipcount you subtract 32, double the result, and find the nearest sqrt (square root).
For example, you have a count of 83–93 (after wastage adjustment, or with no wastage adjustment needed).
Nack57: 83 -> 50 -> 100 -> 10
Nack58: 83 -> 51 -> 102 -> 10
As you can see, Nack 57 and Nack58 arrive at the same answer. They do not yield answers a pip apart up and down the line, as some people seem to think. They only do so at certain changeover counts; e.g., at 78 and 88, where Nack57 has the take differential a pip low (as does Trice62, which has additional ones a pip low as well).
Nack57 was the first and only perfect fit of the Gold Standard Table (except at a leader count of 111 it's a pip low). Nack58 is a similarly perfect fit to the adjusted Gold Standard Table (adjustments based on Neil's XG rollouts).
The name of Nack58 has a double meaning. One is that 58 is a dividing line between the two formulas used. (The formulas' answers actually coincide at any leader count from 54 to 60.) At or above 58, use the Nack58 formula just described (subt32, double, sqrt). Below 58, use subt5, div7, round down.
The other meaning of Nack58 is that with Naccel you add 58 to the count (instead of subtracting 32 from a traditional count), then proceed identically.
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