Penetration level m---I tried to be kind ML

That is precisely where you made your mistake and it is **not** possible to explain your mistake using your labels etc.

At penetration m, taking m to be the number of cards left, subsets at every suceding round round using *n* number of cards, are at levels m-*n_z*, for all suceeding generations of penetration levels. The sum for suceeding levels of E(m,i) is from sucessive subsets at penetrations m-*n_1*,m-(*n_1+n_2*).... It is not for subsets at penetrations m.

You thus relate the originating subset mean E(m,i) to the deeper penetrations by using a series of strict conventions that do not allow for the propper nesting of penetrations for how subsets the subsets at each penetration, or in other words the subsets for each round, sum to the originating subset.

The actual situation is thus not, relabeling, for total remaining subsets at penetrations *a,b,c,d.....zth*, **but for the subsets for **** the rounds** at penetration points a to b, b to c, c to d, d to e, e to f......

The proper application of Theorem II is thus a demonstration--I won't call it a proof because then you will demand my contentions are only acceptable in the form that got you off track in the first place--of the limits that invoke Theorem III, for dealing with the overall bow effect, when trying to measure by the total remainder subsets instead.

It should be pointed out that bow effects are universal anytime any complex measurement is involved. Just look at my post about the direct reading heat index meter that is in this month's, *Poptronics* magazine. Humidity and temperature when measured together are a complex measurement. Check out the accuracy curves for the RF meter in this month's *QST* magazine. Ditto!

The true count however has this bow-effect in that it has error that accumulates making for more bending as penetration increases. The rest should be obvious: it is not the basic strategy edge that floats, just the ability to measure the composition changes linearly that bends.

These are not difficult topics to master except when the clones have become so anal and pendantic that their demands for psuedo precision have led to missunderstanding the limits of their conventions. You have demonstrated this. I appologize for being so cruel as to hint at each step of the way, but that is only fair considering the tactics you have used, such as claiming I was dellusional to have found a more complete record of that post on bjmath.com etc.