The statement about normality encompasses the true count theorem. As cards are diminished, the expectation is of the same true count, not a drift towards zero. While the running count would be expected to diminish, the smaller divisor for fewer cards makes up for that. The true count theorem is on bjmath I think.
A files revision record is not the whole story; it just means that there was no record or command to delete the link. Bad links happen! You would have to be dellusional to say that they don't.
The evidence of that is to be found in your claiming I have made statements totally opposite to the ones I actually made!
And I see that you have repeted the word limit, and only my format, cr*p that you have posted on before. None of your statements restricting allowable response to oppose you make any sense whatsoever.
Theorem III is a simple restatement of the binomial disbursement from means theorem in statistics. If it did not exist then you could take, for example, an 8 deck shoe, shuffle it together, and start a round at each deck level, and get different basic strategy means with how many decks are left. That is exactly what you are claiming happens, which is ridiculous.
Instead what happens is that each subset is the mean of all subsequent subsets, and is the disburement origin for all new smaller subsets. The total remaining subset size gets smaller, but the cumulative normal distribution from all means grows as well.
What follows is the shortest possible statement that can be made about your error:
All you have really demonstrated, in trying to claim this strong version of the FA exists, is that every subset has a smaller version of itself that has the same card densities.
The file date indicates and fully verifies that no deliberate changes were made from that time. Depending on what variant of UNIX is involved however, deletion of another file, can delete 2 or more files that have some linkage in the directory tree, with only the date of the deletion of the intended file showing. That is why I also posted the message number of where T-Hopper described the Harris post, and included mention that the link included the followup files I have described.
So you not only have me saying I found the files and now they are gone, but you also have the record of T-Hopper describing the same files I say I found, and are now gone. That is a big difference from ML so nastily saying that I am dellusional for saying the files were there and shows the level which he wishes to take discussions to!
If you have a skewed pack of some sort, the most probable subset from that pack is for cards to be removed in direct proportion to the densities of that pack. This usually involves fractions of cards being removed, but the actual cards are removed as whole integer numbers of cards. This usually excedes such reversion tendencies, at least locally, and is a source of further variance from means. This is also still another factor adding to the effects I have outlined, where ML depends upon each subset having a smaller version of itself that has the same card densities, and thus floats as he alleges, while I have clearly pointed out, to those who actually read what I have posted, that normal and binomial disbursement from the means, where here means refers to each subset providing the mean for all future subsets, exactly cancels out such tendencies.
If there is a post with followups, the names of the followups are included in the captions. He has followed that format. If no followups are included, he uses one name in the caption. My guess is T-H remembered the original posts and was citing the followups from memory. But if Richard had included them originally the names of the responders would be included as they are other places.
You have been delusional before and clearly you are again.
To not understanding what you say. I think everybody on the board could equally plead guilty.
You write unintelligably. I think it is on purpose so you can have deniability. And all of your responses have been unintelligable where criticism of any proof can be stated in terms of the proof and in a few words. That you have not done that but responded unintelligably is my criticism. You cannot doubletalk a mathematical proof but that is precisely what you have attempted to do. Either the theorems are wrong, the postulate is wrong, or the math is wrong. All of these have proven correct so far.
This time I am totally done. Have the last word of your patented doubletalk. I will not be able to understand such a response one more time at that response, like all your others will not be direct but delusional.
You only verify my low level comment! You only prove your agenda is to blast at me. I wonder who your client is therefor, due to the effort you put into this.
How Richard Reid sets up his captions is irrelevant. The same format would come from having captions link to a directory. Reid had several instances of different boards pointing to the same files, and recently deleted entire boards.
But the bottom line is that it is entirely possible, from both the board arrangement and UNIX/linus file directory levels, to wipe out one file on one board, and endup actually erasing several files on several boards, and only have the intended file errasure showup in logs.
Bottomline too is that you will stretch the truth as far as needed to maintain your agenda that questioning BJA/DS positions is somehow suspect intrinsicaly.
The mean of every subset is the mean of the means of every possible subset of that original subset. That is Theorem II restated.
You use then the fact that the subset size gets smaller with increased penetration to claim that this sum of means is to the mean of a smaller version of the original subset--having the same card density as the original subset. That is a switching of means.
Once again to ML-- who understands this quite well but seeks to claim everything except the simple truth that he has an agenda to claim I am wrong and DS correct at all times--in step 4 of your proof you use a proof of the bow-effect coming from the variations from mean compositions (which is a proof of the bow-effect without needing to invoke that a Graham-Stokes topomorphic process is involved) but relate it to penetration having increased from the original subset. Doing so within step 4, instead of after step 4, you switch the subset you derive your estimate of the mean from, for the mean of the means of the nested subsets, from the originating subset, to a smaller version of the originating subset.
If you simply take your proof of the bow-effect, and apply it to variations after step 4 you should see your error. What you have done is to apply the effect of increasing penetation decreasing subset size twice: once to the actual subsets, and eroneously to relate the subsets to a smaller version of the originating subset.
That you willnot acknowledge this just proves your posts are totally disingenous!
Again, you are making it impossible for anyone to understand so you can say later you really meant something else.
Again you have not addressed the proof.
The first paragraph does not describe the theorem at all. The theorem has a value the expectation of a set of cards equal to the value of sum of the subsets and has nothing to do with means. It is lumped as all blackjack data dealing with expectations with the mean of certain groups of data but you never once in the paragraph refer to the original set but call every term a subset. Terming a set a subset shows you do not even understand the import of the basic blackjack expectation equation or you have misstated it on purpose.
The second paragraph does not make sense. The m subsets which is the only subsets dealt with are of identical penetration, n-m less fewerr than the original stack. How can there be two penetrations when only one penetration is defined? No means are switched because only one penetration is looked at. You cannot show the proof as having data from any penetration except the penetration that has m cards remaining as that penetration is the only one described anywhere. Where is a term which describes anything else?
I do see a typographical error in step 4 and a couple more which I do apologise for. The first line uses the term k+r and in the second line the r term was written as l. Then it reverts to r for the rest of the paragraph. I had used l originally and my wife suggested the term be changed to r so that little l would not be mistaken for number one and I missed changing it one time in that step. That should not have been your objection, however, because all you would have had to say to make that objection is different letters were being used which could have been pointed out in five words and the confusion would be cleared up. If that is the problem, simply substitute r for l in the second line. The term r is correct at the first and the last line of the averaging process so the typo is clear and minimally confusing IMHO.
But clearly no smaller version or smaller sized subsets are used because, by the postulate, the bow effect is general and not dependent on penetration. The m penetration was used by definition of m, m less than n.
A note: The proof contains a few other typos, again ones which would be apparent as typos. There are two "5's". Of course the second should be 6. In the first step 5, a value x is defined. As originally written, I had used o for this value and, on the advice of my wife changed it so that term would not be confused with zero. I did not change it in other places. But that change in terminology was not pointed out so I assume it did not unduly confuse you because clearly the same value was being used. But, again, I apologise.
If these typos had been pointed out they would have been corrected sooner but these typos have nothing to do with the objections previously stated or stated in the post I am responding to.
Nothing in the post I am responding to addresses the proof, nothing accurately states any of the theorems or anything else or I do not understand anything you said which I think is your method of doing things anyway. You refuse to be intelligible. The only thing intelligible you have said yet is you read something on bjmath now proven not to have been there so when you are intelligible I have to assume you are delusional.
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.
