Undefined values in mathematical proofs

Cant has been posting on this board and others, I am told, I fraudulently switched means some way or another in the proof I posted below. The problem with that is the values he said were means were not means, they were undefined values which is what is invariably used in mathematical proofs of the form posted.

Consider the term x >y. The value of x and y are undefined but everyone understands the term x and y stand for specific undefined values. Clearly, Cant did not understand this elementary, universally used mathematical convention and called terms in my proof something they were not, means rather than undefined values, and then went on to accuse me of fraud when he simply did not understand elementary concepts and said I was saying something I never said at all.

And he did that despite there being internal wording in the proof as to what I was using was undefined values even if he was ignorant of standard forms of mathematical proof and standard notations. Theorem II starts "As cards are removed from a stack of cards, creating subsets of the original set of cards, all the possible subsets of a specific number of cards will demonstrate various true counts, either less than, identical to, or greater than the original true count and the distribution of true counts is normal around the original true count." I clearly stated we were talking about removing from "one stack of cards" and "creating subsets of the *original* (emphasis supplied) set". I did not say original sets or average set but made clear one specific set was being looked at as is required by the rigors of mathematical proof. Further, by coincidence, the proof used an averaging process and used different terminology to set such expressions aside from the expressions which stood for undefined values.

So, because of his ignorance of elementary terminology, even if the terminology should have been apparent in context, he has repeatedly accused me of fraud and said I was doing it because I often agree on things like this with Don Schlesinger and was a clone trying to put Cant down.

His remarks were inaccurate and insulting and I think the appropriate and fair thing to do would be to publicly apologise both here and the other places he posted these insults.

I am going to post on the post by Brett Harris and Don Schlessinger that ML used without propper asignment, for his "proof" post. It used a different sort of conventions as well, so that rather than being an "elementary, universally used mathematical convention" that he used, they were flawed, as was the original paper.

Handy thing this internet, where you can find easily postings of actual sources. I really didn't expect this type of Puiu action from ML though. The Harris and Schlesinger post is on bjmath.com now!

People reading will notice Cant's dumbly mistaking what was unambiguously undefined values for means is neither addressed in the post addressing the issue or the one above. If you don't acknowledge it, it did not happen, Cant? You missed it, Cant, and all your original objections to the proof were based on that mistake. Your ignorance was displayed one more time by equating this proof with anything Brett or Don have written. People can use the search on bjmath and confirm that. A red herring.

Theorem I and II are totally consistent. The reason cutting does not change expectancy is because of Theorem II. Any of the subsets can be cut to the top in the frequency the subsets occur. It can be fairly said a cut brings subsets to the top (but of course the same mix of potential subsets is already at the top).

But whether or not the proof is correct, an apology is due. Cant said I was fraudently switching means in a proof when I was not using means. That no apology has been made demonstrates Cant as a person whose honor matches his mathematical knowledge. He is profoundly deficient in both.

totally missquote me as you have done, and deny how your proof, mixes populations and thus mixes means.

BTW your proof does draw from the closed board discussions posted by DS and BH without attribution, portions of which have been retitled recently. The link provided by T-Hopper originally included the responses from DS and a BH (Brett Harris) that even more closely resemble your post. I hope Richard Reid restores the posting of the source material you did not aknowledge!

If you go there now you will find several boards have been consolidated and that several archives are temporarily not available.

It is unfortunate that this conveiniently means that evidence of prior sources ML has not credited possibly gets lost in that wash.

Originaly the link led to an archive of Brett Harris' original post, here on this board, where Harris postulate of a constant C adding to basic strategy edge with penetration, that much resembled ML's proof post, with the same flaws, was archived with several responses from Don Schlesinger and Brett Harris. That is why T-Hopper posted the link in a reply to me on the CCC. Then and now my response was the same that two different populations: that of all possible packs that can have a specific true count and cards left, and that of the possible subsets, from specific prior subsets of a pack, that can have the same true count and cards left, were involved, in both sets of posts and not properly noted.

That is and always has been my actual response: it will be interesting to see how ML and the usual others (ETF, Cyrus etc.?) will likely claim that I have said something different.

Two misrepresentations.

I am done with this topic but have two remarks to make:

The Brh post to which you refer is a very clever sim showing that if you use a mild multiplier to inflate true counts as cards are exhausted, Nsub0 gets a little better. That is a floating advantage exists. It is not related to my proof in the smallest way. T-Hopper knows better than to say that because he is a competent mathematician and I do not believe he said there was a relation.

The claimed responses do not exist. You made those up, I feel sure. I do remember that thread. There were no proofs in the thread the best I remember and I am about sure no discussion of the bow effect did.

The postulate was correctly applied. The postulate was general and there was no limitation to perfect decks. There is no limitation because it applies IMHO in all situations to the various potential true count expectations as I said in the definition of bow effect and as expressed in the postulate. The mathematical statement incorporated in the postulate was transferred directly to the proof, the proper way to complete a proof.

You have a theory verified by nothing the bow effect only exists in remainders of perfect decks. Nothing in the literature, no calculations, nor sims support that proposition. I provided support for my proposition exactly as written (no reference to perfect decks because none was needed) and wrote it as a postulate because I said I believed it but there was not sufficient proof to term it a theorem. What more could I do to inform the board what I was doing?

Your proposition the bow effect applies only to perfect distributions is a part of your earlier really stupid propositions like posting a ruin formula that did not sim out for either DD' nor myself when the Schlesinger ruin formula did and your other crazy ideas. That you have a crazy idea, unsupported by anything, does not require me to put it in a proof.

It is apparent you never understood the proof at all and apparent you do not even understand proofs and that is why an apology is owed (it has become compounded by your saying I did not attribute correctly and citing sources which do not exist. I guess you thought no one would check). If that thread can be found, nothing about the bow effect will be found.

The upshot: You did not understand the concept of an undefined value. You said I switched means when I did not because the postulate did not define the bow effect the way you wanted me to but never said the corollary was wrong. Your ignorance of the mathematics in at least two instances led you to say I had fraudently switched means when it is clear I did not. Then you posted a fraudulent link which did not say what you said it said. Then you said Reid had changed that part of the board when what he changed was the message boards. Apologies continue to be owed.

You disagree with the postulate. So what? I could care less if an ignorant person disagrees with my thoughts. Your ignorance has shown this time around so the board has learned something.

He says that part of the board is the same as it was when established in 1998. Cant, I cannot believe you have the balls to make up such a bare faced lie when it could be so easily checked.

The apologies owed just keep compounding.

This is my last post because your response will be no good, just another lie. I hope others have learned not to respond to your lies also.

There were further discussion posts, about 3 total, when I first followed the link I gave.

What is made up is your claims that in opposing You that:

I supposedly claimed the bow effect only occurs in perfectly mean decks. My claim is the exact opposite.

That one has to follow the symbolic logic style given onlyas a suggestion in one software program you must be fond of, for tracing logic proofs, to have a valid proof. Tell that to Abdul Jalib etc. LOL!

That one has to condense an answer to less than 20 words or less to have an acceptable objection to your posts. How assymetrical!. Assymetrical in that balanced discussion, is obviously forbidden in your demands.

You are getting so %@%@#^ obvious that everyone reading this should take time to remind me, if I ever become polite to you, in the usual sense--still think there are elements of representation in your posts, that there is a lack of logical sincerity in your posts!

So far you have gotten approximately 87% exactly opposite to what I have actualy posted. About all you have gotten correct is that I have said the squeezed balloon analogy is correct as an explanation of how a true count is topomorphic to an analysis of player edge drawn from exact compositions.

You have a theory verified by nothing the bow effect only exists in remainders of perfect deck this is not what I said; you are lying to say it is.

Your proposition the bow effect applies only to perfect distributions is a part of your earlier really stupid propositions
Ditto!

These are exactly the opposite to what I said: that the basic strategy expectation only grows with penetration overall, for all counts, in perfectly mean packs.

Just what question did you ask Reid again???? Until he posts forget you ML!

There were followups, until last week to the Harris post archived on bjmath.com

Cant said. "These are exactly the opposite to what I said: that the basic strategy expectation only grows with penetration overall, for all counts, in perfectly mean packs."

My proof proved exactly that. If you now accept the postulate, that is the array of expectations of all subsets of smaller size than an arbitrary larger set exhibits the bow effect (and in all the words that have poured out you have not disputed the wording of the postulate, the proof demonstrates the same to be true for stacks not beginning as "perfect". E(i,n), an undefined value, is the value for all possible true counts and all skews which might be seen or imagined in an original n stack. And the proof shows the undifined value of E(i,m) is smaller than E(i,n).

The proof is pure mathematics. No symbolic logic is involved. Except for reordering as allowd by the comutative and associative laws, the math consisted of inserting the mathematical statement of the bow effect as set out in the postulate to the equation established by Theorem II and a demonstration it is necessary the value of E(i,m) be smaller than the value of E(i,n) for the equivalency to hold. Every reordering and the substitution allowed by the bow effect postulate maintained the equivalence. There is no error of math and you have, therefore, of course not pointed one out. There was no error of substitution. You said there was a misapplication but there cannot be a misapplication if the substitution allowed by the postulate was mathematically correct, and you cannot assert it was not mathematically correct because the terms were substituted consistently with the terms of the postulate.

Now, if you say the postulate is correct, the bow effect happening in situations of the original stacks of cards being skewed or unskewed (which is exactly the way I formulated the postulate in the first place because i,n dealt with every initial possibility as an undefined value) then there can be no quarrel. The Theorems were correct, the postulate was correct, and the math, including substitutions, was correct.

The proof being correct, it is your speculation the floating advantage only applies to "perfect decks" which is now proven to be really stupid.

I am emailing Richard to get his clearance to post our emails.

Every such skewing is its own departure point for applying what you termed Theorem II. And from each such point, or in this case deck composition, you have further departures, and thus less reversion to any means, from the ideal perfectly mean pack compositions that apply to each true count and level of penetration.

There are thus two different tendencies at work, and they both involve Theorem II. (1) There is the effect you have found for smaller versions of every mean composition at every true count to have more player edge. (2) There is the effect I have tried to point out, which is from the binomial distribution easy to prove, how every mean composition available, from every prior subset, is less likely with increased penetration.

They cancel, as I have described as my postulated Theorem III, which preserves the fact that the number of sections of a sampled total population left to be sampled, does not change the statistical measure of any given sample. I simply restated a well known Theorem in statistics that you refused to apply to blackjack. Pity, in that I would then have been able to be less nasty (but consider that some trial stylings).

Clark wrote:

There were further discussion posts, about 3 total, when I first followed the link I gave.

Clark:

To which link are you specifically referring?

Sincerely,
Richard Reid

was that it involved discussions from Don Schlesinger and Brett Harris elaborating on the postulated C factor, that true counts inflated with penetration, that resembled the means discussions posted by ML. When I first went to that link, and you can read the discussion with T-Hopper on the yahoo.com blackjackcardcounterscafe group, there were 3 posts included in followup, in your archive. This is not the case anymore.

What ML is missing IMHO is what I have mentioned below, in that what he labeled Theorem II has to be applied in an additional way to the way he posted on. The discussion on allegations of Kerotosis in blackjack, included thoughts that are much like those I put in my post above and labeled Theorem III.

It is my simple contention all along that there is a real bow-effect, but that claims of what I have called, The strong version of the floating edge, are really missperceptions of a real bow-effect (where not all counts rise in expectation with penetration), true count rounding and excxlusion effects, and errors, such as split Schlesinger and Gwynn in their FA research, and a very tiny, statistically insignificant level, real FA that is where perfectly mean subsets, of prior subsets, actually occur at random with increased penetration.

The rest is in my posts here---sorry to be so long winded!

Clark:

What is the URL of the link to which you are referring? Please look it up and let me know the exact URL, so I will know exactly to which one you are referring.

Sincerely,
Richard Reid

T-Hopper posted message #14528 on groups.yahoo.com/group/blackjackcardcounterscafe.

The link which I posted here, was http://www.bjmath.com/bjmath/conseq/float.htm

It was as originally described by T-Hopper originally---sorry I couldn't pass up the pun.

Now it just includes the original post by Brett Harris, that you archived from here on bj21.com Please note also T-Hopper's description in message #14528, which is that this link is to discussion proving a floating edge, as proven by DS and BH. All that remains is BH's post now. So what T-H described, and I found, is not there now.

Clarke:

Thanks. That helps. Back in 1998, there may have been followup messages to Brett's post and I very well may have deleted them at that time.

However, ML is correct in saying that I have not made any recent changes to this file. The latest date that the file was ever modified or uploaded in any way was on Dec 9, 1998. That is the UNIX file date that is currently showing for the file located at http://www.bjmath.com/bjmath/conseq/float.htm.

Sincerely,
Richard Reid

At any level, m smaller than n, there is a statistical spread of true counts related to the original population. The mean of the population for subsets of size m is the starting point. We know that. The proof allows for that. Whether your theorem III which I do not understand and suspect does not happen is not relevant to the proof if theorem II is correct and if you accept the postulate.

But, mathematics aside, you apparently had a delusion there were responses to the Harris post on bjmath when you asserted such an untruth. Your theorem III is similarly delusional because it is outside the universe of the proof which stands for itself based on true statements and accurate mathematics. The thousands of words you have given to this thing have not yet legitimately criticised the proof because they were irrelevant to the theorem, the postulate, and the math. The reason for putting things in mathematical statements is to make criticism of the statements easy, criticism which can be put in only a few words or in a contrary mathematical statement. That you have not done.

There is no point in arguing with a delusional person who imagines things posted which are not. I am done with this thing now that your delusions have now been so clearly shown which was my original intentions in posting the proof. I have accomplished what I set out to do but have to admit I did not suspect the vagaries of how things happen would have accomplished it by your posting such a stark delusional statement now totally disproven.

Dear ML,
I have a decent Mthematical background and when I read your article I read something that doesn't sound exactly right. I could be wrong, I have certainly not studdied this phonomenon nor researched in in the intensity youself and Mr. Cant have. In your Post you state.

Theorem II starts "As cards are removed from a stack of cards, creating subsets of the original set of cards, all the possible subsets of a specific number of cards will demonstrate various true counts, either less than, identical to, or greater than the original true count and the distribution of true counts is normal around the original true count.

The Theorem sounded clear and quite obvious untill the final assertion that

" the distribution of true counts is normal around the original true count."

I am very familiar with the Concept of common sense being wrong it happens to me in mathematics frequently. But shouldn't the distribution be normal about the true count when the true count is Zero and skewed in the direction of Zero whenever the count is not zero.