About ML's proof--No more hinting

I have been accurate but only hinting at what is wrong with ML's proof.

What is really wrong is actually simple. Every time a round is played that subset, of the total reaminders of the original pack, has a definite mean basic strategy expectation, which is the same as the mean of the subsets of each round that will be played from that point.

So you have E(R) for the edge of the total remainder subset, and E(r) for the subsets for each round.

You apply what ML called Theorem II to the edges E(r) and not the edges E(R) as he did.

In no case is there a reversion to the means that excedes the tendency of deeper penetration to result in a trend where the edges increase.

But the true count attempt to measure E(R) is subject to the accumulated divergence from prior means, growing the same way that the true count grows, division by the decreasing number of decks left. Hence the bending of the bow effect increases with penetration.

What I termed Theorem III is the consequence of Theorems I and II applied to different sized groups of E(r).

Is you cannot find an objection to the theorems, the postulate, nor the math so you have been trying to doubletalk the proof to death.

What you said above makes no sense at all. If someone can put it into understandable language perhaps there is something to talk about but. Clearly all you are doing is making assertions without any mathematical basis and continue ducking the elements of the proof.

I may have understood one small part but I am not sure. The bow effect in the postulate was defined in terms of n and defined in words as universal, making n universal as is standard. As written, it applies to n, n-1, n+10 or whatever. The terminology was not mistaken and did not mean the bow effect applied only to n as used in the proof. Just a brief acquaintance with the elements of mathematical proof would have made the terminology apparent. But, clearly, you are unacquainted with the elements of mathematical proof because you think unsupported assertions irrelevant to the proof can counter a proof. Only internal criticism can counter a proof and in your thousands of words you have offered no relevant internal criticism. Saying something is misapplied when it is mathematically correct if the definitions are correct cannot be misapplication. It is like saying the second 2 in 2 + 2 is misapplied to come to 4. The use of the word misapplied in this context is simply absurd.

You simply cannot see or admit just how badly you have blundered when you say that by making your assertions universal there is no change from equating subsets that are the total remainder, with subsets that are the cards used in each round. You failed to see the distinction between how an originating pack, at a larger penetration, is used to evaluate the mean for subsets, at deeper penetrations, and I gave you even the benefit of the doubt on that, but not being able to see how:

a+b+c+d+e......zth, for the cards used in rounds a,b,c....

is different from subsets of total reaminders:

A=a+b+c....+zth, B=b+c+d...zth,

is totally absurd.

But that is what you have claimed that by saying:

The bow effect in the postulate was defined in terms of n and defined in words as universal, making n universal as is standard. As written, it applies to n, n-1, n+10 or whatever. The terminology was not mistaken

LOL, comeon, have you been hanging out with Puiu? Just because you define a realationship as universal does not make it universal. By your logic[sic], a prime rib can be taken as the total of the slices from it, or the total of the prime rib remainders as each slice is taken from it, or total prime rib + remainder when slice a is removed + total remainder when slice b is removed....

By doing so you would have a series sum that is the actual size of the rib roast, in the first example, and a series sum for a rib roast that is 1/2 the number of slices larger than the actual original rib roast in the second example. That in fact is precisely how your interpretation inflates the miniscule tendency I have mentioned, where the pack is hits some perfectly mean composition, for the basic strategy edge to float in any way, into your support of the strong version of the floating advantage.

Get real, though maybe ZenGrifter wants to buy some of your recreational medicinals. Your post is getting me stares from laughing so hard!!!!

If I start with eight decks and examine the sim data for cutting off two decks and examine the sim data for cutting off one deck, the data will not be the same. But if I sim again for one deck and two decks, the data will be the same (with margina of error) for two decks cut off and one deck cut off. That is theorem II because you have to sim a lot to isolate all the possible subsets of eight decks at the one and two deck level. Only one of the subsets will appear each shoe but millions will narrow down the possibilities and get accurate data as to spread and expectations of all possible subsets. Order means nothing in millions of runs because the different possible orders will have appeared. And at the one deck or the two deck level, or whatever, the bow effect will be seen in the data that describes all subsets, according to the postulate.

That you cannot understand such simple things or if you do understand such simple things but cannot express yourself so other human beings can understand what you are saying is not my fault. But it has surely become my curse.

Your rib roast example shows you do not understand Theorem II. All the meat remains or there would not be an equality.

Your assertions remain assertions. In all the literature and all the posts on blackjack only you assert there is only a floating advantage for perfect decks. If someone else asserts that, please have them post here or cite where they asserted it. You are totally by yourself out on your own limb asserting it and then saying your assertion makes it true. Even if your assertions were understandable, they would not necessarily be true. And if they were true they would not be understandable. Double talk and obscurities and irrelevances abound. You have not yet offered any internal criticism of the Theorems, the Postulate, or the math contained in the proof and you never will. The proof is internally consistent as proofs are supposed to be.

If you are LOL why is it you have no support. I have not laughed out loud but have at times felt sorry for you for being such an illiterate and unintelligable misfit but I am done with that and done with you. I will no longer post on this matter here and will not deal with you any longer. Your delusions are beyond repair.

Theorem I excludes the possibility of penetration changing the basic strategy expectation.

Counting to varry your bets does not change that; it just changes your return by weighting more money on when your return is higher.

But this entire claim for a strong version of the floating edge is that by counting the cards to varry one's bets, the basic strategy edge changes with penetration.

You have not yet offered any internal criticism of the Theorems, the Postulate, or the math contained in the proof and you never will.

"Internal criticism" is just the way that you engage in circular reasoning. In this above phrase you are insisting that a false premise be used to criticise a false premise. There is no such claim in mathematics that only "internal criticisms" of a proof are to be accepted. But in fact improper application is considered internal criticism!

Once again, go back to how you define your subsets and you will find that you use Theorem II to apply to subsets that are the total remainders of a pack, while Theorem II only applies to subsets that are the subsets used to play each round. All of your errors stem from this, including the more minor error of associating a total remainder subset with a deeper penetration version of itself as I pointed out earlier.

why is it you have no support. I have not laughed out loud but have at times felt sorry for you for being such an illiterate and unintelligable misfit

I know this is a typo of yours but it is what some people call, "freudian," that you mispunctuate a question in a broken sentence string where you are calling me illiterate. Perhaps it is the simple truth that most posters also wish to sometimes post on rge21.com, and seek advice from DS and the other "Masters," in areas in which they are competant, and have been bullied into silence?

Readers of these posts should wonder how ML claims I have said something while never quoting me saying what he alleges I said?

Can you tell the difference between the cards used to play another round and the total of all cards remaining? Your proof does not!

Posters get bullied all the time by this rigid clone conscensous. Perhaps I should join Green Chip just to shake things up. But this post should tell much about what people really think at times on these boards:

some are Green here and wish to be on the Masters Domains, and on free pages, at rge21.com too

is different from subsets of total reaminders:

A=a+b+c....+zth, B=b+c+d...zth,

The subsets are inflated in the roast example so that you have (a*n)+(b*(n-1)+(c*(n-2) for n slices.

I omitted this from my original post at the end---sorry!

in my Why no replies.... post. You are an obvious one time handle!

As defined, the subset woulds include all different orderings of the same cards as well as all possible combinations of cards and all reordering of each combination for m cards. Equality could not be maintained if each were not included. That you make such a statement underscores one more time you do not even have the mathematical knowledge to have understood the first thing about the proof in the first place. Defining all subsets necessarily have to include all orderings.

P1 The bow-effect exists without any significant change in basic strategy expectation with penetration.

P2 While highly correlated to pack composition, the true count is seperate parameter from pack composition.

P3 As a seperate parameter the true count has bow effects with different ones for pack composition.

Theorem I: the basic strategy edge of a shuffled pack does not change with penetration. This is demonstrated by being able to to cut the pack and tranform any penetration (by cutting the pack) into any other.

Theorem II: Theorem I applies to the total remainder subsets of any pack in that the penetration of a remainder can be transformed as well.

The bow-effect is recognized to be the rise in mean edge versus true count in middle count ranges and the drop in more extreme true count ranges. This bending is also recognized to increase with penetration; as the amplitude of the TC grows with penetration, more bending is required.

Theorem III is that the mean composition of a pack has the same expected value as the mean of the expected values of all the variations of that pack with the same parameters. It is by this Theorem that true counts are evaluated by examining the the mean expected value of mean compositions for a true count.

Theorem IV is a restatement of the distribution about prior outcomes theorem of general statistics for blackjack: distribution about any result is conserved from the original distribution about prior sample points. For blackjack this requires that the distribution from a prior point, or mean is not replaced by a distribution about a new, most probable, mean for the same parameters. The mean pack composition of an initial pack of 8 decks is not replaced by the meann pack composition of 3 decks at the 3 decks left penetration point. Otherwise Theorem I would not be true as the mean expecation of shuffling 3 decks together is higher than that of 8 decks shuffled together. The subsets of all the cards used per round total the original pack---not some smaller pack; 8 decks has subsets totalling 8 decks, not subsets used through 3 decks totaling 3 decks within an 8 deck original pack!

Theorem IV also applies to Theorem II as well; at each penetration level a true count has a most probable configuration, but the distribution conserved from that of the original pack and all prior composition subsets. So the most probable composition for each TC, at each penetration, differs within a pack, from what is most probable from the specified TC and penetration point alone.

The bow-effects arrise from the mean composition predicted by the true count at each penetration level differing from the edge prediction from the actual pack composition, from Theorem IV. One restriction imposed by the Graham-Stokes equation is that the best adjustment for a parameter, like the true count, used to measure a population as it is sampled, must result in errors that cancel out over the measurement range.

Since the true count overestimates edge at more extreme TCs, it must underestimate edge at more central TCs, near zero as well.

The problem is that some take the intersection of the most probable zero count pack with the most overall probable pack, at each penetration point, to imply that the basic strategy edge floats along with the true count. Theorem III is used without regard to Theorem IV or the fact that two population subsets are involved. A pack with 4/13th tens, and 1/13th all other cards, is the mean composition for both the most probable TC=Zero compositions and all compositions from a complete pack.

The variations conserved by Theorem IV, for all true counts, keeps the basic strategy edge invariant with penetration, while the variations that are excluded by having an actual TC=0 leave the variations that involve and cause the bow-effect.

This post had to be made in this informal fashion in that the conventional notation, demanded by ML, does not not allow expression of the exclusion effects of stating the TC is actually zero--with similar for other near zero TCs--in plain text.

Cleaverly or accidently (both are somewhat embarising) ML was demanding that a formal style be used that either would involve an extended set of special symbols this board does not allow in posts, or a set of alternative abreaviations that would have made this post look like a badly written classified ad with equations glopped onto...say for example a personals ad with bizzare abreviations.

This demand of his is straight out of Orwell's newspeak in that he either knew that this would prevent opposing his errors, or that he himself was trapped by his imposed limits.

Such is all too common with all of the clones, and needs to be opposed!

There is no mathematical content.

Your definition of what is and is not math would have excluded posting Abdul Jalib's True Count Theorem. Your definition of what is and not is math would have excluded posting mathboy's post on the limits of the mean (almost the same topic as mine ---hey you did object to that too!). You limit the definition of mathematical content to positions that agree with you. My post above contains all that is wrong with your strong version of the floating advantage claims. But it does not stoop to your clever censorship demands.

If I had used a plugin such as mathsymbol, to put the exclusion effect of prior distribution in my post, it would have been incompatable with the board. Thus my post if made to your style demands would have been crippled and not have been able to oppose yours.

If I had made the post in your demanded style and used common abreviations (such as sub_ for subscript) you then would have had a textual mess and your objection would have been just that. But then you could do the same thing with other posters who have not met your demands... but you didn't when they supported DS.

Funny too, how you never have been able to drag a quote over to support your supposed objections.

No quotes, no citations, and nothing except strange style demands that come straight out your ass.

A pack composition for a zero true count excludes pack compositions that have other true counts, with the conventions and labels he uses in his "proof post," and demands others do the same, despite the fact that such distintions are the entire issue.

IMHO that isthe purpose of ML's posts here. He uses suposed [sic] not doing that properly objections to exclude contrary views.

big t**ds, piled higher and higher. I am supposing you have posted over a hundred times, mostly to yourself, about this bow effect and the floating advantage. Who cares?

You are turning this board into an overflowing toilet. Please cease and desist. Talk about needing Blackjack Therapy!

ML, stop trying to defend your position! Consider the foe and your chances of winning points in this endless debate. Nobody cares! You guys are like the 'Big Brother' group sitting in a bathtub filled with the vilest things imaginable trying to outlast each other. A month on this treadmill is more than enough. How can you engage in a discussion with this guy and keep your self-respect? What a hopeless enterprise! The only logic at work here is, "I speak, therefor, I must be right." You guys need to get a private room and arm wrestle until you have a winner. This forum is no place to continue comparing the size of your sliderules.

I realize that this will have absolutely no effect on the argument or it's conclusion. I just wanted to let the two of you know, that to reasonable people this topic is inane, uninteresting, and inconclusive even if it weren't filled with personal attacks ad nauseum. The bow effect and floating advantage as relevant materials for the adv player hit an iceberg like the Titanic long ago. Let them have a respectful grave at the bottom of the sea.

In General Statistics this is called the distribution of means theorem (at least that is what Wolfram's World of Math calls it). It restricts applicable distributions to (1) the original population--samples form a distribution about the mean of the original population, or (2) the formation of a new distribution from the mean of the current remainder of a population. But never ever is the mean for further distribution that of the mean of the original full population at that level where samples have already been taken.

Even within ML's original proof, that should have been clear if his Theorem II have been properly applied.

In the binomial form the exception of the sampling resulting in a remaining population with the same mean as the original population is allowed though it is excluded in the normal distribution version. That exception is insignificant.

Then the precise equation form of the assertion I made is:

for samples n from orignal population p, comparing distribution at x samples: cumulative normal distribution of p(x) is equal to cumulative normal normal distribution of p(n) at x, but cumulative normal distribution of p(x) is not equal to cumulative normal distribution of p(mean[p(n)]), at sample point x. These are the critical distributions ignored by the general assertion made by ML, in his step 4 application of what he labeled Theorem II. The proper application of Theorem IV modifies the assertion ML tried to limit discussion to, and demonstrates independence in actual means predicted by your true count within a given shoe, and for all possible shoes, where otherwise only the true count and the penetration are given.

The specific argument against the basic strategy edge floating is simply that the floating of the true counts near zero is positive (see the information in newer edition of the Theory of Blackjack by Peter Griffin) and negative for the more extreme counts from zero. Those floating effects cancel, given that the proper distribution effects ignored by ML are included. Then the means intersection problem, that ML's insistance on improper formality ignores, is solved.

The existance of that intersection is the only real assertion of bow effects also requiring the basic strategy edge to float.

Now if this does not meet ML's imposed standards so what? This is real math, just not clone pendantism.

they both try to ignore the effects of the extreme. Paraphrasing both:

Frank: My progression won't crash. How many times do you lose 19 hands in a row.

ML: Basic strategy still floats. How often do you see true counts so high that the bow effect is minus?