What can be exploited from the Sausage of the Floating Edge...

See below for why I think the claims made are so highly inflated coming from the clones...

The bow effect is most interesting IMHO, because it shows how a linear measure fails. Your count, and any other type of overall effect of removal, drops in overall efficiency with deeper depletion. What analysis of the bow effect does---once you filter out the grouping of true count errors that the clones will never admit to-- is show that this drop in efficiency, using a linear measure, has a shape.

What can be done is not so much get more overall edge--because what you gain in the middle TC ranges is given up at the higher end of your spread--but you can give a shape to how your linear measure starts to fail.

Your count misses the bowing to about the same degree that its efficiency drops. But knowing something about the bias will let you restore some of that lost efficiency, and probably for both playing efficiency and betting efficiency.

Stay tuned. It is not much extra money involved. But it does seem that some interesting theoretical information can be gained.

But not by leaving errors in how you group together true counts in the "filler.".

As usual Cant is spreading blackjack misinformation on blackjack boards. Normally his posts which supposedly are to impart information are so unintelligible he can deny that what was said was what was really meant to be said. This time he is in a position where he cannot use this dodge and dodge because he has been unusally clear for him.

He has said the floating edge is a sausage mixture which is misperceived because:

1. The bow effect (which is real) means overall expectancy remains unchanged as decks are depleted but that more expectancy is crowded into the middle of the distribution. That is, the expectancy might look better in the middle of the distribution but similar increases in expectancy as cards are depleted do not happen at extreme counts so overall expectancy stays the same. Expectancy does not change "across the board."

2. The accounting for counts which are greater in actuality because true counts are higher than running counts when less than a deck remains.

Both of these statements are inaccurate and the results of sims I ran today show them to be inaccurate.

The sims are SBA. SBA allows you to stack a deck like you please so I stacked decks in the following ways:

1. I added one 2-6 and took away four tens and an ace, creating decks with a true count of -10.

2. I took out one 2-6 and added four tens and an ace, creating decks with a true count of +10.

I ran sims of fifty rounds from eight decks and one round from single deck, using basic strategy, S17 DAS split 3, 30M rounds.

Results:

-10 eight deck---------(-.0718463)---std error .0002

-10 single deck--------(-.0662448)

Difference-------------(+.0056015)

+10 single deck--------(+.040048)------std error .0002

+10 eight deck---------(+.035596)

Difference-------------(+.004452)

Calculated difference for standard decks

Eight Deck---(-.004)

Single Deck--(+.0012)

Difference---(+.0052)

Anyone can run similar sims to check my data.

Everyone will notice two things consistent with my previous posts.

1. An advantage occurs of the magnitude I predicted for both extreme low counts and extreme high counts and the magnitude of the advantages track the magnitude of the difference in original expectations for eight deck and single deck even at the extreme. I used the word "track" which was meant to convey very similar differences without predicting identical differences. The floating advantage occurs across the board.

2. Only one round was dealt from the single deck so inflated running counts cannot be a factor in the differences seen.

As I have said before, I have a theory not accepted by others as to why the phenomonon occurs but that is not of import here because these sims clearly show it does occur in the magnitudes I predicted across count ranges. If getting things right is being a clone, please address me as Mr. Clone.

I hope this post demonstrates to the board another important point because I will not again spend the time or energy to address Cant's nonsense (and I really, really, mean it this time). Cant's imperfect knowledge of mathematics and his imperfect knowledge of blackjack even if he does know some of the vocabulary tend, at least for persons not familar with the nonsense, to add legitimacy to illegitimate conclusions. When confronted he goes into the no nothing populist mode saying a person who disagrees with him disagrees because he wants to curry favor with Cant's hated Don Schlesinger.

As a matter of historical accuracy, I have disagreed with Don a number of times. One time was on this very subject when I criticised Don's analogy of a balloon where the floating edge occurred from squeezing air from the sides and inflating the middle, insisting instead it was an across the count phenomonon. Also, for historical accuracy, most of the times I disagreed with Don I was demonstrably wrong as most people who disagree with Don are wrong.

The point I am making is that I hope people reading this post will understand the import. It is not that my earlier observations were correct and Cant's were wrong. It is that any Cant post should be viewed with extreme caution.

All you have done is show that a perfectly at the mean 1 and 8 deck pack for TCs of +10 and -10, shows normal differences.

What you ignore is that that mean densitities are less likely as a population size grows. Back to the Pascal triangle for you perhaps?

A Perfectly mean deck at the one deck penetration point is a very small sample of all possible decks and says nothing about how a count evaluates betting advantage for all possible decks at this penetration and set of true counts.

I suggest you go over to Norm Wattenberger's charts again and look at how TCs of +1 vanish, at 26 cards, and how every rounded TC peaks just before they are excluded---the simple fact is that all true counts are discrete and must have values, where N is all integers, of N*52/ (#cards left). The average of all possible TCs in a given range is close to the mean TC in a given range until you get past the one deck penetration point. Then the possible TCs in a given range for rounding inflate until that range is excluded. Where a set of every other TC ranges becomes excluded, remaining possible TCs start at the low end of their rounding range. Edge using basic strategy follows.

The peaks and valleys in Norm's results follow exactly this rounding error.

Deliberately missleading statements about results for mean decks, at the 8 deck and 1 deck penetration points, WHICH ARE THE SAME AS COMPOSED NEW ONE AND 8 DECK PACKS, have no meaning whatsoever.

The question to be answered is whether the floating advantage is a phenomonon occurring at all counts. You say it does not. Don and I and others say it does. Your criticism of the "mean" distribution, that is my making the assumption the distribution would be the same in one deck that it would be at eight decks is irrelevant. Sure, if the -10 was formed with more fives and fewer twos or whatever, there would be some minor changes in expectancy at one deck but these would be minor and you should know better than to assert there might be a change in the vicinity of .005, depending on the mixture. -10 expectation is going to give a very similar expectancy, however it is formed. An elementary knowledge of blackjack and sampling which apparently you do not possess makes the proposition very clear.

You discuss the less than one deck situation as being relevant even if I purposely made it irrelevant by only dealing one round.

Again I call readers' attention to your mistatements and double talk and repeat my caution Cant postings should not be taken seriously. They are not serious.

A mean density deck for all denominations is much less probable with 8 decks initially than 1 deck initially. Comparing TCs and actual edges in complete 1 deck and 8 decks packs is meaningless.

The bow effect does occur in all counts: in some edge decreases; in some edge increases. Actually the squeezed balloon analogy is the accurate one. It was apparently abandoned to avoid admiting that the limits of what edge you can gain from conventional counting methods have been hit and further improvement requires tracking and location and hole card plays, by appealing to new claims that are based on an elementary grouping and rounding error. That and that alone is how the claim comes forth that all counts have increased edges.

In my original post on RGE, in response to a post which seemed to me to overestimate the effects the floating advantage has I said the effects were minimal, not quite enough to lower bet levels at the one deck level but maybe at slightly under a deck because an inverse relationaship as Griffin described is in effect because the advantage tracks the advantage derived from fewer decks. Further, using the number of deck rule of thumb, the difference between six decks and one decks is about .004 which is an expectancy rise less than the expectancy rise for one count. This was certainly hyping nothing but putting it in the mathematical context in which it exists.

Of course the bow effect exists. Griffin said it did and sims like mine show the existence. The one deck -10 is more than two percentage points more minus than the one deck +10 is positive in a starting -.003 game. But it is irrelevant as to the actual figures (except as to my unaccepted theories as to why a floating count exists at all). But the fact the differential for -10, 0, and +10 stacks of 312 cards and 52 cards are similar has to mean the effect is across the board. Further, saying expectancies of different permutations making up -10 and +10 is absurd. Expectancies for similar counts whatever the permutations of the cards adding to the counts are similar because both are defined by a surplusage or devicit of cards favorable to the player. Your proposition cannot be proven.

My proposition was.

Take an deck shoe. Burn one deck and play basic strategy for one spot and round. Now burn cards until you get to the one deck left point. The basic strategy result mean will be exactly the same for BOTH rounds..

Counting does not change this. Count down the first deck as you burn those cards. Divide that count by 7 for your true count. Don't change the true count at all for the deeper round. That true count will have exactly the same correlation to both rounds. Counting does NOT change the basic strategy mean.

Not only is the mean the same but the distribution of results will be the same.

There is however the bow effect. The linear measure we call the true count overestimates the edge on extreme counts. Notice again that the basic strategy results mean doesn't change. Since the basic strategy mean remains the same, the predicted edge given by the count is too low in the middle ranges, and too high in the extreme ranges.

Now count all the cards up to the deep round. You will find, as is well known (but forgotten by the _____?), that the count for the shallow round will actually have a higher correlation to results than the count for the deep round. There is more information, but there is also more accumulated variance.

What also changes is the distribution of the true count. More of the true count is in extreme ranges. Thus the bow effect is greater. Remember the cards, the basic mean edge has never changed; the difference between the true count's predictions and the results is all that changes.

The claims that the mean floats is pure nonsense only explained by this rounding error I claim. Mixed together the clone's FA claims are sausage. The mean has never changed. Counting the cards never changed the results or the cards we get, shallow or deep. Counting only provides a prediction set, and only the prediction accuracy and profitability changed.

T-Hopper has reported, on bjrnet.com, simulation results I call the "HI OPT II mystery." He simmed HI OPT II and found that its higher playing efficiency resulted in more expected value gains than could be explained by the playing gains themselves. This is the only part of the FA discussion ML and ETF have correct: playing gains will cut down the bow effect.

IMHO what has been demonstrated is that playing index use has cut down the bow effect, and thus kept the betting correlation from falling off, as much as it would if only basic strategy were used. These gains actually excede, keeping the betting efficiency from slacking off, the extra playing gains.

Mystery solved.

Or possibly intentional deception. Again, this post by Cant shows again why readers should not trust the contents of his post.

The floating advantage is inaccurately defined in the post. The phenomonon is defined by specific counts and has never been defined otherwise.

Anyone knows expectancy anywhere in a stack of blackjack cards, whatever the number is the same for the basic strategist. That is, the last fifty-two cards has the same expectancy overall as the first fifty-two cards. But that is irrelevant to the floating advantage which simply describes the fact (original formulation) a zero count has a more favorable expectation as cards are dealt. From this starting point, it has been theorized (and shown by sims), the same holds true for all other counts. Cant's comparison of an arbitrary fifty-two card sample and a zero count fifty-two card example shows how little he understands what other people have said.

I guess that is fair because we others seldom understand what Cant says.

Not a simple case of the inaccuracy of the counting systems correlation with effects of removal for Griffin's single deck EOR's.
Hence the slight excess in ev predicted in a 13 card subset.
Or there is other explanations? Please explain?

Forget ML's blather here, which ignores the same cards point that all should get. By the time you get down to a smaller fraction of a population that you have tracked with any sort of counting system, even Griffin's EORs, for certain games there is a bias to the error involved in evaluating a non-linear system with a linear measure. In blackjack the result is the bow effect.

The same occurs where Griffin notes how his EORs have a near 100% efficiency in general, off the top, and less efficiency deeper.

Arg! What part of the fact that the same mean occurs with basic strategy decisions anywhere in the pack don't the clones understand, or are just pretending not to understand to hide thier leaders error(s)?