Trying to get a straight, understandable answer from Cant

My proof said the expected value of all the data points of expectation of all subsets of a larger set which have a true count identical to the true count of the set is a larger value than the value of the expectation of the original set.

Now either the proof is accurate and the expected value is larger or the proof is inaccurate and the expected value is either identical or larger.

While you have ducked the concept of expected value repeatedly, please remember expected value is a specific value. It is not a range of values but a definite mathematical term which cannot have multiple values because it is the mean of the expectation of all possible subsets of size m with a true count the same as the starting set's true count as samples taken of the random variable which is the expectation of all of the subsets approach infinity and since the random variables are finite is one specific ascertainable value.

Yes or no will suffice and then you can explain to your heart's content.

If history is a guide there will be no yes or no answer but a filibuster. But please remember if that occurs the answer will be "no".

are present.

Now either the proof is accurate and the expected value is larger or the proof is inaccurate and the expected value is either identical or larger.

Once again you are trying to edit out reality at the extremes of distribution, just like Frank, the FLaw, Stanton does. This time you are presenting a falsely limited slate of choices. Your proof is not accurate. The basic strategy expected value tends to be larger in the middle of the distribution, and smaller in the extremes, and indentical overall to that of the starting pack.

Now for a real question: Your proof admittedly deals only with the middle of the distributions. That precise middle distribution of compositions is the most probable composition. Given 3 different starting packs: 1, 2 and 8 decks, the most probable composition is the same as a one deck complete pack, when 1 deck is left, for all 3 different starting packs. Any random simulation that starts with these 3 different sized packs (well in this case random shuffles of the 2 and 8 deck packs, will show different expected values with rounds drawn with one deck left

Your proof--no more cr*p about "having to oppose a proof internally", whining to the PBers, or refusing to be able to admit that you have already conceded, etc.--"my proof only deals with the middle compositions," quoting you, only deals with compositions that are identical to one complete deck, and in all of its steps, from 3 onwards, depends upon this being representative, and uses a Theorem on the postulate that the mean composition is representative, that Griffin said was a "leap of faith," in Theory of Blackjack, and Thorp, in Beat the Dealer said was, only "a useful assumption for estimating strategy," and is not actually a theorem at all when sims, my paper/post, a unit loss normal integral analysis discussed by Griffin, and the cut card theorem also in my paper, show that the differences between different sized starting packs will always remain.

So how come you omitted this effect of different "distribution widths," to coin a term, from different sized starting packs? I don't think your posts are at all honest in that this is so obvious!

Find something where one of you would predict one outcome and the other one would predict something different. Agree on this, run a sim, and then it will all be over!

Cant said sims were not reliable. That I relied on them too much.

Any sim will show the effect since it is universal. Any sim using rounding will show the expected value (totally equivalent to a sim result) with a value larger than the overall expectation for perfect starting decks or decks stacked any way one wishes for the true count identical to the starting true count.

This would not happen if there were not a floating advantage.

Perhaps someone like you could run about five sims using rounding. Use eight decks cut at one. Start +10, +5, 0, -5, -10. Let Cant select the makeup of the ones not 0.

If you have the time, I would appreciate your doing this because repeatedly Cant has implied you have a position identical to him on this matter.

If the overall expectation of the starting true count is greater than the overall expectation, we can be assured a floating advantage always exists. The difference will not be as distinct as simming at the m level because what will be observed is the average floating advantage but any difference proves the point.

The lack of an answer and the filibuster is instructive. The answer a filibuster gives is "NO" and I will accept that.

Now another yes or no which again you will filibuster.

When you use the phrase "The basic strategy expected value tends to be larger in the middle of the distribution, and smaller in the extremes, and indentical overall to that of the starting pack." I take it you are talking about distribution of the subsets of true count i derived from a stack of true count i.

That must be the distribution you are talking about because addressing other distributions would be totally irrelevant to the proof. No conclusions were reached for any count except i and I think it would have been exceedingly messy for even you to confuse the subsets of true count i with other subsets when other subsets had nothing to do with the proof.

So answer yes or no. I will take no straight answer and a filibuster as a yes because referring to other true counts are irrelevant to my proof.

Ends up at about 52 cards left. Can use any counting system, flat bet, basic.

well enough to agree on what the other party would predict, and for both of you to agree on what the expected outcome would be according to either side. After this many posts, you should at least be able to do that.

However, understanding what Cant writes is difficult, to say the least. I think his garble is purposeful to protect deniability. If no one understands what another says, then the person can claim to have said anything.

My proposition is simple. If there is no floating advantage when basic strategy is used and cards are not exhausted, the total Ev for the total stack will equal the expectation off the top. If the beginning true count of the stack is arbitrary and rounding is used and the Ev for that true count consistently is larger than the overall expectation, the effect must be caused by a floating advantage because nothing else would explain the difference.

My proof did not and could not address the magnitude of the floating advantage because it was a comparison as is necessary for mathematical proofs of that sort. It did not and could not address any distributions except the distribution of subsets of the size m derived from a set of size n which also have a true count identical to the starting true count. Since the data from a sim I set up as described would amount to the expected value of all subsets of the specific true count derived from the starting set of all sizes from n to n-m the magnitude of difference would be smaller than would be the magnitude of difference between E(i,n) and E(i,m), any difference would demonstrate a floating advantage exists.

BTW, is it your proposition, as Cant claimed, I stole my proof from the Brh article on bjmath?

aren't you the genius who said
"I respect Grosjean but those figures, like El Burros, have to be wrong".

Even though I haven't read any of above discussion, based on your track record and minimal credibility, I'm gonna have lean towards the Cant side.

Clarke has never been able to commit to anything that could be proved or disproved via simulation (the "put up or shut up test"), and your proof is way too long for me to wade through, so I'll restrict my remarks to the subject instead.

The count distribution in blackjack is asymmetrical, even with a fixed number of rounds dealt. This happens simply because it takes more small cards than big cards to complete a round. I don't know if you tried to do this, but you can't just take X number of cards from a Y card pack and call that a representative subset.

Also, using rounding doesn't work, if that is important to your proof. The average count between x - 0.5 and x + 0.5 will tend to be farther from 0 with deeper penetration, since the shape of the distibution curve flattens out as more cards are dealt.

And no, of course I didn't accuse you of stealing any posts from bjmath.com. Didn't he also accuse you of removing some files from the server to cover it up? You have to remember that this is someone who thought the movie "Conspiracy Theory" with Mel Gibson was a documentary!

"Even though I haven't read any of above discussion, based on your track record and minimal credibility, I'm gonna have lean towards the Cant side."

Man, oh man. What "track record"??!

It is quite obvious that you are in the dark about ML's contributions to our understanding of Blackjack-related mathematical concepts. On the basis of his one reluctance to accept as fact a game wich yields profits far in excess of vanilla counting (ML never claimed to be more than a mildly interested, if not bored, counter), you have no use for his "track record"??

I'm gonna impose to myself a 3-day vow of complete silence (including radio silence) if you could explain to us what the fuck Clarke Cant is saying ! I put it to you that you don't even know what he's saying, let alone support what he's saying. You're just posting out of spite.

1) I really did not think you had told Cant I stole something from bjmath but his post stated you had done that and it is nice the matter is cleared up.

2) The frequencies above and below are not symmetric but close even with no cut card for the reasons you describe. To the extent I said the distributions are normal the proof is not precise as you point out. I noticed there was about a half a percentage point difference for +1 and -1 frequencies after I had published the posts and did some sims like the ones I suggested and remembered I had seen that before. I did not know the reason for the phenomonon and appreciate your explaining it. That makes sense. I did not worry about the discrepancy as to the proof, however, because the bias towards larger frequencies is to the negative so the averaging step which presumed identical frequencies would end up smaller than the proof presumed and the relationships used in the proof would hold. All that is needed to account for these discrepancies is a statement the lower frequencies would be greater than the higher frequencies but, for the purposes of the proof it would be assumed them greater or equal and the inequalities would still hold.

3) I was interested in your comments as to "representative subsets." The proof did not use representative subsets as Cant continues to insist. It used expected values of expectation for all subsets which also had the same true count as the beginning true count so as to duck matters of representative subsets. As I have remarked a number of times, that value is the value which would be given by simulation given the simulation number is the mean of "hits" of true counts of a specific number after many repeated trials.

4) Rounding or the brand of counting used was irrelevant to the proof. I thought it would be the better method for simming because it is symmetric around the starting value while "flooring" for a perfect deck would be symmetric around both + and -1 true counts rather than 0 for the "perfect" decks situation where the beginning count is 0 and the floor of 0. The proof allows for such a generality with the only condition being identical true counts recokoned the same way.

Thanks for the comments.

ML was wrong about holecarding and still won't admit it. Grosjean (backed by others)puts the optimal edge at 13%, with normal cover the edge is at 10%, twice what ML insists upon.

I make as much money at my day job as do "pros" like you. And when sitting at a blackjack table I would not be described like you as the one "sitting on his face trying to look at the hole card".

you "Don't need to". On top of not needing to, you CAN'T because you don't have what it takes.

I, on the other hand, have a choice between a lucrative (as much as I desire) "normal" day job and my current job as a pro player.

"I would not be described like you as the one "sitting on his face trying to look at the hole card"." plllllease. I educate you a bit on hole carding and you think that's all I do and in addition i "sit on my face". I only look when they show it to me. and For those of us with an open mind, there are plenty of ways to beat the casino MORE lucrative than looking for a dang hole card. Hint: you ain't gonna find it at home on your computer arguing about floating advantage.

I thought it was your unnatural hunching over that was being described. Perhaps it was another person.

As to your ability to be a success at a day job. I doubt it. Arrogant know-it-alls are normally rejected in the real world. misfits don't fit in.

I make as much money at my day job as do "pros" like you.

Isn't that special! Except this isn't a bankruptcy attorney board, it's allrgedly an advantage player site.

And when sitting at a blackjack table I would not be described like you as the one "sitting on his face trying to look at the hole card".

I have no idea what you're talking about here and i'm sure neither do you, but the point remains you're wrong about the mathematics of the edge at holecarding. Since you've already stated you don't play but are solely interested in the math, odd that you keep having your postbuster friends bust this post.

I will accept Grosjean's figures. I was wrong.

to all the real players.

But nooooo, "i'm mr. know-it-all so i must be right and continue to make an ass out of myself"

You know that "arrogant know-it-all" you were talking about above. Well look in the mirror wise guy.

I do not know how you were raised but since you boast of your ivy league experiences and other things I would assume privileged. I was raised rural and poor in a poor and relatively uneducated part of the country but at least I was taught manners. Clearly you were not because you exhibit no manners.

The figures are not "apparent". First, my remarks were made in response to a truly idiotic post equating the oranges of an entirely different game with the apples of blackjack and drawing a conclusion from the absurd comparison.

Secondly, I accept Grosjean as more knowledgeable in analysis of gambling games so I am accepting the 13+ edge he is quoted as claiming for perfect hole card play even if that figure seems incredible. It seems incredible because there is a close relation between perfect hole carding and double exposure with no cover. For practical purposes, the only bad rules for double exposure is dealer takes pushes which is about a 9% edge. That edge is about made up by the ability to see all the cards which would give perfect hole carding about a 9% edge flatbetting. A 13+ edge means Grosjean has found a way to improve the edge by more than 4% which in turn means he should be able to get a +4% edge anytime he wishes to sit at a double exposure table and that is a remarkable figure. I trust it if Grosjean says it because he is good at what he does but it is remarkably high it seems to me.

A ten per cent edge flat bet after corrections for diminished number of hands played (it is doubtful both the dealer and relief dealer can both be read most of the time) and the internal variance of blackjack could come close to yielding a $5,000 SCORE.

However, figuring the flat bet edge at 9% which is the difference in double exposure and blackjack yields a much smaller SCORE. First if it is discounted for cover to the same extent as Grosjean does, the invariant edge would be about 5.5%. Ev^2 would be about .003 or thirty dollars profit per hand for a $10000 bankroll. Variance is probably more but if blackjack variance of 4/3 is used, profit per hand in terms of score becomes about $22.50 per hand and if the relief dealer is taken into account and twenty minutes per hour remains unplayed, SCORE would be calculated at around $1500 which is hardly $5,000. If a higher Ev is derived from ranging bets variance would increase drastically and the SCORE would need to be adjusted downward for that.

So I suggest three things:

1. Learn some manners. This is just a discussion board, not anything to lose dignity over.

2. Don't compare apples and oranges if you do not want to be called on it.

3. If you wish to assert a SCORE is $5000, support your assertion with figures showing a 10% edge can be gained without ranging bets.

3.