I hate posting this on the FA dustup, But see for yourself.

But I should state how that I was able to discern the rounding error in Norm Wattenberger's post on his sims, that was being used to support the theories oon FA, where I was chased off for daring to challenge them. Try it yourself and you can isolate the bow effect elements from the rouding errors.

The url posted and linked by Norm was qfit.com/fal.jpg Start with the equation I gave that any possible true count has to match: N*52/(# of cards left). Follow the line along the TC=+1 line to where it peaks and vanishes. Every valid report on true counting will have such a peak where at some number of cards left that true count never appears. If the rounding is to the nearest half true count, then TCs of +1 vanish when less than 52/1.5 cards are left. If the rounding for reporting is to the range +1 to +2, then TCs of +1 vanish at the 26 cards left point.

That establishes the rounding used.

Now go over the peak line. Notice that the rotation of the 3D chart obscures the display past this peak line. Pity because then it would have been clear that certain true counts are not always possible, and the slope of the drift within the rounding range would have been clear. Then it would also have been possible to determine if the highest TC displayed, TC=+10, was ever shown to be rolling off as per the bow effect at some point. All that appears is this peak line, which is a little before the exclusion depth, but the view is not the best. The numberic charts are at bit massaged to match how the graph is displayed and don't add much info to these areas.

It is suspicious in a 30 Billion hand simulation that no hands at the high ranges are graphed until the penetration is fairly deep. Comeon there must have been a few rounds?

Norm it is a great chart and great software, but the views and rounding chosen does not really give as much information as is needed to isolate the data that actually matters. What matters is what happens to the edge when the possible TCs drift upward in a range of TCs used for segmenting the data and being sure to compare equivalent true counts. The final range where you can have an actual given TC showup is a good checkpoint.

The less than one deck inflation of values you describe is accurate but it has nothing to do with the floating advantage and I was careful to keep my sims at the one deck level to keep that error from creeping in.

Let me explain one more and the last time why the expectation at fewer cards rises at identical true counts, that is why the floating advantage occurs. The bow effect has a lot to do with the thing as apparently you and I agree.

Now let me make a few comments with which anyone except you will certainly agree.

1. The expectation in any arbitrary stack containing multiple decks is the same at all levels.

2. As more cards are removed, the standard deviation of true counts of remaining cards gets larger. That is, the true count from an original stack of six decks is more likely to be extreme at the two deck level than at the four deck level and more likely to be extreme at the one deck level than at the two deck level.

3. The overall expectation at any level is the summation of all possibilities of expectations for all true counts. That is, the frequency of all true counts multiplied by the overall expectation of all true counts then summed defines the overall expectancy and this overall expectancy remains unchanged.

4. The bow effect as you call it simply means expectation on the plus side does not rise as quickly for basic strategy as it falls on the minus size so the summation of plus counts of a specific value do not cancel out minus counts of the same value. In fact, as extreme counts become more of the population, the portion of the overall expectation attributable to those counts will comprise more of the overall expectation which would require overall expectation to be lowered if something else did not compensate. But we already know overall expectation cannot change. It has to be accounted for, compensate for, somewhere else in the possible distributions and the only place it can be found is between the extreme counts.

5. The set of all combinations of 104 cards has the same expectation as the set of all combinations of 52 cards but the set of all combinations of 52 cards has more extreme counts than the set of all 104 cards. The overall lowered expectations of these extreme counts must be compensated for and the only possible compensation is to raise the expectation of counts in between.

6. And that is precisely what sims demonstrate and why the floating advantage exists. There has to be a rule of conservation of expectancy happening if expectation remains unchanged while counts diverge.

I realize you will not attempt to understand this because your mind is made up but perhaps others will.

5.

"You will not attempt to understand this because your mind is made up."

Thank God you are polite..

This is far different than your previous.

The point lost on you is that you cannot properly seperate bow effect from rounding error potentials in Norm's chart and table as he posted them. Your sims report is simply on mean deck compositions that truly don't extend too well. Your fellows at rge21.com, ETF and others, told you the same thing.

I for one would like all charts to be shown without such rounding and the charts to be continous and show actual true counts. Otherwise they are just spectacular graphics and not much more. It would be nice if the axises were rotated to view the line where every TC "expires." Then I would be happy and would love to see Norm try again with these mutual criticisms in mind.

What we disagree about is the claims of how much bow effect is there, and that is why I posted my sausage post. As for my post on ruin formulas it was specificaly to counter you and Cyrus using this subject as a stop discussion card, and nothing more. You really can apply Chebayev polynomial analysis to ANYBODY's ruin formulas and extract an error versus #hands spectrum. I said not one word in any asparaging Don's formula. The only point made along those lines is that saying one singular is the formula is wrong and never right. Just the potential alone of having to do some unusual combination of ruin criteria makes for my original having some application. Absolute error rates are seldom any consideration as long as they are reasonable. Most should stick with DS' except for very unusual circomstances. But such do occur. It is also handy for one to have a 2 term trip ruin that is in exponential form considering how often one can have one's computer "gone over" these days. I have posted on that too.

The fact of history is that these same equations, including one similar to Don's trip ruin, by an economist named Ramov, were, in an economic context, part of an all too similar political witch-hunt used by Stalin and Yazov to have Kondratiev executed.

Same formulas or very close, and the same Stalinist BS from the clones. That is my final point.

My proposition, shown by sims, is the expectation for the same true count rises as cards are exhausted; that a floating advantage not related to true count inflation below one deck exists. You have repeatedly said my position was the overall expectation for a sample of fifty two cards from a population of more decks was larger than the overall expectation of the total population while my position was definitely not that.

My post above explains why that has never been my position.

Your proposition is the floating advantage is illusory; my proposition is the floating advantage is real. My original post on RGE in this matter was it exists but is not large and only seldomly of benefit to the player. I stick by my proposition and respectfully suggest to the board that it ignore your inaccurate statement in this instance and highly suspect your posts on any topic which are the most part inaccuracies masked by obfuscations which are purposefully used to give yourself deniability IMHO.

Your claim was that the "basic strategy" edge rose, and the claims made on rge21.com was that the "edge shows a rise for all counts." There is a bow effect but no such rise for all counts.

Funny how you came up with an fairly accuarate summary above.

I said the expectation rises for comparison at all identical true counts as cards are diminished and expectation does. I said earlier the difference is the dispersion and exclusion of possibilities. For example, if the cards happened to be -10 at the two deck level, there is some liklihood the cards would be at -15 at the one deck level. There is no liklihood -10 at the one deck level with be anything except -10. Therefore, the expectation for a true count of -10 at the two deck level is worse than the expectation at the one deck level. The same can be said for any plus or minus count.

The import of my earlier posts should should have been apparent to any person with a rudimentary knowledge of these things. Your knowledge continues to be below rudimentary and the board should be apprised of this fact.

This is a fraud

Posted By: ML on 2 April 02, 5:59 a.m. in response to: If you wanna know (El Burro)

El Burro says he does not play anything except four digit Score games. That means he would win over $1,000 per hour optimally betting a $10,000 bankroll. There are no such games.

For some time the boasting and defensiveness of El Burro along with certain inaccurate statements like the 1000 plus SCORE has made me suspect the board is dealing with just another one of the big talkers who spread blacks at will in SD games.

In the September 2001 issue of Blackjack Forum James Grosjean writes:

In terms of the numbers, the SCORE of this game is around $5000. We are underbetting, though, because we are afraid that Caesars might not be able to stomach the action.

Since we all know Grosjean is a true advantage player with ahem, a fair math backround, and that ML is a theory geek who bets red chips i ask the masses to see for themselves who the fraud is.

Doubles a bankroll in about 200 plays which means it has an Nsub0 of less than 200.

The Nsub0 for a uniformly flat bet game (no variance) at a 2% invariant advantage is 1/.0004 = 2500, over ten times as bad or less than 500 and in the range of knowing the hole card all the time.

I respect Grosjean but those figures, like El Burros, have to be wrong.

but what else is new?

in the rest of my threads. Should there be an appeal for sims against the clones? All they listen to is sims.

Frankly they know they are wrong but simply because it is me against this DS folly they will do literally anything, even to possibly DD having finked out T-Hopper, to hide this and continue to promote what they know is wrong to the masses and newbies that they always use as their excuse for such attacks.

That is why I am starting to sound like Matt Drudge!

Since we all know Grosjean is a true advantage player

Really?, I thought he was a metaphorical advantage player.

ML,

You can get into flame wars with anyone you want, but if you're going to invoke my name, I'd appreciate it if you knew something about what you're talking about.

Do you know what game I was referring to that had a $5000 SCORE?

Do you know what our flat-bet edge was?

Do you know how many hands per hour we were playing?

I didn't think so. I suggest you read the Spring 2001 BJF article.

ML: and in the range of knowing the hole card all the time.

As the kids said in the '80s, "No duh!" Do you think we're talking about count games here? 2% edge? You're not even in the ballpark. The game we were playing had a 35% edge on every hand. Oh, yeah, I forgot, those games don't exist.

I thought that my book might help some counters get their heads out of the sand. I guess my friend was right when he told me, "You can't save them all."

(Now you're probably thinking that if the edge was 35%, then a $5000 SCORE is too LOW. No, it's not.)