KO BE questions

I compared KO's BE with AO11 with ACE side count and ZEN in single deck playing about 500 rounds.

I have observed for KO's RC at 2 and 3 it seems to overestimate
the advantage for betting because corresponding TC's for AO11 and ZEN
are either zero or negative sometimes but at pivot(RC=4) its very accurate.

Which is correct ? ZEN seems to differ a lot compared to AO11.

Thanks,
KOKO

BC (Betting Correlation) or BE (Betting Efficiency) for the systems you name are as follows:

Zen =.962
KO =.977
AOII =.989

These numbers come from Richard Reid's site, Mathematics of Blackjack.

Just a note. 500 rounds of any blackjack game is nowhere near enough to draw any conclusions about the efficiency of any blackjack system. 25 million rounds is the bare minimum, and some would say that you need at least 40 million rounds.

I just wanted to add a note of clarification. Figures quoted for betting correlation are based upon true-counts. They would apply to KO if you were using it in True Count mode.

Many (Most?) KO players use Running Count Mode. The correlation would be less.

that in using RC the betting advantage is not precise. Either one
underbets are overbets compared to betting using TC.

MathProf, do you know of any simulators that show BC figures? I've got the CVSim series, including CVCX and CVData, but if they show it, I haven't found the right button. I also have Auston's BJRM 2000, but I don't think it's in there either. The only published BC figure I have seen for KO is the one on Reid's site. I don't think the book includes a BC number.

Short of that, is there a formula for determining BC?

It is a best fit sum of squares calculation comparing the real values of the different cards with the tag values.

I will commit some heresy and say I have always felt uncomfortable with that calculation because removal will generally have some uniformity and after some removal higher valued removals like five will tend to balance lower valued removals like a two. It seems to me the Griffin method values off the top and not through the deck. But since I am comparing the views of Griffin and ML, the odds are overwhelmingly strong I am wrong.

As ML suggested, Betting Correlations are simply computed by taking Effects of Removal and correlating them with count tags. There is a very simple formula for computing the correlation between two variables (which has applications far outside of BJ) ; I can post it if you want. You may find it described explicitly in Griffin. Griffin tended to work with balanced counts, which gives an simpler formula in which one of the terms is 0. He may have only listed he simpler formula, I am not sure.

Now BC only gives us an approximation of a count's power. Griffin defined "Betting Efficiency" as the Betting gain of a count system divided by the gain available from a perfect count system. There is a theorem that if your game is approximately even off the top, and your plan is to bet 1 unit when you have an advantage, and 0 otherwise, then your betting efficiency is approximately proportional to your betting correlation.

In single deck game, betting is not that far from a model of "Max Bet at any advantage" and these ideas can give good approximations. But if your betting proportionally, then the square of the Betting Correlation is a better predictor of Betting Efficiency. I believe that Shoe play more closely fits into this model.

You could do your own sim of betting efficiency by doing Sims with your favorite count system, and doing another sim with a "perfect system". Your efficiency would depend somewhat on the game you were playing. This itself would be just an approximation, because your "perfect" system wouldn't be perfect, it would simply the best Linear count system available. Another idea would be to use CA to determine "perfect betting", and compare your count system(s) to that.

There are a lot of subtle issues that I have swept under the rug here, in order to try to keep this a bit brief. I can elaborate on them if needed.

There was a very old discussion about this in the old rec.gambling between Steve Jacobs and Abdul Jalib M'Hall (see groups.google.com). I seem to recall discussing it with Cacarulo. All seemed to agree the through-the-deck concept could produce superior results, and it is very unlikely all of us could be mistaken.
I do not incidentally think this is a question of Griffin being correct. Griffin devised some workable approximations. It is a bit arbitary to say an approximation is too approximate, and Griffin's method served a useful purpose in times when high-speed computers were not widely available.

I have seen the statement before about betting efficiency being the square of the betting correlation in the multideck, large spread situation but have never understood why. The way I look at it this requires the assumption more extreme counts are less reliable but I am not sure that is necessarily so. If there is linear unreliability at extreme counts, I could see how spreading approximates an exponential function but if your max is +4 for example, the unreliability would seem to me to be OK except in the margins like a count of barely +4.

Perhaps I am missing something.