I would like to get details on FBM system so I can run Correlation Coefficients on it since the FBM system has been touted as a such a great system. It uses a side count of Aces so I already do not like it from an accuracy point of view as an ASC depends on an estimate of decks played and plus/minus side counts are exact.

I would first run CC for the Illustrious 18 as I have included in an attached PDF for KO with AA89mTc and 5m9c which I compare with HO2 w ASC and with HL for the I18. I can run the CC of the I18 in like 15 minutes and get an exactly accurate gauge on the power or the system. If the results of the CC of the Illustrious 18 show promise then I can run the full WACC, OCCC, LSCC and Betting CC.

The attached PDFs show that my CC method is just as good as sims and that they complement each other and can be used to cross check each other.

Disadvantages of Simulations:

- Take a long time to run and are tedious to set up.
- Require the calculation of indices for each playing strategy (another potential source of error} for the counts being compared.
- There is also the problem of variance with simulations which is reduced by increasing the number of hands simulated.

Advantages of Correlation Coefficients:

- WACC and BCC can be done in a matter of minutes.
- WACC and BCC are exact with zero variance.
- WACC and BCC used to compare various counts require no indices.

Correlation Coefficients are calculated with the tag values of the count being analyzed and the EoR. EoR are LSL estimates, so they assume that blackjack is linear. Simulations have no assumptions on blackjack being linear. With less than one deck is remaining, non-linearity kicks in.

It should be noted that for every count system that simulations were run for, when more strategy changes were added, which increased the weighted correlation coefficients, the SCORE increased even when the increase in the weighted correlation coefficients was as small as one percent. This is a testimony to the accuracy of the weighted correlation coefficients, the accuracy the LSL (Least Squares Line} method used to calculate the optimal values of "k" and corresponding indices for each playing strategy departure and the accuracy of the twenty billion round simulations done each time more playing strategy changes were added.

Refer to Simulation 1: HL w AA78mTc, listed earlier in this Introduction. The increase in SCORE occurred even for very minor additional HL w AA78mTc strategy changes.

The major HL w AA78mTc strategy changes were the six top strategy changes of insurance and standing on hard 12 v 2, 3, 4, S and 6. This added the bulk of the playing strategy gain from adding AA78mTc to the HL as indicated in the simulations as HiLo + AA78mTc 6. The increase in the weighted correlation was significant and the increase in the SCORE likewise was significant.

When another additional minor six strategy changes were added to the HL as indicated by HiLo + AA78mTc 12, which resulted in a very minor increase in the weighted correlation coefficients, the SCORE also increased, also by a very small amount, in sync with the small increase in the weighted correlation coefficients.

When a final additional fourteen very esoteric strategy changes were added to the HL as indicated by HiLo + AA78mTc 26, the result was another very small increase in the weighted correlation coefficients and the SCORE likewise increased by a very small amount, again, in sync, with the very small increase in the weighted correlation coefficients.

HL with 7m9c was analyzed. I had used my LSL technique to calculate the values of "k' that maximized the correlation coefficient between the derived count and the effects of removal for the top six strategy changes shown below.

Each of these changes involved huge increases in stand along HL correlation coefficients. So, when simulations were done, I would expect the SCORE of HL + k*(7m9c) to exceed the SCORE of stand-alone HL. However, when sims were done the SCORE decreased that made no sense. Gronbog's sims involved 20 billion hand simulations. So, I suggested to Gronbog to test each of these strategies changed individually with just 100 million hands, which could be done in less than one hour, to see which of these situations decreased the SCORE. The result was that each simulation increased the score except surrender hard 14 v T which Gronbog later discovered he had miscoded with hard 14 v T hit/stand. Once the error was fixed then each strategy change taken individually increased the SCORE. This highlights the sensitive and accuracy of the Correlation Coefficient method of comparing various count systems and that it is a good check on the simulation results. It should also be noted that the indices calculated with the LSL technique matched indices calculated with sim programs. The LSL indices were used in the sims which also proves the accuracy of the LSL calculation of indices. So weighted Correlation Coefficients and Simulation results should both be used as cross checks for errors.

I am attaching PDFs with HL w 7m9c Weighted CC analysis and with the Sim results and proof that the CC works as well as sims.

01 KO w AA89mTc and 5m7c sim.pdf

02 HL w AA78mTc sim.pdf

03 WACC for various primary count systems.pdf

04 HL w 7m9c sims.pdf

05 KO w AA89mTc and 5m9c Illustrious 18.pdf

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