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Thread: Zenfighter: Griffin, Fantasies, and Pocket Calculators

  1. #1
    Zenfighter
    Guest

    Zenfighter: Griffin, Fantasies, and Pocket Calculators

    Playing Efficiency

    Normally this is a linear estimate (not realistic for small subsets of cards) of the ratio of profit by using a card counting system, to the total profit one could gain over basic strategy, if one could track every card and perfectly determine the change in outcome. For us, mere mortals who use a single parameter card counting system to locate favourable opportunities, so as to bet extra units and deviate also from basic strategy if we presume a gain of any sort, a certain portion of the "cake" is the maximum we can strive for, while using it.


    Optimal systems for variations of strategy

    {TOB}: A noteworthy observation is that, if the ace is to be counted zero, improvement in the second decimal cannot be achieved beyond level three.

    So for all practical purposes his third raw of the table (TOB, page 46) is the champion, for maximum efficiency with a single parameter count.

     

    A 2 3 4 5 6 7 8 9 T Efficiency

    0 1 2 2 3 2 2 1 -1 -3 0.690




    Ken (Kenneth S. Uston) quickly picked-up the count and with the aid of his friend Stanley Roberts (Gambling Times Incorporated) his book MDBJ went
    to the presses in the year 1981. The famous UAPC went public. A "Rolls-Royce" for strategic departures. Dynamite for hand-held games!

    Curiously, when striving for maximizing overall strategic efficiency, the ace is not to be neutralized. TOB absolute single parameter champion is this one:

     

    A 2 3 4 5 6 7 8 9 T Efficiency

    51 60 85 125 169 122 117 43 -52 -180 0.703




    If we divide by 200 we get:

    Table 1
     

    A 2 3 4 5 6 7 8 9 T

    0.255 0.300 0.425 0.625 0.845 0.610 0.585 0.215 -0.260 -0.900



    A sort of EoR`s table, isn`tit? Believe it or not, researchers and publishers have used this one to evaluate the playing correlations of their own systems.


    Learning by example: The Uston Advanced Count


    A short formula and a pocket calculator enough to extract playing correlation and efficiencies for your selected point count.

    1) Find first the correlation coefficient for the above playing EoR`s that correspond to your counting system. E.g. UAPC

    Corr = (inner product)/ (sqr (ss eors * ss point tags))

    Inner product = (1 * .300) + (2 *.425) + (2 *.625) + (3 *.845) + (2 *.610) + (2 * .585) + (1 * .215) + (-1 * -.260) + (4 * -3 *-.900) = 18.600

    EoR`s sum of squares = 5.50845

    Tags sum of squares = 64

    Solving

    cc = 18.600/ (sqr (5.50845 * 64)) = 18.600/18.7761 = .9906

    UAPC playing correlation = .9906

    In other words almost as good as the reference from above.

    Another question is the efficiency as outlined in the first paragraph of the article. So despite the fact that efficiency tends to increase as a function of the deck being depleted (penetration), its approximation to the cc only occurs as a limit.

    Playing efficiency formula:

    PE = (1.405 -(1-cc)) * (cc/2)

    UAPC tested:

    PE = (1.405 -(1 -.9906))*(.9906/2) = .691

    UAPC Playing efficiency = .691

    Don`t be timid and find the PC and PE from the Hi-Lo count for yourself!


    For the selected playing counts from BJA3, Table D18, page 522, we get the following PE results with the same procedure outlined above:

     

    Hi-Lo Hi-Opt I RPC AOII Halves

    0.511 0.609 0.554 0.671 0.565



    Carlson`s Omega emerges as a winner here? No surprise at all. Just put the AOII tags, ace through ten (0, 1, 1, 2, 2, 2, 1, 0-1,-2) below Table I,
    and the reason for it will appear in front of your eyes.

    Can we put some competition to UAPC with another three-level count?

    Approximating the EoR`s from Table I, we can build three groups here.

    1) Aces, deuces, threes, eights and nines
    2) Fours, sixes and sevens
    3) Fives and tens

    So putting equivalent tags below we get

    1, 1, 1, 2, 3, 2, 2, 1,-1,-3

    A heretic three-level count (aces = + 1, huh!) but with the following numbers:

    PC = .997
    PE = .699

    Make no mistakes here. Once any betting spread is involved this count won`t beat UAPC with a side count of aces.

    The reason for this is its meagre betting correlation.

    Betting correlation = .8393 Our dreams reduced to ashes!

    While the saying, There is Nothing New Under the Sun, seems to be often the case, it doesn`t hurt to look at old things with new eyes, anyway.

    Finally, let`s check both playing correlations.


    IL18 multi-deck playing correlations

     

    Heretic UAPC

    16 v T 0.706246 * 0.704785
    16 v 9 0.498523 0.503510 *
    15 v T 0.900817 * 0.892171
    13 v 3 0.943059 * 0.924748
    13 v 2 0.933367 * 0.912163
    12 v 6 0.876600 * 0.843130
    12 v 5 0.902709 0.904753 *
    12 v 4 0.909761 0.912085 *
    12 v 3 0.895447 * 0.878108
    12 v 2 0.827060 * 0.807781
    11 v A 0.980394 * 0.968034
    10 v A 0.908509 0.949819 *
    10 v T 0.741422 0.813861 *
    9 v 7 0.785766 0.825422 *
    9 v 2 0.896061 0.905951 *
    T,T v 6 0.855622 0.897604 *
    T,T v 5 0.849197 0.900497 *
    Insurance 0.915811 * 0.901388




    A tough fight among both, with UAPC leading the double downs and the splits, but Don`s multi-deck Super-Illustrious are: Insurance, 16 v T, 15 v T
    and 12 v 3, plays for what the first count shows some superiority.

    After watching delighted Norm`s new site (with beautiful colours, yes), the card-eater fantasy is crossing my mind, but instead of having seated at the table our garden-variety Hi-Lo`s counter, with one of the above two guys. They could "handle" our hand, too. A pristine colour-fantasy, but for High-Stakes and rich card counters, I am afraid. These guys look expensive, damn! :-)

    Zf

  2. #2
    Don Schlesinger
    Guest

    Don Schlesinger: Re: Griffin, Fantasies, and Pocket Calculators

    Spectacular piece of work, as usual! Thank you for this beautiful demonstration. All DD readers should print out, or bookmark, this post.

    > For the selected playing counts from BJA3, Table D18,
    > page 522, we get the following PE results with the
    > same procedure outlined above:
    >
    > Hi-Lo Hi-OptI RPC AOII Halves
    > 0.511 0.609 0.554 0.671 0.565

    Imagine! None of this in BJA3!!! You will shame me yet into BJA4!! :-)

    > Carlson`s Omega emerges as a winner here? No surprise
    > at all. Just put the AOII tags, ace through ten (0, 1,
    > 1, 2, 2, 2, 1, 0-1,-2) below Table I,

    And yet, there is Hi-OptII, with 0.668, but a much higher insurance correlation no?? Not sure why we didn't include it in the BJA3 p. 522 charts. Perhaps too similar to AOII?

    Don

    Don


  3. #3
    Zenfighter
    Guest

    Zenfighter: Re: Griffin, Fantasies, and Pocket Calculators

    And yet, there is Hi-OptII, with 0.668, but a much
    higher insurance correlation no?? Not sure why we
    didn't include it in the BJA3 p. 522 charts. Perhaps
    too similar to AOII?


    The calculated PE for HiOptII is exactly. It's IC is higher too, IC = .9085 (w/o removing the dealer's up-card), but for the standard 6dks and AC rules, Omega's betting correlation yields .9867, while HiOptII gives us .9848 for the same rules and decks. All in all, Omega will beat HiOptII, as a zero-neutralized-ace count and thus deserves being the representative for these kind of two-level counts.

    Glad to hear, you have enjoyed the article.

    Zf

  4. #4
    Don Schlesinger
    Guest

    Don Schlesinger: Re: Griffin, Fantasies, and Pocket Calculators

    > And yet, there is Hi-OptII, with 0.668, but a much
    > higher insurance correlation no?? Not sure why we
    > didn't include it in the BJA3 p. 522 charts. Perhaps
    > too similar to AOII? The calculated PE for HiOptII
    > is exactly. It's IC is higher too, IC = .9085 (w/o
    > removing the dealer's up-card), but for the standard
    > 6dks and AC rules, Omega's betting correlation yields
    > .9867, while HiOptII gives us .9848 for the same rules
    > and decks. All in all, Omega will beat HiOptII, as a
    > zero-neutralized-ace count and thus deserves being the
    > representative for these kind of two-level counts.

    Guess "it all depends." See BJA3, p. 172. :-)

    > Glad to hear, you have enjoyed the article.

    I always do, amigo!

    Don

    > Zf

  5. #5
    bfbagain
    Guest

    bfbagain: I agree! Beautiful work Z. Thank you *NM*


  6. #6
    Norm Wattenberger
    Guest

    Norm Wattenberger: Neat stuff *NM*


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