Page 1 of 4 123 ... LastLast
Results 1 to 10 of 33

Thread: Cacarulo: The HALVES vs ZEN dispute

  1. #1
    Cacarulo
    Guest

    Cacarulo: The HALVES vs ZEN dispute

    The HALVES vs ZEN dispute

    Game Analyzed: 6D,S17,DOA,DAS,SPA1,SPL3,NS,5/6,C22 indices (floored),
    Heads Up,Play-All,10000 Million rounds (double than what I used in my previous
    sims)

    Note: All the sims in this post were run using SBA 5.52. The indices
    were also created with SBA (5 sigma). The reason for choosing SBA and not
    CVData is simply because I already have a C-program that imports the SBA
    output data which is then used to create the following tables:

    A) HALVES x 2 (using full-deck indices and full-deck estimation)

     play-all | rounds played = 100.00% 
    spread ev/h sd/h ror% n0 di score ekb avb unit kelly
    ------------------------------------------------------------------------------
    1 - 1 -0.309 11.612 100.00 0 0.00 0.00 10000.00 1.000 1.000 0.000
    1 - 2 0.083 15.870 13.53 3685022 0.52 0.27 3046.39 1.289 3.283 1.000
    1 - 3 0.457 20.222 13.53 195874 2.26 5.11 894.97 1.523 11.174 1.000
    1 - 4 0.794 23.789 13.53 89788 3.34 11.14 712.81 1.677 14.029 1.000
    1 - 5 1.106 27.156 13.53 60252 4.07 16.60 666.57 1.810 15.002 1.000
    1 - 6 1.396 30.264 13.53 47030 4.61 21.26 656.31 1.927 15.237 1.000
    1 - 7 1.672 33.299 13.53 39646 5.02 25.22 663.01 2.038 15.083 1.000
    1 - 8 1.931 36.100 13.53 34962 5.35 28.60 675.01 2.138 14.815 1.000
    1 - 9 2.176 38.778 13.53 31744 5.61 31.50 690.89 2.232 14.474 1.000
    1 - 10 2.421 41.511 13.53 29392 5.83 34.02 711.65 2.329 14.052 1.000
    1 - 11 2.654 44.089 13.53 27607 6.02 36.22 732.56 2.419 13.651 1.000
    1 - 12 2.881 46.640 13.53 26201 6.18 38.17 754.94 2.507 13.246 1.000
    1 - 13 3.116 49.333 13.53 25070 6.32 39.89 781.11 2.601 12.802 1.000
    1 - 14 3.331 51.758 13.53 24140 6.44 41.43 804.16 2.685 12.435 1.000
    1 - 15 3.548 54.231 13.53 23359 6.54 42.81 828.85 2.770 12.065 1.000
    1 - 16 3.761 56.663 13.53 22697 6.64 44.06 853.64 2.854 11.714 1.000
    1 - 17 3.960 58.900 13.53 22125 6.72 45.20 876.10 2.930 11.414 1.000
    1 - 18 4.163 61.223 13.53 21627 6.80 46.24 900.33 3.010 11.107 1.000
    1 - 19 4.370 63.613 13.53 21189 6.87 47.20 925.96 3.092 10.800 1.000
    1 - 20 4.566 65.848 13.53 20802 6.93 48.07 949.71 3.169 10.530 1.000


    B) HALVES x 2 (using half-deck indices and half-deck estimation)

     play-all | rounds played = 100.00% 
    spread ev/h sd/h ror% n0 di score ekb avb unit kelly
    ------------------------------------------------------------------------------
    1 - 1 -0.310 11.606 100.00 0 0.00 0.00 10000.00 1.000 1.000 0.000
    1 - 2 0.081 15.851 13.53 3809335 0.51 0.26 3093.62 1.289 3.232 1.000
    1 - 3 0.472 21.106 13.53 199827 2.24 5.00 943.50 1.578 10.599 1.000
    1 - 4 0.780 23.537 13.53 91059 3.31 10.98 710.27 1.672 14.079 1.000
    1 - 5 1.111 27.425 13.53 60910 4.05 16.42 676.85 1.830 14.774 1.000
    1 - 6 1.374 29.917 13.53 47413 4.59 21.09 651.42 1.919 15.351 1.000
    1 - 7 1.658 33.114 13.53 39868 5.01 25.08 661.18 2.037 15.124 1.000
    1 - 8 1.920 36.006 13.53 35157 5.33 28.44 675.13 2.142 14.812 1.000
    1 - 9 2.152 38.428 13.53 31886 5.60 31.36 686.20 2.225 14.573 1.000
    1 - 10 2.396 41.156 13.53 29498 5.82 33.90 706.83 2.321 14.148 1.000
    1 - 11 2.648 44.069 13.53 27693 6.01 36.11 733.35 2.425 13.636 1.000
    1 - 12 2.889 46.838 13.53 26288 6.17 38.04 759.40 2.523 13.168 1.000
    1 - 13 3.091 49.015 13.53 25150 6.31 39.76 777.31 2.597 12.865 1.000
    1 - 14 3.301 51.359 13.53 24208 6.43 41.31 799.08 2.677 12.514 1.000
    1 - 15 3.517 53.821 13.53 23418 6.53 42.70 823.62 2.762 12.142 1.000
    1 - 16 3.738 56.372 13.53 22748 6.63 43.96 850.22 2.851 11.762 1.000
    1 - 17 3.962 58.990 13.53 22173 6.72 45.10 878.39 2.942 11.384 1.000
    1 - 18 4.184 61.594 13.53 21676 6.79 46.13 906.83 3.033 11.027 1.000
    1 - 19 4.364 63.592 13.53 21239 6.86 47.08 926.75 3.101 10.790 1.000
    1 - 20 4.549 65.677 13.53 20850 6.93 47.96 948.33 3.172 10.545 1.000


    C) ZEN (using full-deck indices and full-deck estimation)

     play-all | rounds played = 100.00% 
    spread ev/h sd/h ror% n0 di score ekb avb unit kelly
    ------------------------------------------------------------------------------
    1 - 1 -0.292 11.613 100.00 0 0.00 0.00 10000.00 1.000 1.000 0.000
    1 - 2 0.099 16.694 13.53 2859696 0.59 0.35 2823.09 1.357 3.542 1.000
    1 - 3 0.462 20.063 13.53 188984 2.30 5.29 872.20 1.507 11.465 1.000
    1 - 4 0.795 23.622 13.53 88209 3.37 11.34 701.58 1.662 14.253 1.000
    1 - 5 1.102 26.889 13.53 59544 4.10 16.79 656.12 1.790 15.241 1.000
    1 - 6 1.377 29.734 13.53 46595 4.63 21.46 641.83 1.895 15.580 1.000
    1 - 7 1.642 32.573 13.53 39339 5.04 25.42 646.06 1.998 15.479 1.000
    1 - 8 1.900 35.396 13.53 34714 5.37 28.81 659.49 2.097 15.163 1.000
    1 - 9 2.139 37.987 13.53 31538 5.63 31.71 674.61 2.187 14.823 1.000
    1 - 10 2.376 40.604 13.53 29212 5.85 34.23 693.99 2.278 14.410 1.000
    1 - 11 2.619 43.389 13.53 27449 6.04 36.43 718.85 2.375 13.911 1.000
    1 - 12 2.834 45.759 13.53 26064 6.19 38.37 738.75 2.455 13.536 1.000
    1 - 13 3.057 48.287 13.53 24946 6.33 40.09 762.65 2.541 13.112 1.000
    1 - 14 3.285 50.926 13.53 24028 6.45 41.62 789.38 2.632 12.668 1.000
    1 - 15 3.496 53.326 13.53 23261 6.56 42.99 813.29 2.714 12.296 1.000
    1 - 16 3.702 55.668 13.53 22607 6.65 44.23 837.00 2.793 11.947 1.000
    1 - 17 3.913 58.092 13.53 22045 6.74 45.36 862.51 2.875 11.594 1.000
    1 - 18 4.126 60.580 13.53 21557 6.81 46.39 889.44 2.960 11.243 1.000
    1 - 19 4.334 62.997 13.53 21129 6.88 47.33 915.70 3.042 10.921 1.000
    1 - 20 4.527 65.207 13.53 20751 6.94 48.19 939.30 3.116 10.646 1.000


    D) ZEN (using half-deck indices and half-deck estimation)

     play-all | rounds played = 100.00% 
    spread ev/h sd/h ror% n0 di score ekb avb unit kelly
    ------------------------------------------------------------------------------
    1 - 1 -0.293 11.609 100.00 0 0.00 0.00 10000.00 1.000 1.000 0.000
    1 - 2 0.088 15.547 13.53 3146906 0.56 0.32 2758.00 1.265 3.626 1.000
    1 - 3 0.468 20.493 13.53 191414 2.29 5.22 896.59 1.530 11.153 1.000
    1 - 4 0.779 23.475 13.53 90800 3.32 11.01 707.38 1.666 14.137 1.000
    1 - 5 1.085 26.780 13.53 60894 4.05 16.42 660.83 1.794 15.132 1.000
    1 - 6 1.375 30.036 13.53 47697 4.58 20.97 655.97 1.918 15.245 1.000
    1 - 7 1.614 32.345 13.53 40182 4.99 24.89 648.36 1.996 15.424 1.000
    1 - 8 1.871 35.188 13.53 35387 5.32 28.26 661.92 2.096 15.108 1.000
    1 - 9 2.137 38.304 13.53 32121 5.58 31.13 686.50 2.207 14.567 1.000
    1 - 10 2.380 41.061 13.53 29772 5.80 33.59 708.48 2.304 14.115 1.000
    1 - 11 2.584 43.209 13.53 27968 5.98 35.76 722.59 2.375 13.839 1.000
    1 - 12 2.798 45.587 13.53 26540 6.14 37.68 742.66 2.456 13.465 1.000
    1 - 13 3.020 48.121 13.53 25388 6.28 39.39 766.74 2.542 13.042 1.000
    1 - 14 3.247 50.764 13.53 24443 6.40 40.91 793.65 2.633 12.600 1.000
    1 - 15 3.478 53.487 13.53 23656 6.50 42.27 822.65 2.727 12.156 1.000
    1 - 16 3.711 56.270 13.53 22992 6.59 43.49 853.22 2.823 11.720 1.000
    1 - 17 3.901 58.417 13.53 22422 6.68 44.60 874.74 2.895 11.432 1.000
    1 - 18 4.084 60.467 13.53 21923 6.75 45.61 895.30 2.964 11.169 1.000
    1 - 19 4.271 62.605 13.53 21483 6.82 46.55 917.60 3.035 10.898 1.000
    1 - 20 4.463 64.812 13.53 21093 6.89 47.41 941.28 3.109 10.624 1.000


    The most important thing to understand from these tables is that full-deck indices
    with full-deck estimation is far better than half-deck indices with half-deck
    estimation! This means that the correct comparison would be A) against C) which
    again shows ZEN outperforming HALVES.

    If anyone wanted the input/output data from SBA just let me know and I'll post it
    here. Besides, it is useful is you want to use BJRM.

    Also, just in case SBA 5.52 were not enough to convince you I did run another lengthy sim
    but with my own simulator. The advantage of it is that it does not require any imports
    which allows me to get a little more precision. Here it goes:

    E) HALVES x 2 (using full-deck indices and full-deck estimation)

     play-all | rounds played = 100.00% 
    spread ev/h sd/h ror% n0 di score ekb avb unit kelly
    ------------------------------------------------------------------------------
    1 - 1 -0.308 11.613 100.00 0 0.00 0.00 10000.00 1.000 1.000 0.000
    1 - 2 0.084 15.874 13.53 3597675 0.53 0.28 3010.89 1.289 3.321 1.000
    1 - 3 0.458 20.201 13.53 194812 2.27 5.13 891.60 1.521 11.216 1.000
    1 - 4 0.796 23.798 13.53 89471 3.34 11.18 711.85 1.676 14.048 1.000
    1 - 5 1.105 27.074 13.53 60044 4.08 16.65 663.41 1.805 15.074 1.000
    1 - 6 1.397 30.246 13.53 46868 4.62 21.34 654.78 1.925 15.272 1.000
    1 - 7 1.673 33.258 13.53 39519 5.03 25.30 661.15 2.035 15.125 1.000
    1 - 8 1.932 36.070 13.53 34854 5.36 28.69 673.40 2.135 14.850 1.000
    1 - 9 2.174 38.677 13.53 31644 5.62 31.60 688.01 2.226 14.535 1.000
    1 - 10 2.420 41.419 13.53 29298 5.84 34.13 708.95 2.323 14.105 1.000
    1 - 11 2.655 44.050 13.53 27520 6.03 36.34 730.74 2.414 13.685 1.000
    1 - 12 2.884 46.607 13.53 26120 6.19 38.29 753.23 2.503 13.276 1.000
    1 - 13 3.119 49.305 13.53 24993 6.33 40.01 779.47 2.597 12.829 1.000
    1 - 14 3.331 51.667 13.53 24066 6.45 41.55 801.51 2.678 12.476 1.000
    1 - 15 3.548 54.145 13.53 23288 6.55 42.94 826.27 2.764 12.103 1.000
    1 - 16 3.767 56.663 13.53 22628 6.65 44.19 852.35 2.851 11.732 1.000
    1 - 17 3.966 58.905 13.53 22059 6.73 45.33 874.87 2.927 11.430 1.000
    1 - 18 4.170 61.233 13.53 21563 6.81 46.38 899.16 3.007 11.121 1.000
    1 - 19 4.377 63.627 13.53 21128 6.88 47.33 924.84 3.089 10.813 1.000
    1 - 20 4.575 65.896 13.53 20743 6.94 48.21 949.05 3.167 10.537 1.000


    F) ZEN (using full-deck indices and full-deck estimation)

     play-all | rounds played = 100.00% 
    spread ev/h sd/h ror% n0 di score ekb avb unit kelly
    ------------------------------------------------------------------------------
    1 - 1 -0.292 11.614 100.00 0 0.00 0.00 10000.00 1.000 1.000 0.000
    1 - 2 0.099 16.699 13.53 2839117 0.59 0.35 2813.71 1.357 3.554 1.000
    1 - 3 0.463 20.083 13.53 188394 2.30 5.31 871.70 1.508 11.472 1.000
    1 - 4 0.796 23.607 13.53 87992 3.37 11.36 700.26 1.661 14.280 1.000
    1 - 5 1.103 26.883 13.53 59386 4.10 16.84 655.11 1.790 15.265 1.000
    1 - 6 1.378 29.705 13.53 46457 4.64 21.53 640.26 1.894 15.619 1.000
    1 - 7 1.645 32.572 13.53 39220 5.05 25.50 645.05 1.997 15.503 1.000
    1 - 8 1.903 35.399 13.53 34610 5.38 28.89 658.56 2.097 15.185 1.000
    1 - 9 2.143 38.004 13.53 31445 5.64 31.80 673.91 2.187 14.839 1.000
    1 - 10 2.380 40.625 13.53 29127 5.86 34.33 693.33 2.278 14.423 1.000
    1 - 11 2.624 43.411 13.53 27371 6.04 36.54 718.18 2.375 13.924 1.000
    1 - 12 2.840 45.784 13.53 25991 6.20 38.48 738.11 2.455 13.548 1.000
    1 - 13 3.063 48.315 13.53 24877 6.34 40.20 762.03 2.542 13.123 1.000
    1 - 14 3.292 50.957 13.53 23962 6.46 41.73 788.78 2.633 12.678 1.000
    1 - 15 3.502 53.330 13.53 23197 6.57 43.11 812.23 2.713 12.312 1.000
    1 - 16 3.708 55.674 13.53 22545 6.66 44.36 835.95 2.792 11.962 1.000
    1 - 17 3.919 58.101 13.53 21985 6.74 45.49 861.47 2.875 11.608 1.000
    1 - 18 4.133 60.592 13.53 21498 6.82 46.52 888.40 2.959 11.256 1.000
    1 - 19 4.337 62.953 13.53 21072 6.89 47.46 913.82 3.039 10.943 1.000
    1 - 20 4.530 65.166 13.53 20694 6.95 48.33 937.43 3.114 10.668 1.000


    For me this is case closed

    Sincerely,
    Cac

  2. #2
    Don Schlesinger
    Guest

    Don Schlesinger: Sorry, can't agree

    > The most important thing to understand from
    > these tables is that full-deck indices
    > with full-deck estimation is far better than
    > half-deck indices with half-deck
    > estimation!

    Let's start with that statement. Why would you think this is true? What sense does it make to you? In what way does being more accurate with deck estimation lead to less desirable results? I can't accept that as being true. It flies in the face of logic.

    > This means that the correct
    > comparison would be A) against C) which
    > again shows ZEN outperforming HALVES.

    Do you have any explanation for the Zen-Halves comparisons of BJA3, p. 172, Table 9.21, where Halves outperforms Zen on every line?

    I'd love to accept your data, but they make no sense to me.

    Finally, I offer you the following from CVCX:

    Zen I18 s17, 5/6, das, 1-16 spread: SCORE = 36.75
    Halves I18 s17, 5/6, das, 1-16 spread: SCORE = 41.57.

    Not even close!

    > For me this is case closed

    Clearly, not for me, by a very long shot.

    Don


  3. #3
    Cacarulo
    Guest

    Cacarulo: Re: Sorry, can't agree

    > Let's start with that statement. Why would
    > you think this is true? What sense does it
    > make to you? In what way does being more
    > accurate with deck estimation lead to less
    > desirable results? I can't accept that as
    > being true. It flies in the face of logic.

    > Do you have any explanation for the
    > Zen-Halves comparisons of BJA3, p. 172,
    > Table 9.21, where Halves outperforms Zen on
    > every line?

    > I'd love to accept your data, but they make
    > no sense to me.

    > Finally, I offer you the following from
    > CVCX:

    > Zen I18 s17, 5/6, das, 1-16 spread: SCORE =
    > 36.75
    > Halves I18 s17, 5/6, das, 1-16 spread: SCORE
    > = 41.57.

    > Not even close!

    > Clearly, not for me, by a very long shot.

    None of the sims you are pointing me to are the same as the ones I posted. I think this discussion doesn't make sense if nobody else is willing to prove what I wrote so, at least for me Zen clearly outperforms Halves under the mentioned conditions.

    Sincerely,
    Cac

  4. #4
    Don Schlesinger
    Guest

    Don Schlesinger: Re: Sorry, can't agree

    > None of the sims you are pointing me to are
    > the same as the ones I posted.

    Do you think that there's something about LS or adding four indices that would so drastically turn the results? That just isn't fair to suggest.

    And CVCX was done without LS, so everything was identical, except for the four additional indices for Catch-22, which surely aren't going to magically render Zen more powerful than Halves.

    Finally, It was SBA that John used to generate the charts in BJA3, so we truly have a strange dilemma, no?

    > I think this
    > discussion doesn't make sense if nobody else
    > is willing to prove what I wrote so, at
    > least for me Zen clearly outperforms Halves
    > under the mentioned conditions.

    You're entitled to believe that, of course. I'm entitled to believe that a level-2 balanced, true-counted system isn't going to outperform the Rolls Royce of level-3 balanced, true counted systems (99+% BC) in a shoe game with a 1-16 spread. :-)

    Don


  5. #5
    JohnAuston
    Guest

    JohnAuston: Try running both sims again, . . .

    . . . but don't let either system use an Insurance index.

    That should help isolate the negative effect on Insurance, of Halves counting the nine.

  6. #6
    Cacarulo
    Guest

    Cacarulo: ZEN indices (Full-Deck, Precision = 5 sigma)

     
    // Indices generated by SBA STRATEGY GENERATOR, Version 5.52


    // NOTE: the indices are reversal for:
    // splitting 8,8 vs. T, 8,8 vs. 9, 3,3 vs. 7, and late surrender 17 vs. A up


    INSURANCE = 5; // Buy insurance if true count >= INSURANCE




    // 2 3 4 5 6 7 8 9 T A (Dealer's up cards)


    // hard standing table (stand if >= number, hit if < number)
    DEFTBL HHT
    (
    5, 2, 0, -2, -2, 99, 99, 99, 99, 99, // hard 12
    -1, -3,-99,-99,-99, 99, 99, 99, 99, 99, // hard 13
    -99,-99,-99,-99,-99, 99, 99, 99, 99, 99, // hard 14
    -99,-99,-99,-99,-99, 99, 99, 99, 6, 99, // hard 15
    -99,-99,-99,-99,-99, 99, 99, 9, 0, 99, // hard 16
    -99,-99,-99,-99,-99,-99,-99,-99,-99,-99) // hard 17

    // soft standing table (stand if >= number, hit if < number)
    DEFTBL SHT
    (
    -99,-99,-99,-99,-99,-99,-99, 99, 99, 99) // soft 18

    // hard doubling table (double if >= number)
    DEFTBL HDT
    (
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, // hard 7
    99, 99, 99, 6, 3, 99, 99, 99, 99, 99, // hard 8
    1,-99,-99,-99,-99, 6, 99, 99, 99, 99, // hard 9
    -99,-99,-99,-99,-99,-99,-99,-99, 6, 6, // hard 10
    -99,-99,-99,-99,-99,-99,-99,-99,-99, 2) // hard 11

    // soft doubling table (double if >= number)
    DEFTBL SDT
    (
    99, 99, 99,-99,-99, 99, 99, // A,2
    99, 99, 99,-99,-99, 99, 99, // A,3
    99, 99,-99,-99,-99, 99, 99, // A,4
    99, 99,-99,-99,-99, 99, 99, // A,5
    99,-99,-99,-99,-99, 99, 99, // A,6
    99,-99,-99,-99,-99, 99, 99, // A,7
    99, 99, 99, 2, 1, 99, 99, // A,8
    99, 99, 99, 99, 99, 99, 99, // A,9
    99, 99, 99, 99, 99, 99, 99) // A,T

    if (DAS) // doubling is allowed after splitting

    // splitting table for DAS (split if >= number, except reversals)
    DEFTBL SPT
    (
    -99,-99,-99,-99,-99,-99, 99, 99, 99, 99, // 2,2
    -99,-99,-99,-99,-99, 99, 99, 99, 99, 99, // 3,3
    99, 99, 99,-99,-99, 99, 99, 99, 99, 99, // 4,4
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, // 5,5
    -99,-99,-99,-99,-99, 99, 99, 99, 99, 99, // 6,6
    -99,-99,-99,-99,-99,-99, 99, 99, 99, 99, // 7,7
    -99,-99,-99,-99,-99,-99,-99, 99, 99,-99, // 8,8
    -99,-99,-99,-99,-99, 99,-99,-99, 99, 99, // 9,9
    99, 99, 99, 9, 8, 99, 99, 99, 99, 99, // T,T
    -99,-99,-99,-99,-99,-99,-99,-99,-99,-99) // A,A

    else // doubling is not allowed after splitting

    // splitting table for no DAS (split if >= number, except reversals)
    DEFTBL SPT
    (
    99, 99,-99,-99,-99,-99, 99, 99, 99, 99, // 2,2
    99, 99,-99,-99,-99, 99, 99, 99, 99, 99, // 3,3
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, // 4,4
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, // 5,5
    99,-99,-99,-99,-99, 99, 99, 99, 99, 99, // 6,6
    -99,-99,-99,-99,-99,-99, 99, 99, 99, 99, // 7,7
    -99,-99,-99,-99,-99,-99,-99, 99, 99,-99, // 8,8
    -99,-99,-99,-99,-99, 99,-99,-99, 99, 99, // 9,9
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, // T,T
    -99,-99,-99,-99,-99,-99,-99,-99,-99,-99) // A,A
    endif

  7. #7
    Cacarulo
    Guest

    Cacarulo: ZEN indices (Half-Deck, Precision = 5 sigma)

     
    // Indices generated by SBA STRATEGY GENERATOR, Version 5.52


    // NOTE: the indices are reversal for:
    // splitting 8,8 vs. T, 8,8 vs. 9, 3,3 vs. 7, and late surrender 17 vs. A up


    INSURANCE = 3; // Buy insurance if true count >= INSURANCE




    // 2 3 4 5 6 7 8 9 T A (Dealer's up cards)


    // hard standing table (stand if >= number, hit if < number)
    DEFTBL HHT
    (
    3, 1, 0, -1, -1, 99, 99, 99, 99, 99, // hard 12
    -1, -2,-99,-99,-99, 99, 99, 99, 99, 99, // hard 13
    -99,-99,-99,-99,-99, 99, 99, 99, 99, 99, // hard 14
    -99,-99,-99,-99,-99, 99, 99, 99, 3, 99, // hard 15
    -99,-99,-99,-99,-99, 99, 99, 4, 0, 99, // hard 16
    -99,-99,-99,-99,-99,-99,-99,-99,-99,-99) // hard 17

    // soft standing table (stand if >= number, hit if < number)
    DEFTBL SHT
    (
    -99,-99,-99,-99,-99,-99,-99, 99, 99, 99) // soft 18

    // hard doubling table (double if >= number)
    DEFTBL HDT
    (
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, // hard 7
    99, 99, 99, 3, 2, 99, 99, 99, 99, 99, // hard 8
    1,-99,-99,-99,-99, 3, 99, 99, 99, 99, // hard 9
    -99,-99,-99,-99,-99,-99,-99,-99, 3, 3, // hard 10
    -99,-99,-99,-99,-99,-99,-99,-99,-99, 1) // hard 11

    // soft doubling table (double if >= number)
    DEFTBL SDT
    (
    99, 99, 99,-99,-99, 99, 99, // A,2
    99, 99, 99,-99,-99, 99, 99, // A,3
    99, 99,-99,-99,-99, 99, 99, // A,4
    99, 99,-99,-99,-99, 99, 99, // A,5
    99,-99,-99,-99,-99, 99, 99, // A,6
    99,-99,-99,-99,-99, 99, 99, // A,7
    99, 99, 99, 1, 1, 99, 99, // A,8
    99, 99, 99, 99, 99, 99, 99, // A,9
    99, 99, 99, 99, 99, 99, 99) // A,T

    if (DAS) // doubling is allowed after splitting

    // splitting table for DAS (split if >= number, except reversals)
    DEFTBL SPT
    (
    -99,-99,-99,-99,-99,-99, 99, 99, 99, 99, // 2,2
    -99,-99,-99,-99,-99, 99, 99, 99, 99, 99, // 3,3
    99, 99, 99,-99,-99, 99, 99, 99, 99, 99, // 4,4
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, // 5,5
    -99,-99,-99,-99,-99, 99, 99, 99, 99, 99, // 6,6
    -99,-99,-99,-99,-99,-99, 99, 99, 99, 99, // 7,7
    -99,-99,-99,-99,-99,-99,-99, 99, 99,-99, // 8,8
    -99,-99,-99,-99,-99, 99,-99,-99, 99, 99, // 9,9
    99, 99, 99, 4, 4, 99, 99, 99, 99, 99, // T,T
    -99,-99,-99,-99,-99,-99,-99,-99,-99,-99) // A,A

    else // doubling is not allowed after splitting

    // splitting table for no DAS (split if >= number, except reversals)
    DEFTBL SPT
    (
    99, 99,-99,-99,-99,-99, 99, 99, 99, 99, // 2,2
    99, 99,-99,-99,-99, 99, 99, 99, 99, 99, // 3,3
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, // 4,4
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, // 5,5
    99,-99,-99,-99,-99, 99, 99, 99, 99, 99, // 6,6
    -99,-99,-99,-99,-99,-99, 99, 99, 99, 99, // 7,7
    -99,-99,-99,-99,-99,-99,-99, 99, 99,-99, // 8,8
    -99,-99,-99,-99,-99, 99,-99,-99, 99, 99, // 9,9
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, // T,T
    -99,-99,-99,-99,-99,-99,-99,-99,-99,-99) // A,A
    endif

  8. #8
    Cacarulo
    Guest

    Cacarulo: HALVES indices (Full-Deck, Precision = 5 sigma)

     
    / Indices generated by SBA STRATEGY GENERATOR, Version 5.52


    // NOTE: the indices are reversal for:
    // splitting 8,8 vs. T, 8,8 vs. 9, 3,3 vs. 7, and late surrender 17 vs. A up


    INSURANCE = 7; // Buy insurance if true count >= INSURANCE




    // 2 3 4 5 6 7 8 9 T A (Dealer's up cards)


    // hard standing table (stand if >= number, hit if < number)
    DEFTBL HHT
    (
    7, 3, 0, -3, -2, 99, 99, 99, 99, 99, // hard 12
    -2, -4,-99,-99,-99, 99, 99, 99, 99, 99, // hard 13
    -99,-99,-99,-99,-99, 99, 99, 99, 99, 99, // hard 14
    -99,-99,-99,-99,-99, 99, 99, 99, 7, 99, // hard 15
    -99,-99,-99,-99,-99, 99, 99, 9, 0, 99, // hard 16
    -99,-99,-99,-99,-99,-99,-99,-99,-99,-99) // hard 17

    // soft standing table (stand if >= number, hit if < number)
    DEFTBL SHT
    (
    -99,-99,-99,-99,-99,-99,-99, 99, 99, 99) // soft 18

    // hard doubling table (double if >= number)
    DEFTBL HDT
    (
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, // hard 7
    99, 99, 99, 8, 4, 99, 99, 99, 99, 99, // hard 8
    2,-99,-99,-99,-99, 7, 99, 99, 99, 99, // hard 9
    -99,-99,-99,-99,-99,-99,-99,-99, 7, 7, // hard 10
    -99,-99,-99,-99,-99,-99,-99,-99,-99, 2) // hard 11

    // soft doubling table (double if >= number)
    DEFTBL SDT
    (
    99, 99, 99,-99,-99, 99, 99, // A,2
    99, 99, 99,-99,-99, 99, 99, // A,3
    99, 99,-99,-99,-99, 99, 99, // A,4
    99, 99,-99,-99,-99, 99, 99, // A,5
    99,-99,-99,-99,-99, 99, 99, // A,6
    99,-99,-99,-99,-99, 99, 99, // A,7
    99, 99, 99, 3, 1, 99, 99, // A,8
    99, 99, 99, 99, 99, 99, 99, // A,9
    99, 99, 99, 99, 99, 99, 99) // A,T

    if (DAS) // doubling is allowed after splitting

    // splitting table for DAS (split if >= number, except reversals)
    DEFTBL SPT
    (
    -99,-99,-99,-99,-99,-99, 99, 99, 99, 99, // 2,2
    -99,-99,-99,-99,-99, 99, 99, 99, 99, 99, // 3,3
    99, 99, 99,-99,-99, 99, 99, 99, 99, 99, // 4,4
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, // 5,5
    -99,-99,-99,-99,-99, 99, 99, 99, 99, 99, // 6,6
    -99,-99,-99,-99,-99,-99, 99, 99, 99, 99, // 7,7
    -99,-99,-99,-99,-99,-99,-99, 99, 99,-99, // 8,8
    -99,-99,-99,-99,-99, 99,-99,-99, 99, 99, // 9,9
    99, 99, 99, 10, 9, 99, 99, 99, 99, 99, // T,T
    -99,-99,-99,-99,-99,-99,-99,-99,-99,-99) // A,A

    else // doubling is not allowed after splitting

    // splitting table for no DAS (split if >= number, except reversals)
    DEFTBL SPT
    (
    99, 99,-99,-99,-99,-99, 99, 99, 99, 99, // 2,2
    99, 99,-99,-99,-99, 99, 99, 99, 99, 99, // 3,3
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, // 4,4
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, // 5,5
    99,-99,-99,-99,-99, 99, 99, 99, 99, 99, // 6,6
    -99,-99,-99,-99,-99,-99, 99, 99, 99, 99, // 7,7
    -99,-99,-99,-99,-99,-99,-99, 99, 99,-99, // 8,8
    -99,-99,-99,-99,-99, 99,-99,-99, 99, 99, // 9,9
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, // T,T
    -99,-99,-99,-99,-99,-99,-99,-99,-99,-99) // A,A
    endif

  9. #9
    Cacarulo
    Guest

    Cacarulo: HALVES indices (Half-Deck, Precision = 5 sigma)

     
    // Indices generated by SBA STRATEGY GENERATOR, Version 5.52


    // NOTE: the indices are reversal for:
    // splitting 8,8 vs. T, 8,8 vs. 9, 3,3 vs. 7, and late surrender 17 vs. A up


    INSURANCE = 3; // Buy insurance if true count >= INSURANCE




    // 2 3 4 5 6 7 8 9 T A (Dealer's up cards)


    // hard standing table (stand if >= number, hit if < number)
    DEFTBL HHT
    (
    4, 2, 0, -2, -1, 99, 99, 99, 99, 99, // hard 12
    -1, -2,-99,-99,-99, 99, 99, 99, 99, 99, // hard 13
    -99,-99,-99,-99,-99, 99, 99, 99, 99, 99, // hard 14
    -99,-99,-99,-99,-99, 99, 99, 99, 4, 99, // hard 15
    -99,-99,-99,-99,-99, 99, 99, 5, 0, 99, // hard 16
    -99,-99,-99,-99,-99,-99,-99,-99,-99,-99) // hard 17

    // soft standing table (stand if >= number, hit if < number)
    DEFTBL SHT
    (
    -99,-99,-99,-99,-99,-99,-99, 99, 99, 99) // soft 18

    // hard doubling table (double if >= number)
    DEFTBL HDT
    (
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, // hard 7
    99, 99, 99, 4, 2, 99, 99, 99, 99, 99, // hard 8
    1,-99,-99,-99,-99, 4, 99, 99, 99, 99, // hard 9
    -99,-99,-99,-99,-99,-99,-99,-99, 4, 4, // hard 10
    -99,-99,-99,-99,-99,-99,-99,-99,-99, 1) // hard 11

    // soft doubling table (double if >= number)
    DEFTBL SDT
    (
    99, 99, 99,-99,-99, 99, 99, // A,2
    99, 99, 99,-99,-99, 99, 99, // A,3
    99, 99,-99,-99,-99, 99, 99, // A,4
    99, 99,-99,-99,-99, 99, 99, // A,5
    99,-99,-99,-99,-99, 99, 99, // A,6
    99,-99,-99,-99,-99, 99, 99, // A,7
    99, 99, 99, 1, 1, 99, 99, // A,8
    99, 99, 99, 99, 99, 99, 99, // A,9
    99, 99, 99, 99, 99, 99, 99) // A,T

    if (DAS) // doubling is allowed after splitting

    // splitting table for DAS (split if >= number, except reversals)
    DEFTBL SPT
    (
    -99,-99,-99,-99,-99,-99, 99, 99, 99, 99, // 2,2
    -99,-99,-99,-99,-99, 99, 99, 99, 99, 99, // 3,3
    99, 99, 99,-99,-99, 99, 99, 99, 99, 99, // 4,4
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, // 5,5
    -99,-99,-99,-99,-99, 99, 99, 99, 99, 99, // 6,6
    -99,-99,-99,-99,-99,-99, 99, 99, 99, 99, // 7,7
    -99,-99,-99,-99,-99,-99,-99, 99, 99,-99, // 8,8
    -99,-99,-99,-99,-99, 99,-99,-99, 99, 99, // 9,9
    99, 99, 99, 5, 5, 99, 99, 99, 99, 99, // T,T
    -99,-99,-99,-99,-99,-99,-99,-99,-99,-99) // A,A

    else // doubling is not allowed after splitting

    // splitting table for no DAS (split if >= number, except reversals)
    DEFTBL SPT
    (
    99, 99,-99,-99,-99,-99, 99, 99, 99, 99, // 2,2
    99, 99,-99,-99,-99, 99, 99, 99, 99, 99, // 3,3
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, // 4,4
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, // 5,5
    99,-99,-99,-99,-99, 99, 99, 99, 99, 99, // 6,6
    -99,-99,-99,-99,-99,-99, 99, 99, 99, 99, // 7,7
    -99,-99,-99,-99,-99,-99,-99, 99, 99,-99, // 8,8
    -99,-99,-99,-99,-99, 99,-99,-99, 99, 99, // 9,9
    99, 99, 99, 99, 99, 99, 99, 99, 99, 99, // T,T
    -99,-99,-99,-99,-99,-99,-99,-99,-99,-99) // A,A
    endif

  10. #10
    Cacarulo
    Guest

    Cacarulo: ZEN Report I

     
    * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
    * S T A T I S T I C A L B L A C K J A C K A N A L Y Z E R *
    * Version 5.52, 1995-2003 *
    * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *


    ************************************************** **************************

    Simulation started on (MM/DD/YY): 03-15-2005 at 23:56:59
    Simulation finished on (MM/DD/YY): 03-16-2005 at 2:41:15
    Random seed = 1234567890


    * * * * * * * * * * * * * * * * * * *
    * R U L E S & C O N D I T I O N S *
    * * * * * * * * * * * * * * * * * * *

    6 decks

    Shufflepoint 260 cards, (83.33% penetration)

    Face up game

    Head on game

    System used is ZEN with indices table zen_c22

    SBA floors when calculating the true count
    Remaining decks estimated exactly for true count conversion

    American rules - hole card game

    Surrender is not allowed

    Dealer stands on all 17

    Doubling is allowed on any two cards

    Doubling is allowed after splitting

    Hand can be split 3 times, up to 4 hands

    No resplit of aces

    Only one card to split aces

    Different tens can be split

    Insurance is 1 half of a bet

    Predefined variables:
    INSURANCE = 5 Buy insurance if true count >= INSURANCE
    H7710 = 99 Hit 7,7 versus dealer's 10 if true count < H7710

    No user defined variables


    No leaving the shoe at any count

    Betting units are: 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0

    For corresponding AC: -1, 0, 1, 2, 3, 4, 5

    Num. of hands played: 1, 1, 1, 1, 1, 1, 1

    Player's bankroll is 100

    Aim bankroll is 200


    ************************************************** **************************


    * * * * * * * * * * * * * * * * * * * *
    * S I M U L A T I O N R E S U L T S *
    * * * * * * * * * * * * * * * * * * * *

    ----------------------------------------------------------------------------

    COUNT STATISTICS (PRIMARY):


    TC PERCEN AC PERCEN ST. ERR. IBA ST. ERR. SDROUND ACTION

    -25 0.0466 -25 0.04656 0.000022 -10.502 0.0581 1.2540 1.2278
    -24 0.0189 -24 0.01891 0.000014 -8.709 0.0901 1.2387 1.2129
    -23 0.0249 -23 0.02488 0.000016 -7.990 0.0783 1.2349 1.2092
    -22 0.0331 -22 0.03309 0.000018 -7.765 0.0676 1.2302 1.2054
    -21 0.0460 -21 0.04600 0.000021 -7.203 0.0572 1.2262 1.2011
    -20 0.0618 -20 0.06179 0.000025 -6.810 0.0491 1.2216 1.1969
    -19 0.0804 -19 0.08037 0.000028 -6.350 0.0430 1.2179 1.1931
    -18 0.1148 -18 0.11483 0.000034 -5.873 0.0358 1.2135 1.1890
    -17 0.1363 -17 0.13633 0.000037 -5.441 0.0328 1.2097 1.1853
    -16 0.1887 -16 0.18870 0.000043 -5.057 0.0278 1.2058 1.1818
    -15 0.2461 -15 0.24612 0.000050 -4.669 0.0242 1.2020 1.1781
    -14 0.2971 -14 0.29715 0.000054 -4.319 0.0220 1.1982 1.1746
    -13 0.4388 -13 0.43882 0.000066 -3.978 0.0180 1.1943 1.1709
    -12 0.5539 -12 0.55392 0.000074 -3.602 0.0160 1.1906 1.1675
    -11 0.7121 -11 0.71214 0.000084 -3.274 0.0141 1.1867 1.1639
    -10 0.9321 -10 0.93212 0.000096 -2.970 0.0123 1.1832 1.1607
    -9 1.1994 -9 1.19945 0.000109 -2.670 0.0108 1.1796 1.1573
    -8 1.6172 -8 1.61722 0.000126 -2.365 0.0092 1.1760 1.1541
    -7 2.0978 -7 2.09781 0.000143 -2.088 0.0081 1.1726 1.1509
    -6 2.8074 -6 2.80744 0.000165 -1.813 0.0070 1.1693 1.1477
    -5 3.6921 -5 3.69207 0.000189 -1.529 0.0061 1.1661 1.1446
    -4 5.0943 -4 5.09433 0.000220 -1.275 0.0052 1.1632 1.1416
    -3 6.8610 -3 6.86096 0.000253 -1.008 0.0044 1.1607 1.1386
    -2 9.6273 -2 9.62732 0.000295 -0.751 0.0037 1.1581 1.1358
    -1 11.0609 -1 11.06088 0.000314 -0.504 0.0035 1.1560 1.1334
    0 16.3251 0 16.32507 0.000370 -0.241 0.0029 1.1563 1.1328
    1 9.1983 1 9.19830 0.000289 0.102 0.0038 1.1572 1.1327
    2 6.6722 2 6.67222 0.000250 0.409 0.0045 1.1585 1.1334
    3 4.8331 3 4.83307 0.000214 0.728 0.0053 1.1557 1.1316
    4 3.6600 4 3.65996 0.000188 1.029 0.0060 1.1551 1.1372
    5 2.7012 5 2.70118 0.000162 1.347 0.0071 1.1590 1.1552
    6 2.0596 6 2.05961 0.000142 1.689 0.0081 1.1625 1.1713
    7 1.5337 7 1.53370 0.000123 2.049 0.0094 1.1588 1.1737
    8 1.2036 8 1.20361 0.000109 2.399 0.0105 1.1563 1.1744
    9 0.8957 9 0.89573 0.000094 2.785 0.0123 1.1637 1.1829
    10 0.6986 10 0.69862 0.000083 3.141 0.0141 1.1743 1.1924
    11 0.5212 11 0.52121 0.000072 3.491 0.0163 1.1791 1.1953
    12 0.3899 12 0.38992 0.000062 3.887 0.0189 1.1801 1.1956
    13 0.3376 13 0.33757 0.000058 4.300 0.0203 1.1786 1.1943
    14 0.2426 14 0.24260 0.000049 4.640 0.0239 1.1761 1.1926
    15 0.1779 15 0.17789 0.000042 4.962 0.0278 1.1733 1.1905
    16 0.1391 16 0.13906 0.000037 5.283 0.0314 1.1705 1.1888
    17 0.1114 17 0.11140 0.000033 5.699 0.0350 1.1678 1.1869
    18 0.0799 18 0.07990 0.000028 5.976 0.0412 1.1654 1.1850
    19 0.0588 19 0.05880 0.000024 6.383 0.0480 1.1631 1.1837
    20 0.0474 20 0.04736 0.000022 6.761 0.0533 1.1603 1.1818
    21 0.0325 21 0.03249 0.000018 6.990 0.0642 1.1574 1.1799
    22 0.0251 22 0.02505 0.000016 7.336 0.0730 1.1550 1.1780
    23 0.0183 23 0.01832 0.000014 7.566 0.0851 1.1517 1.1760
    24 0.0135 24 0.01353 0.000012 7.909 0.0988 1.1496 1.1749
    25 0.0346 25 0.03462 0.000019 8.903 0.0614 1.1423 1.1700

    ----------------------------------------------------------------------------

    PRIMARY STATISTICS:


    Initial bet advantage (IBA):-0.29218%, St. Err. 0.001161%

    Total bets advantage (TBA): -0.25579%

    SCORE: 0.00

    Risk of Ruin: 100%

    Estim. payoff per 100,000 rounds played is -292.18, with estim. std. 367.24

    Average st. dev. per round: 1.16131

    Av. std. per round per unit: 1.16131

    Average bet per round: 1.00000

    Average bet total: 1.14225

    Insurance contribution: 0.02377%
    Insurance contrib. to TBA: 0.02186%

    Number of sessions won: 531995
    Number of sessions lost: 827616
    Total number of sessions: 1359611
    Percentage of sessions won: 39.1285%, St. Err. 0.04185%
    Surplus bank: 344210.5

    Number of shoes played: 208646487

    Number of rounds played: 10000000023

    ----------------------------------------------------------------------------

    SECONDARY STATISTICS:


    AC BLJACK PUSH HDOUBL SDOUBL SPLIT SURREN INSUR INSADV ACDIST

    -10 3.712 9.214 10.472 2.025 3.076 0.000 0.000 0.000 0.947
    -9 3.816 9.204 10.232 1.989 3.034 0.000 0.000 0.000 1.215
    -8 3.921 9.207 10.000 1.955 2.991 0.000 0.000 0.000 1.634
    -7 4.026 9.201 9.768 1.923 2.950 0.000 0.000 0.000 2.114
    -6 4.136 9.198 9.540 1.890 2.912 0.000 0.000 0.000 2.821
    -5 4.245 9.189 9.320 1.856 2.872 0.000 0.000 0.000 3.700
    -4 4.355 9.171 9.104 1.822 2.833 0.000 0.000 0.000 5.091
    -3 4.465 9.120 8.895 1.789 2.793 0.000 0.000 0.000 6.839
    -2 4.579 9.086 8.697 1.756 2.756 0.000 0.000 0.000 9.573
    -1 4.680 9.048 8.534 1.725 2.721 0.000 0.000 0.000 10.976
    0 4.783 8.944 8.518 1.715 2.688 0.000 0.000 0.000 16.190
    1 4.906 8.886 8.490 1.783 2.648 0.000 0.002 -0.666 9.122
    2 5.019 8.892 8.550 1.814 2.614 0.000 0.019 0.445 6.620
    3 5.137 8.922 8.389 1.780 2.580 0.000 0.171 0.630 4.788
    4 5.284 8.999 8.453 1.755 2.561 0.000 1.431 0.779 3.644
    5 5.483 9.188 8.949 1.745 2.566 0.000 4.530 1.205 2.732
    6 5.670 9.332 9.547 1.730 2.563 0.000 7.059 2.094 2.112
    7 5.821 9.336 9.468 1.699 2.536 0.000 7.999 3.283 1.576
    8 5.954 9.349 9.218 1.660 2.726 0.000 8.360 4.533 1.237
    9 6.084 9.312 8.901 1.612 3.721 0.000 8.593 5.874 0.928
    10 6.211 9.294 8.566 1.555 4.848 0.000 8.682 7.441 0.729


    InsTC INSUR INSADV ST. ERR.

    5 7.322 0.650 0.016
    6 7.335 2.127 0.018
    7 7.336 3.614 0.021
    8 7.348 5.154 0.024
    9 7.347 6.471 0.028
    10 7.358 8.022 0.031



    CUMULATIVE FREQUENCY OF OCCURRENCE:

    Frequency of blackjack: 4.744%

    Frequency of pushing: 9.030%

    Frequency of hard doubling: 8.824%

    Frequency of soft doubling: 1.770%

    Frequency of splitting: 2.894%

    Frequency of insurance: 0.859%
    Insurance advantage: 5.538%



    CORRELATION COEFFICIENTS:

    AC Correlation Coef.

    -10 N/A
    -9 N/A
    -8 N/A
    -7 N/A
    -6 N/A
    -5 N/A
    -4 N/A
    -3 N/A
    -2 N/A
    -1 N/A
    0 N/A
    1 N/A
    2 N/A
    3 N/A
    4 N/A
    5 N/A
    6 N/A
    7 N/A
    8 N/A
    9 N/A
    10 N/A


    D E A L E R'S S T A T I S T I C S

    Up card 17 18 19 20 21 BJ Bust

    2 13.9722 13.4447 13.0049 12.4026 11.8374 -- 35.3382
    3 13.4399 13.0601 12.5250 12.0793 11.4928 -- 37.4030
    4 13.0673 12.4168 12.1309 11.6467 11.1853 -- 39.5530
    5 12.1974 12.2546 11.7663 11.1815 10.7934 -- 41.8068
    6 16.5780 10.6302 10.6511 10.1594 9.7289 -- 42.2524
    7 36.9021 13.8012 7.8510 7.8724 7.3841 -- 26.1893
    8 12.8964 35.9742 12.8784 6.9287 6.9519 -- 24.3705
    9 12.0373 11.7373 35.1630 12.0416 6.0934 -- 22.9274
    10 11.1970 11.1724 11.1961 33.9776 3.4856 7.7165 21.2547
    ace 13.0124 13.0915 13.0671 13.0919 5.3540 30.8382 11.5449


    Distribution of the final number of cards in Dealer's hand:

    Cards: 2 3 4 5 6 7 8 9 10
    Freq.: 45.5095 36.3555 14.8215 2.9449 0.3424 0.0251 0.0012 0.0000 0.0000


    Distribution of cards drawn to Dealer's initial two cards:

    Card: 2 3 4 5 6 7 8 9 10 ace
    Freq.: 7.6415 7.6478 7.6478 7.6548 7.6652 7.6934 7.7054 7.7103 30.9221 7.7116

Page 1 of 4 123 ... LastLast

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •  

About Blackjack: The Forum

BJTF is an advantage player site based on the principles of comity. That is, civil and considerate behavior for the mutual benefit of all involved. The goal of advantage play is the legal extraction of funds from gaming establishments by gaining a mathematic advantage and developing the skills required to use that advantage. To maximize our success, it is important to understand that we are all on the same side. Personal conflicts simply get in the way of our goals.