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Thread: Composition dependent indices for Insurance (Hi-Lo)

  1. #1


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    Composition dependent indices for Insurance (Hi-Lo)

    Here are some C-D indices for Insurance.
    In 2008 I had published a work similar to this, although at that time I used an algebraic formula and insurance EORs.
    On this occasion the indices were calculated through combinatorial analysis.
    The indices are floored and the division by remaining decks is exact.
    BTW, all the indices were verified by simulation.

    Enjoy!

    Sincerely,
    Cac

    Code:
    ---------------------------------------------------------------------------------------------------------------------
    
    T = Ten
    A = Ace
    Z = 7,8,9
    L = 2,3,4,5,6
    
    1) 1D, Hi-Lo
    
    +----------+-------+-----+----------+----------+----------+
    |   Play   | Decks |  CR | TC Index | TC Index | TC Index |
    +----------+-------+-----+----------+----------+----------+
    | Generic  |   1   |  20 |      2   |    1.4   |   1.36   |
    +----------+-------+-----+----------+----------+----------+
    |    AA    |   1   |  20 |     -3   |   -2.5   |  -2.42   |
    +----------+-------+-----+----------+----------+----------+
    |    AT    |   1   |  20 |      1   |    1.1   |   1.18   |
    +----------+-------+-----+----------+----------+----------+
    |    AL    |   1   |  20 |      0   |    0.0   |   0.00   |
    +----------+-------+-----+----------+----------+----------+
    |    AZ    |   1   |  20 |      0   |   -1.4   |  -1.37   |
    +----------+-------+-----+----------+----------+----------+
    |    TT    |   1   |  20 |      3   |    3.0   |   3.05   |
    +----------+-------+-----+----------+----------+----------+
    |    TL    |   1   |  20 |      2   |    2.4   |   2.41   |
    +----------+-------+-----+----------+----------+----------+
    |    TZ    |   1   |  20 |      1   |    1.3   |   1.33   |
    +----------+-------+-----+----------+----------+----------+
    |    LL    |   1   |  20 |      2   |    1.9   |   1.92   |
    +----------+-------+-----+----------+----------+----------+
    |    LZ    |   1   |  20 |      1   |    1.1   |   1.10   |
    +----------+-------+-----+----------+----------+----------+
    |    ZZ    |   1   |  20 |      0   |    0.0   |   0.00   |
    +----------+-------+-----+----------+----------+----------+
    
    2) 6D, Hi-Lo
    
    +----------+-------+-----+----------+----------+----------+
    |   Play   | Decks |  CR | TC Index | TC Index | TC Index |
    +----------+-------+-----+----------+----------+----------+
    | Generic  |   6   |  78 |      3   |    3.0   |   3.03   |
    +----------+-------+-----+----------+----------+----------+
    |    AA    |   6   |  78 |      2   |    2.4   |   2.39   |
    +----------+-------+-----+----------+----------+----------+
    |    AT    |   6   |  78 |      3   |    2.8   |   2.83   |
    +----------+-------+-----+----------+----------+----------+
    |    AL    |   6   |  78 |      3   |    2.7   |   2.75   |
    +----------+-------+-----+----------+----------+----------+
    |    AZ    |   6   |  78 |      3   |    2.6   |   2.58   |
    +----------+-------+-----+----------+----------+----------+
    |    TT    |   6   |  78 |      3   |    3.3   |   3.29   |
    +----------+-------+-----+----------+----------+----------+
    |    TL    |   6   |  78 |      3   |    3.2   |   3.19   |
    +----------+-------+-----+----------+----------+----------+
    |    TZ    |   6   |  78 |      3   |    3.0   |   3.02   |
    +----------+-------+-----+----------+----------+----------+
    |    LL    |   6   |  78 |      3   |    3.1   |   3.10   |
    +----------+-------+-----+----------+----------+----------+
    |    LZ    |   6   |  78 |      3   |    2.9   |   2.93   |
    +----------+-------+-----+----------+----------+----------+
    |    ZZ    |   6   |  78 |      3   |    2.8   |   2.77   |
    +----------+-------+-----+----------+----------+----------+

  2. #2


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    Here is what I came up with in order to compute a "mean" true count index. The example I use is single deck insurance TC ins index for a hand of A-A.

    This is my insurance data for A-A, single deck. (I display points where ins EV >= 0. At point where 48 cards remain, ins EV=0.)

    Code:
    Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
    Decks: 1
    Insurance Data (considers hand comp)
    No subgroup (removals) are defined
    
    **** Player hand: 1-1 ****
    Cards   RC      TC ref
    
    48      -3      -3.25
    47      -2      -2.21
    46      -1      -1.13
    45      -2      -2.31
    41      -1      -1.27
    21      0       0.00
    3       1       17.33
    2       0       0.00
    1       1       52.00
    It's theoretically possible to take insurance with 1 card remaining so the mean is at mid-shoe. Since 3 aces are accounted for given hand of A-A versus A, there are 49 cards remaining to consider. If no cards are specifically removed mid-shoe is 26 cards. For 3 aces specifically removed mid-shoe is (theoretically) 24.5 cards. To get data for 24.5 cards data from 24 and 25 cards is averaged.

    From the data ins EV >= 0 (p[10] >= 1/3) when RC=-1 with 24 or 25 cards remaining. ins EV < 0 (p[10] < 1/3) when RC=-2 with 24 or 25 cards remaining.

    Code:
    Cards   RC         p[10]
    
    25      -1         .33638
    24      -1         .33551
    
    25      -2         .31791
    24      -2         .31627
    
    24.5    -1         .335945
    24.5    -2         .31709
    
    24.5    -1.1385    1/3
    
    TC = 52*(-1.1385)/24.5 = -2.416
    I am not claiming this is exactly right but it seems reasonable and is fairly simple. Also it would be possible to adapt the TC index to differing shoe cut card positions by using a mean halfway to the cut card.

    Any thoughts?

    k_c

  3. #3


    Did you find this post helpful? Yes | No
    Quote Originally Posted by k_c View Post
    Here is what I came up with in order to compute a "mean" true count index. The example I use is single deck insurance TC ins index for a hand of A-A.

    This is my insurance data for A-A, single deck. (I display points where ins EV >= 0. At point where 48 cards remain, ins EV=0.)

    Code:
    Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
    Decks: 1
    Insurance Data (considers hand comp)
    No subgroup (removals) are defined
    
    **** Player hand: 1-1 ****
    Cards   RC      TC ref
    
    48      -3      -3.25
    47      -2      -2.21
    46      -1      -1.13
    45      -2      -2.31
    41      -1      -1.27
    21      0       0.00
    3       1       17.33
    2       0       0.00
    1       1       52.00
    It's theoretically possible to take insurance with 1 card remaining so the mean is at mid-shoe. Since 3 aces are accounted for given hand of A-A versus A, there are 49 cards remaining to consider. If no cards are specifically removed mid-shoe is 26 cards. For 3 aces specifically removed mid-shoe is (theoretically) 24.5 cards. To get data for 24.5 cards data from 24 and 25 cards is averaged.

    From the data ins EV >= 0 (p[10] >= 1/3) when RC=-1 with 24 or 25 cards remaining. ins EV < 0 (p[10] < 1/3) when RC=-2 with 24 or 25 cards remaining.

    Code:
    Cards   RC         p[10]
    
    25      -1         .33638
    24      -1         .33551
    
    25      -2         .31791
    24      -2         .31627
    
    24.5    -1         .335945
    24.5    -2         .31709
    
    24.5    -1.1385    1/3
    
    TC = 52*(-1.1385)/24.5 = -2.416
    I am not claiming this is exactly right but it seems reasonable and is fairly simple. Also it would be possible to adapt the TC index to differing shoe cut card positions by using a mean halfway to the cut card.

    Any thoughts?

    k_c
    The exact number would be -2.418605 (-2/43) which is pretty close to what you got: -2.416
    You would have to try different penetrations, since with 21 cards remaining or less the index is always the same: -2.418605
    If 22 cards remain, the index changes to -2.476190 (-2/42)
    And with 46 cards remaining it is -2.212766 (-2/47)

    Sincerely,
    Cac

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