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Thread: Double Down on Soft 12

  1. #51


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    Quote Originally Posted by Cacarulo View Post
    I'll give you an idea of ??what I do. Maybe this can help you.
    Let's use as an example a deck of 52 cards and the unbalanced count of tens (1 1 1 1 1 1 1 1 1 -2).
    1) Remove an ace from the pack (which is the ace the dealer receives)

    The other array is used to know the frequency of each TC.
    Cac
    I store my data in a list.

    If I construct a list with a specific pen and rc for the insurance count it will contain either 0 or 1 entries (elems) depending upon rc. If elems = 0, probRC = 0.

    This is what I presently do:
    Code:
    list = new subsetList (inputCount, decks, pen, rc, specificRem);
    list->getProbRC(rc, probRC, pRank);
    long elems = list->elems;
    delete list;
    list = NULL;
    What I used to do was construct a list with all rc possible to use. For more complicated counts too much data crashes program.
    For the insurance count where pen = 26 there are 17 entries in the list and sum of probRC of each entry = 1. For any count sum of probRC of entries in list = 1 regardless of number of entries.

    What I could do is something like this:
    Code:
    list = new subsetList (inputCount, decks, pen, specificRem);
    
    for (rc = minValue; rc <= maxValue; ++rc)
         list->getProbRC(rc, probRC, pRank);
    
    long elems = list->elems;
    I can relate to probRC, but probTC? (relative to simple insurance count)

    k_c

  2. #52


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    Quote Originally Posted by Cacarulo View Post
    Going back to the s12v3 topic (S17 and H17), there are some differences like the ones I already mentioned and in which I see
    that instead of looking for where the problem may be, the discrepancy focuses on discussing the methodology I use.
    I do not intend to enter into this discussion, but instead I can offer my results based on simulation and combinatorial analysis.
    Please don't construe my questions as an attack on your methodology. My intent was not to question the validity of your methods (and those of others), but rather to ask questions about these methods in an effort to understand them better. With a better understanding of what we all do, a more focused investigation of the source of any differences can be made.

    I appreciate that we all have worked hard on our software over many years and that we do not necessarily want to divulge the details of algorithms that we have created and tested over the course of that time. I also appreciate the details which have been posted nonetheless. There's a lot here to consider and I will be reading each post carefully over the course of the next few days.
    Last edited by Gronbog; 10-03-2022 at 10:01 AM.

  3. #53


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    Quote Originally Posted by Cacarulo View Post
    The indices are fine, but there is a little detail that was overlooked in their generation. For example:
    AAv6 assumes that two aces and a six were removed from the pack and this implies that when you receive that hand you are NOT able to split the pair of aces.
    What would have to be done is to remove three aces and a six to make the calculation since the soft-12 appears after splitting the first pair.
    In the mean time, until I can find time to digest what has been posted with respect to methodology, it might be reasonable to run this experiment.

    Rather than removing an ace, I think the equivalent adjustment for my software would be to discard and count an ace at the start of each shoe (after the burn card). This would place all instances of A,A vs ? into a context where at least three aces have been observed and counted just they would be when playing A,A after splitting.

    Does this sound reasonable?

  4. #54


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    Quote Originally Posted by k_c View Post
    I store my data in a list.

    If I construct a list with a specific pen and rc for the insurance count it will contain either 0 or 1 entries (elems) depending upon rc. If elems = 0, probRC = 0.

    This is what I presently do:
    Code:
    list = new subsetList (inputCount, decks, pen, rc, specificRem);
    list->getProbRC(rc, probRC, pRank);
    long elems = list->elems;
    delete list;
    list = NULL;
    What I used to do was construct a list with all rc possible to use. For more complicated counts too much data crashes program.
    For the insurance count where pen = 26 there are 17 entries in the list and sum of probRC of each entry = 1. For any count sum of probRC of entries in list = 1 regardless of number of entries.

    What I could do is something like this:
    Code:
    list = new subsetList (inputCount, decks, pen, specificRem);
    
    for (rc = minValue; rc <= maxValue; ++rc)
         list->getProbRC(rc, probRC, pRank);
    
    long elems = list->elems;
    I can relate to probRC, but probTC? (relative to simple insurance count)

    k_c
    I don't understand where you're stuck. You have all the data and algorithms correct. The only thing left for you is to calculate the TC as TC = floor (RC / Cards_Left * 52).
    Here it is worth a clarification: the previous formula calculates the exact TC where the remaining decks (Cards_Left / 52) are calculated exactly without rounding or truncating.
    In my program I can calculate the remaining decks in various ways.

    Perhaps viewing the following RC distributions as a function of Cards_Left will help:

    1) HiLo

    Code:
     51 |  -1 
     50 |  -2  -1   0 
     49 |  -3  -2  -1   0   1 
     48 |  -4  -3  -2  -1   0   1   2 
     47 |  -5  -4  -3  -2  -1   0   1   2   3 
     46 |  -6  -5  -4  -3  -2  -1   0   1   2   3   4 
     45 |  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5 
     44 |  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6 
     43 |  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7 
     42 | -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8 
     41 | -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9 
     40 | -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10 
     39 | -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11 
     38 | -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12 
     37 | -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13 
     36 | -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14 
     35 | -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15 
     34 | -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16 
     33 | -19 -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17 
     32 | -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18 
     31 | -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19 
     30 | -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19 
     29 | -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19 
     28 | -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19 
     27 | -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19 
     26 | -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19 
     25 | -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19 
     24 | -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19 
     23 | -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19 
     22 | -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19 
     21 | -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19 
     20 | -20 -19 -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19 
     19 | -19 -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18  19 
     18 | -18 -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17  18 
     17 | -17 -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16  17 
     16 | -16 -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15  16 
     15 | -15 -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15 
     14 | -14 -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13  14 
     13 | -13 -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12  13 
     12 | -12 -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11  12 
     11 | -11 -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10  11 
     10 | -10  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9  10 
      9 |  -9  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8   9 
      8 |  -8  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7   8 
      7 |  -7  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6   7 
      6 |  -6  -5  -4  -3  -2  -1   0   1   2   3   4   5   6 
      5 |  -5  -4  -3  -2  -1   0   1   2   3   4   5 
      4 |  -4  -3  -2  -1   0   1   2   3   4 
      3 |  -3  -2  -1   0   1   2   3
      2 |  -2  -1   0   1   2 
      1 |  -1   0   1
    2) UnbalancedTen

    Code:
     51 |  -3 
     50 |  -5  -2 
     49 |  -7  -4  -1 
     48 |  -9  -6  -3   0 
     47 | -11  -8  -5  -2   1 
     46 | -13 -10  -7  -4  -1   2 
     45 | -15 -12  -9  -6  -3   0   3 
     44 | -17 -14 -11  -8  -5  -2   1   4 
     43 | -19 -16 -13 -10  -7  -4  -1   2   5 
     42 | -21 -18 -15 -12  -9  -6  -3   0   3   6 
     41 | -23 -20 -17 -14 -11  -8  -5  -2   1   4   7 
     40 | -25 -22 -19 -16 -13 -10  -7  -4  -1   2   5   8 
     39 | -27 -24 -21 -18 -15 -12  -9  -6  -3   0   3   6   9 
     38 | -29 -26 -23 -20 -17 -14 -11  -8  -5  -2   1   4   7  10 
     37 | -31 -28 -25 -22 -19 -16 -13 -10  -7  -4  -1   2   5   8  11 
     36 | -33 -30 -27 -24 -21 -18 -15 -12  -9  -6  -3   0   3   6   9  12 
     35 | -35 -32 -29 -26 -23 -20 -17 -14 -11  -8  -5  -2   1   4   7  10  13 
     34 | -34 -31 -28 -25 -22 -19 -16 -13 -10  -7  -4  -1   2   5   8  11  14 
     33 | -33 -30 -27 -24 -21 -18 -15 -12  -9  -6  -3   0   3   6   9  12  15 
     32 | -32 -29 -26 -23 -20 -17 -14 -11  -8  -5  -2   1   4   7  10  13  16 
     31 | -31 -28 -25 -22 -19 -16 -13 -10  -7  -4  -1   2   5   8  11  14  17 
     30 | -30 -27 -24 -21 -18 -15 -12  -9  -6  -3   0   3   6   9  12  15  18 
     29 | -29 -26 -23 -20 -17 -14 -11  -8  -5  -2   1   4   7  10  13  16  19 
     28 | -28 -25 -22 -19 -16 -13 -10  -7  -4  -1   2   5   8  11  14  17  20 
     27 | -27 -24 -21 -18 -15 -12  -9  -6  -3   0   3   6   9  12  15  18  21 
     26 | -26 -23 -20 -17 -14 -11  -8  -5  -2   1   4   7  10  13  16  19  22 
     25 | -25 -22 -19 -16 -13 -10  -7  -4  -1   2   5   8  11  14  17  20  23 
     24 | -24 -21 -18 -15 -12  -9  -6  -3   0   3   6   9  12  15  18  21  24 
     23 | -23 -20 -17 -14 -11  -8  -5  -2   1   4   7  10  13  16  19  22  25 
     22 | -22 -19 -16 -13 -10  -7  -4  -1   2   5   8  11  14  17  20  23  26 
     21 | -21 -18 -15 -12  -9  -6  -3   0   3   6   9  12  15  18  21  24  27 
     20 | -20 -17 -14 -11  -8  -5  -2   1   4   7  10  13  16  19  22  25  28 
     19 | -19 -16 -13 -10  -7  -4  -1   2   5   8  11  14  17  20  23  26  29 
     18 | -18 -15 -12  -9  -6  -3   0   3   6   9  12  15  18  21  24  27  30 
     17 | -17 -14 -11  -8  -5  -2   1   4   7  10  13  16  19  22  25  28  31 
     16 | -16 -13 -10  -7  -4  -1   2   5   8  11  14  17  20  23  26  29  32 
     15 | -15 -12  -9  -6  -3   0   3   6   9  12  15  18  21  24  27  30 
     14 | -14 -11  -8  -5  -2   1   4   7  10  13  16  19  22  25  28 
     13 | -13 -10  -7  -4  -1   2   5   8  11  14  17  20  23  26 
     12 | -12  -9  -6  -3   0   3   6   9  12  15  18  21  24 
     11 | -11  -8  -5  -2   1   4   7  10  13  16  19  22 
     10 | -10  -7  -4  -1   2   5   8  11  14  17  20 
      9 |  -9  -6  -3   0   3   6   9  12  15  18 
      8 |  -8  -5  -2   1   4   7  10  13  16 
      7 |  -7  -4  -1   2   5   8  11  14 
      6 |  -6  -3   0   3   6   9  12 
      5 |  -5  -2   1   4   7  10 
      4 |  -4  -1   2   5   8 
      3 |  -3   0   3   6 
      2 |  -2   1   4 
      1 |  -1   2

    Sincerely,
    Cac

  5. #55


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    Quote Originally Posted by Gronbog View Post
    In the mean time, until I can find time to digest what has been posted with respect to methodology, it might be reasonable to run this experiment.

    Rather than removing an ace, I think the equivalent adjustment for my software would be to discard and count an ace at the start of each shoe (after the burn card). This would place all instances of A,A vs ? into a context where at least three aces have been observed and counted just they would be when playing A,A after splitting.

    Does this sound reasonable?
    Perfectly reasonable. That is what I suggested in a previous post. I think there's a semantic issue about removing an ace, but it's exactly what you're proposing. That's why we're counting it.
    In my program I don't burn any cards although I don't think that affects the results.

    Sincerely,
    Cac

  6. #56


    Did you find this post helpful? Yes | No
    Quote Originally Posted by Cacarulo View Post
    I don't understand where you're stuck. You have all the data and algorithms correct. The only thing left for you is to calculate the TC as TC = floor (RC / Cards_Left * 52).
    Here it is worth a clarification: the previous formula calculates the exact TC where the remaining decks (Cards_Left / 52) are calculated exactly without rounding or truncating.
    In my program I can calculate the remaining decks in various ways.

    Perhaps viewing the following RC distributions as a function of Cards_Left will help:


    2) UnbalancedTen

    Code:
     51 |  -3 
     50 |  -5  -2 
     49 |  -7  -4  -1 
     48 |  -9  -6  -3   0 
     47 | -11  -8  -5  -2   1 
     46 | -13 -10  -7  -4  -1   2 
     45 | -15 -12  -9  -6  -3   0   3 
     44 | -17 -14 -11  -8  -5  -2   1   4 
     43 | -19 -16 -13 -10  -7  -4  -1   2   5 
     42 | -21 -18 -15 -12  -9  -6  -3   0   3   6 
     41 | -23 -20 -17 -14 -11  -8  -5  -2   1   4   7 
     40 | -25 -22 -19 -16 -13 -10  -7  -4  -1   2   5   8 
     39 | -27 -24 -21 -18 -15 -12  -9  -6  -3   0   3   6   9 
     38 | -29 -26 -23 -20 -17 -14 -11  -8  -5  -2   1   4   7  10 
     37 | -31 -28 -25 -22 -19 -16 -13 -10  -7  -4  -1   2   5   8  11 
     36 | -33 -30 -27 -24 -21 -18 -15 -12  -9  -6  -3   0   3   6   9  12 
     35 | -35 -32 -29 -26 -23 -20 -17 -14 -11  -8  -5  -2   1   4   7  10  13 
     34 | -34 -31 -28 -25 -22 -19 -16 -13 -10  -7  -4  -1   2   5   8  11  14 
     33 | -33 -30 -27 -24 -21 -18 -15 -12  -9  -6  -3   0   3   6   9  12  15 
     32 | -32 -29 -26 -23 -20 -17 -14 -11  -8  -5  -2   1   4   7  10  13  16 
     31 | -31 -28 -25 -22 -19 -16 -13 -10  -7  -4  -1   2   5   8  11  14  17 
     30 | -30 -27 -24 -21 -18 -15 -12  -9  -6  -3   0   3   6   9  12  15  18 
     29 | -29 -26 -23 -20 -17 -14 -11  -8  -5  -2   1   4   7  10  13  16  19 
     28 | -28 -25 -22 -19 -16 -13 -10  -7  -4  -1   2   5   8  11  14  17  20 
     27 | -27 -24 -21 -18 -15 -12  -9  -6  -3   0   3   6   9  12  15  18  21 
     26 | -26 -23 -20 -17 -14 -11  -8  -5  -2   1   4   7  10  13  16  19  22 
     25 | -25 -22 -19 -16 -13 -10  -7  -4  -1   2   5   8  11  14  17  20  23 
     24 | -24 -21 -18 -15 -12  -9  -6  -3   0   3   6   9  12  15  18  21  24 
     23 | -23 -20 -17 -14 -11  -8  -5  -2   1   4   7  10  13  16  19  22  25 
     22 | -22 -19 -16 -13 -10  -7  -4  -1   2   5   8  11  14  17  20  23  26 
     21 | -21 -18 -15 -12  -9  -6  -3   0   3   6   9  12  15  18  21  24  27 
     20 | -20 -17 -14 -11  -8  -5  -2   1   4   7  10  13  16  19  22  25  28 
     19 | -19 -16 -13 -10  -7  -4  -1   2   5   8  11  14  17  20  23  26  29 
     18 | -18 -15 -12  -9  -6  -3   0   3   6   9  12  15  18  21  24  27  30 
     17 | -17 -14 -11  -8  -5  -2   1   4   7  10  13  16  19  22  25  28  31 
     16 | -16 -13 -10  -7  -4  -1   2   5   8  11  14  17  20  23  26  29  32 
     15 | -15 -12  -9  -6  -3   0   3   6   9  12  15  18  21  24  27  30 
     14 | -14 -11  -8  -5  -2   1   4   7  10  13  16  19  22  25  28 
     13 | -13 -10  -7  -4  -1   2   5   8  11  14  17  20  23  26 
     12 | -12  -9  -6  -3   0   3   6   9  12  15  18  21  24 
     11 | -11  -8  -5  -2   1   4   7  10  13  16  19  22 
     10 | -10  -7  -4  -1   2   5   8  11  14  17  20 
      9 |  -9  -6  -3   0   3   6   9  12  15  18 
      8 |  -8  -5  -2   1   4   7  10  13  16 
      7 |  -7  -4  -1   2   5   8  11  14 
      6 |  -6  -3   0   3   6   9  12 
      5 |  -5  -2   1   4   7  10 
      4 |  -4  -1   2   5   8 
      3 |  -3   0   3   6 
      2 |  -2   1   4 
      1 |  -1   2

    Sincerely,
    Cac
    I have previously never used floor funtion.

    When I change output of TC using floor function and change nothing else this is output:
    Code:
    Count tags {-1,-1,-1,-1,-1,-1,-1,-1,-1,2}
    Decks: 1
    Insurance Data (without regard to hand comp)
    No subgroup (removals) are defined
    
    **** Player hand: x-x ****
    Cards   RC      TC ref
    
    48      0       0.00
    47      1       1.00
    46      2       2.00
    45      0       0.00
    44      1       1.00
    43      2       2.00
    42      0       0.00
    41      1       1.00
    40      2       2.00
    39      0       0.00
    38      1       1.00
    37      2       2.00
    36      0       0.00
    35      1       1.00
    34      2       3.00
    33      0       0.00
    32      1       1.00
    31      2       3.00
    30      0       0.00
    29      1       1.00
    28      2       3.00
    27      0       0.00
    26      1       2.00
    25      2       4.00
    24      0       0.00
    23      1       2.00
    22      2       4.00
    21      0       0.00
    20      1       2.00
    19      2       5.00
    18      0       0.00
    17      1       3.00
    16      2       6.00
    15      0       0.00
    14      1       3.00
    13      2       8.00
    12      0       0.00
    11      1       4.00
    10      2       10.00
    9       0       0.00
    8       1       6.00
    7       2       14.00
    6       0       0.00
    5       1       10.00
    4       2       26.00
    3       0       0.00
    2       1       26.00
    1       2       104.00
    How can we transition from this and simply say TC index = 0.00 in all cases?

    k_c

  7. #57


    Did you find this post helpful? Yes | No
    How can we transition from this and simply say TC index = 0.00 in all cases?
    Read again the methodology that I sent you earlier. The answer is there.
    Once you assemble the arrays you will see it more clearly. This is what I get from the arrays:

    Code:
    |       104 |  0.00871477100434657 |  2.00000000000000000 |
    |        94 |  0.00000000000157696 |  1.81282495667244370 |
    |        93 |  0.00000000002582721 |  1.79999999999999982 |
    |        92 |  0.00000000291990962 |  1.77090909090909099 |
    |        91 |  0.00000001888279004 |  1.75000000000000000 |
    |        89 |  0.00000011539482804 |  1.72727272727272685 |
    |        88 |  0.00000061443999346 |  1.70000000000000018 |
    |        86 |  0.00000290322938725 |  1.66666666666666630 |
    |        85 |  0.00000000001263757 |  1.64705882352941169 |
    |        84 |  0.00001232995767432 |  1.62500000000000000 |
    |        83 |  0.00000000204895869 |  1.60000000000000075 |
    |        81 |  0.00004748601158011 |  1.57142857142857140 |
    |        80 |  0.00000010700247691 |  1.53846153846153832 |
    |        79 |  0.00000000000264831 |  1.52631578947368407 |
    |        78 |  0.00016704038144613 |  1.50000000000000044 |
    |        76 |  0.00000000104259939 |  1.47058823529411731 |
    |        75 |  0.00000280244582382 |  1.45454545454545459 |
    |        74 |  0.00000001001713137 |  1.43750000000000000 |
    |        72 |  0.00054354543772864 |  1.40000000000000013 |
    |        71 |  0.00000000033898419 |  1.36842105263157876 |
    |        70 |  0.00000043364161695 |  1.35714285714285721 |
    |        69 |  0.00004387543124798 |  1.33333333333333348 |
    |        68 |  0.00000215788328434 |  1.30769230769230749 |
    |        67 |  0.00000003892371046 |  1.29411764705882293 |
    |        66 |  0.00000000005561459 |  1.28571428571428559 |
    |        65 |  0.00169413476984208 |  1.25000000000000000 |
    |        62 |  0.00000142216800880 |  1.20011666964613362 |
    |        61 |  0.00003468047098998 |  1.18181818181818166 |
    |        60 |  0.00000012776135551 |  1.16666666666666696 |
    |        59 |  0.00044653704872974 |  1.14285714285714279 |
    |        58 |  0.00000078431276579 |  1.11764705882352944 |
    |        57 |  0.00011494953741622 |  1.10000000000000009 |
    |        56 |  0.00002466219327307 |  1.07692334951209756 |
    |        55 |  0.00000387542778391 |  1.06250000000000000 |
    |        54 |  0.00000038131483604 |  1.05237716471420817 |
    |        52 |  0.00557287748507175 |  1.00000000000000000 |
    |        49 |  0.00000098985500915 |  0.95024721217439700 |
    |        48 |  0.00006574386419129 |  0.93037593984962408 |
    |        47 |  0.00024697563712821 |  0.90909115571936860 |
    |        46 |  0.00000495213522480 |  0.89473684210526305 |
    |        45 |  0.00091596628308714 |  0.87500000000000000 |
    |        44 |  0.00017428659431586 |  0.84629621318248338 |
    |        43 |  0.00002064258472653 |  0.83333333333333326 |
    |        42 |  0.00000084422952156 |  0.82608695652173880 |
    |        41 |  0.00355000323823723 |  0.79999999999999993 |
    |        40 |  0.00000500312850994 |  0.77276324321463064 |
    |        39 |  0.00053207026460195 |  0.75197575923828264 |
    |        38 |  0.00004212583313604 |  0.73676600341560983 |
    |        37 |  0.00235642369969060 |  0.71428571428571419 |
    |        36 |  0.00001024331819497 |  0.69565217391304324 |
    |        35 |  0.00021420777749855 |  0.68736137655442942 |
    |        34 |  0.00160784843995766 |  0.66666534073775563 |
    |        33 |  0.00119028157534114 |  0.63725719265324676 |
    |        32 |  0.00079238019541892 |  0.61562675968216229 |
    |        31 |  0.00053494269277241 |  0.60003142672513032 |
    |        30 |  0.00058621117922467 |  0.58461036843821323 |
    |        29 |  0.00024998750897103 |  0.56785934865976717 |
    |        28 |  0.00002061509815479 |  0.55440322652129603 |
    |        26 |  0.02831763219996664 |  0.50000000000000000 |
    |        23 |  0.00017953786589658 |  0.44632471376367122 |
    |        22 |  0.00114804178525575 |  0.43265146754851591 |
    |        21 |  0.00209148765373934 |  0.41546099791878849 |
    |        20 |  0.00447136480366181 |  0.39093339124937432 |
    |        19 |  0.00056184058125404 |  0.37492946689727213 |
    |        18 |  0.00515434319090128 |  0.36020785934513228 |
    |        17 |  0.00627889499237681 |  0.33385621431956813 |
    |        16 |  0.00331551428946029 |  0.31459958099531204 |
    |        15 |  0.00164849153076835 |  0.30304918220143839 |
    |        14 |  0.01180284911857132 |  0.28377075011933750 |
    |        13 |  0.00831900989971149 |  0.25415565796320805 |
    |        12 |  0.00444586248330500 |  0.23660929562690006 |
    |        11 |  0.00491463032112485 |  0.22331489610256541 |
    |        10 |  0.02168642985412893 |  0.19999999999999990 |
    |         9 |  0.00644723933782312 |  0.17778520825362779 |
    |         8 |  0.01422232357584844 |  0.15916454008745787 |
    |         7 |  0.00944368618281479 |  0.14108362235274344 |
    |         6 |  0.01711522515242123 |  0.12463070776752874 |
    |         5 |  0.01605857014446175 |  0.10583558658162687 |
    |         4 |  0.02216349669607403 |  0.08640204440221574 |
    |         3 |  0.02408297229015970 |  0.06586101585896612 |
    |         2 |  0.02559654723463824 |  0.04650772469795619 |
    |         1 |  0.02940911552579521 |  0.02693192982359423 |
    |        -2 |  0.04680045940086009 | -0.02585514096402246 |
    |        -3 |  0.05839132204279256 | -0.04592230359816294 |
    |        -4 |  0.07090358504550298 | -0.06614055023135565 |
    |        -5 |  0.03502125088674130 | -0.08663693722547899 |
    |        -6 |  0.04592331313814468 | -0.10415894876732154 |
    |        -7 |  0.03468944744545854 | -0.12489370469198741 |
    |        -8 |  0.03636714909623130 | -0.14466592458066274 |
    |        -9 |  0.02420005793126845 | -0.16451936561462860 |
    |       -10 |  0.02486080551606965 | -0.18353544056261387 |
    |       -11 |  0.02038495612294155 | -0.20354595308019077 |
    |       -12 |  0.01532869795078525 | -0.22259503687233592 |
    |       -13 |  0.03894686613946247 | -0.24954723803196077 |
    |       -14 |  0.00080989335537749 | -0.26795849902205870 |
    |       -15 |  0.01093248186377699 | -0.27882703196169500 |
    |       -16 |  0.01406786328230392 | -0.30114621791639995 |
    |       -17 |  0.00481905158117618 | -0.31896326089162186 |
    |       -18 |  0.01126052264892294 | -0.33420239515465161 |
    |       -19 |  0.00762527797492671 | -0.35497267983234110 |
    |       -20 |  0.00537093486559662 | -0.37316482762760189 |
    |       -21 |  0.01801042182419816 | -0.39999853302049365 |
    |       -22 |  0.00129906745042194 | -0.42137186852973024 |
    |       -23 |  0.00396274715883349 | -0.43423415635535390 |
    |       -24 |  0.00524302171262204 | -0.45346298679295921 |
    |       -25 |  0.00289832384058324 | -0.47175178783928612 |
    |       -26 |  0.01044042271488793 | -0.49957257348688450 |
    |       -27 |  0.00022173003543806 | -0.50606119544374928 |
    |       -28 |  0.00357199862289537 | -0.53351642333846871 |
    |       -29 |  0.00079307750523909 | -0.55079027561422045 |
    |       -30 |  0.00644165281717133 | -0.57141013454565792 |
    |       -31 |  0.00032944637150629 | -0.59028248638169123 |
    |       -32 |  0.00130362128163072 | -0.60131673732001456 |
    |       -33 |  0.00418993054904777 | -0.62500000000000011 |
    |       -34 |  0.00062257914666534 | -0.64668475755092125 |
    |       -35 |  0.00278975680418676 | -0.66666577754524736 |
    |       -36 |  0.00023555528866450 | -0.68407953715517900 |
    |       -37 |  0.00187454179945584 | -0.70000491647215080 |
    |       -38 |  0.00134223589377089 | -0.72646282678620899 |
    |       -39 |  0.00086745082199328 | -0.74965167535242383 |
    |       -40 |  0.00056156501838238 | -0.76910060208855813 |
    |       -41 |  0.00036102366584841 | -0.78567292568131819 |
    |       -42 |  0.00022880167207248 | -0.79999069392982158 |
    |       -43 |  0.00022828057142051 | -0.81666643961004726 |
    |       -44 |  0.00008039959467130 | -0.83653844120138621 |
    |       -45 |  0.00002999390339164 | -0.85424028268551233 |
    |       -46 |  0.00000425403966710 | -0.87313860252004571 |
    |       -47 |  0.00000015328441153 | -0.89098134070490687 |
    |       -48 |  0.00000000042684590 | -0.90693430656934315 |
    |       -52 |  0.04034992234489480 | -1.00000000000000000 |


    Note that there is no TC floored equal to zero or equal to minus one. The index is clearly +1 since from +1 the expected value is positive.

    Code:
    +----------+-------+-----+-----+------------+------------+----------------------+----------------------+
    |   Play   | Decks |  CR | IRC |  TC Index  |  RC Index  | Total EV >= TC Index | Total EV >= RC Index |
    +----------+-------+-----+-----+------------+------------+----------------------+----------------------+
    |    Ins   |   1   |   0 |  -4 |         1  |      1     |  0.08558354668387291 |  0.08558183737933568 |
    +----------+-------+-----+-----+------------+------------+----------------------+----------------------+


    The decimal index is +1.1

    Sincerely,
    Cac

  8. #58


    Did you find this post helpful? Yes | No
    Quote Originally Posted by Cacarulo View Post
    Read again the methodology that I sent you earlier. The answer is there.
    Once you assemble the arrays you will see it more clearly. This is what I get from the arrays:

    Code:
    |       104 |  0.00871477100434657 |  2.00000000000000000 |
    |        94 |  0.00000000000157696 |  1.81282495667244370 |
    |        93 |  0.00000000002582721 |  1.79999999999999982 |
    |        92 |  0.00000000291990962 |  1.77090909090909099 |
    |        91 |  0.00000001888279004 |  1.75000000000000000 |
    |        89 |  0.00000011539482804 |  1.72727272727272685 |
    |        88 |  0.00000061443999346 |  1.70000000000000018 |
    |        86 |  0.00000290322938725 |  1.66666666666666630 |
    |        85 |  0.00000000001263757 |  1.64705882352941169 |
    |        84 |  0.00001232995767432 |  1.62500000000000000 |
    |        83 |  0.00000000204895869 |  1.60000000000000075 |
    |        81 |  0.00004748601158011 |  1.57142857142857140 |
    |        80 |  0.00000010700247691 |  1.53846153846153832 |
    |        79 |  0.00000000000264831 |  1.52631578947368407 |
    |        78 |  0.00016704038144613 |  1.50000000000000044 |
    |        76 |  0.00000000104259939 |  1.47058823529411731 |
    |        75 |  0.00000280244582382 |  1.45454545454545459 |
    |        74 |  0.00000001001713137 |  1.43750000000000000 |
    |        72 |  0.00054354543772864 |  1.40000000000000013 |
    |        71 |  0.00000000033898419 |  1.36842105263157876 |
    |        70 |  0.00000043364161695 |  1.35714285714285721 |
    |        69 |  0.00004387543124798 |  1.33333333333333348 |
    |        68 |  0.00000215788328434 |  1.30769230769230749 |
    |        67 |  0.00000003892371046 |  1.29411764705882293 |
    |        66 |  0.00000000005561459 |  1.28571428571428559 |
    |        65 |  0.00169413476984208 |  1.25000000000000000 |
    |        62 |  0.00000142216800880 |  1.20011666964613362 |
    |        61 |  0.00003468047098998 |  1.18181818181818166 |
    |        60 |  0.00000012776135551 |  1.16666666666666696 |
    |        59 |  0.00044653704872974 |  1.14285714285714279 |
    |        58 |  0.00000078431276579 |  1.11764705882352944 |
    |        57 |  0.00011494953741622 |  1.10000000000000009 |
    |        56 |  0.00002466219327307 |  1.07692334951209756 |
    |        55 |  0.00000387542778391 |  1.06250000000000000 |
    |        54 |  0.00000038131483604 |  1.05237716471420817 |
    |        52 |  0.00557287748507175 |  1.00000000000000000 |
    |        49 |  0.00000098985500915 |  0.95024721217439700 |
    |        48 |  0.00006574386419129 |  0.93037593984962408 |
    |        47 |  0.00024697563712821 |  0.90909115571936860 |
    |        46 |  0.00000495213522480 |  0.89473684210526305 |
    |        45 |  0.00091596628308714 |  0.87500000000000000 |
    |        44 |  0.00017428659431586 |  0.84629621318248338 |
    |        43 |  0.00002064258472653 |  0.83333333333333326 |
    |        42 |  0.00000084422952156 |  0.82608695652173880 |
    |        41 |  0.00355000323823723 |  0.79999999999999993 |
    |        40 |  0.00000500312850994 |  0.77276324321463064 |
    |        39 |  0.00053207026460195 |  0.75197575923828264 |
    |        38 |  0.00004212583313604 |  0.73676600341560983 |
    |        37 |  0.00235642369969060 |  0.71428571428571419 |
    |        36 |  0.00001024331819497 |  0.69565217391304324 |
    |        35 |  0.00021420777749855 |  0.68736137655442942 |
    |        34 |  0.00160784843995766 |  0.66666534073775563 |
    |        33 |  0.00119028157534114 |  0.63725719265324676 |
    |        32 |  0.00079238019541892 |  0.61562675968216229 |
    |        31 |  0.00053494269277241 |  0.60003142672513032 |
    |        30 |  0.00058621117922467 |  0.58461036843821323 |
    |        29 |  0.00024998750897103 |  0.56785934865976717 |
    |        28 |  0.00002061509815479 |  0.55440322652129603 |
    |        26 |  0.02831763219996664 |  0.50000000000000000 |
    |        23 |  0.00017953786589658 |  0.44632471376367122 |
    |        22 |  0.00114804178525575 |  0.43265146754851591 |
    |        21 |  0.00209148765373934 |  0.41546099791878849 |
    |        20 |  0.00447136480366181 |  0.39093339124937432 |
    |        19 |  0.00056184058125404 |  0.37492946689727213 |
    |        18 |  0.00515434319090128 |  0.36020785934513228 |
    |        17 |  0.00627889499237681 |  0.33385621431956813 |
    |        16 |  0.00331551428946029 |  0.31459958099531204 |
    |        15 |  0.00164849153076835 |  0.30304918220143839 |
    |        14 |  0.01180284911857132 |  0.28377075011933750 |
    |        13 |  0.00831900989971149 |  0.25415565796320805 |
    |        12 |  0.00444586248330500 |  0.23660929562690006 |
    |        11 |  0.00491463032112485 |  0.22331489610256541 |
    |        10 |  0.02168642985412893 |  0.19999999999999990 |
    |         9 |  0.00644723933782312 |  0.17778520825362779 |
    |         8 |  0.01422232357584844 |  0.15916454008745787 |
    |         7 |  0.00944368618281479 |  0.14108362235274344 |
    |         6 |  0.01711522515242123 |  0.12463070776752874 |
    |         5 |  0.01605857014446175 |  0.10583558658162687 |
    |         4 |  0.02216349669607403 |  0.08640204440221574 |
    |         3 |  0.02408297229015970 |  0.06586101585896612 |
    |         2 |  0.02559654723463824 |  0.04650772469795619 |
    |         1 |  0.02940911552579521 |  0.02693192982359423 |
    |        -2 |  0.04680045940086009 | -0.02585514096402246 |
    |        -3 |  0.05839132204279256 | -0.04592230359816294 |
    |        -4 |  0.07090358504550298 | -0.06614055023135565 |
    |        -5 |  0.03502125088674130 | -0.08663693722547899 |
    |        -6 |  0.04592331313814468 | -0.10415894876732154 |
    |        -7 |  0.03468944744545854 | -0.12489370469198741 |
    |        -8 |  0.03636714909623130 | -0.14466592458066274 |
    |        -9 |  0.02420005793126845 | -0.16451936561462860 |
    |       -10 |  0.02486080551606965 | -0.18353544056261387 |
    |       -11 |  0.02038495612294155 | -0.20354595308019077 |
    |       -12 |  0.01532869795078525 | -0.22259503687233592 |
    |       -13 |  0.03894686613946247 | -0.24954723803196077 |
    |       -14 |  0.00080989335537749 | -0.26795849902205870 |
    |       -15 |  0.01093248186377699 | -0.27882703196169500 |
    |       -16 |  0.01406786328230392 | -0.30114621791639995 |
    |       -17 |  0.00481905158117618 | -0.31896326089162186 |
    |       -18 |  0.01126052264892294 | -0.33420239515465161 |
    |       -19 |  0.00762527797492671 | -0.35497267983234110 |
    |       -20 |  0.00537093486559662 | -0.37316482762760189 |
    |       -21 |  0.01801042182419816 | -0.39999853302049365 |
    |       -22 |  0.00129906745042194 | -0.42137186852973024 |
    |       -23 |  0.00396274715883349 | -0.43423415635535390 |
    |       -24 |  0.00524302171262204 | -0.45346298679295921 |
    |       -25 |  0.00289832384058324 | -0.47175178783928612 |
    |       -26 |  0.01044042271488793 | -0.49957257348688450 |
    |       -27 |  0.00022173003543806 | -0.50606119544374928 |
    |       -28 |  0.00357199862289537 | -0.53351642333846871 |
    |       -29 |  0.00079307750523909 | -0.55079027561422045 |
    |       -30 |  0.00644165281717133 | -0.57141013454565792 |
    |       -31 |  0.00032944637150629 | -0.59028248638169123 |
    |       -32 |  0.00130362128163072 | -0.60131673732001456 |
    |       -33 |  0.00418993054904777 | -0.62500000000000011 |
    |       -34 |  0.00062257914666534 | -0.64668475755092125 |
    |       -35 |  0.00278975680418676 | -0.66666577754524736 |
    |       -36 |  0.00023555528866450 | -0.68407953715517900 |
    |       -37 |  0.00187454179945584 | -0.70000491647215080 |
    |       -38 |  0.00134223589377089 | -0.72646282678620899 |
    |       -39 |  0.00086745082199328 | -0.74965167535242383 |
    |       -40 |  0.00056156501838238 | -0.76910060208855813 |
    |       -41 |  0.00036102366584841 | -0.78567292568131819 |
    |       -42 |  0.00022880167207248 | -0.79999069392982158 |
    |       -43 |  0.00022828057142051 | -0.81666643961004726 |
    |       -44 |  0.00008039959467130 | -0.83653844120138621 |
    |       -45 |  0.00002999390339164 | -0.85424028268551233 |
    |       -46 |  0.00000425403966710 | -0.87313860252004571 |
    |       -47 |  0.00000015328441153 | -0.89098134070490687 |
    |       -48 |  0.00000000042684590 | -0.90693430656934315 |
    |       -52 |  0.04034992234489480 | -1.00000000000000000 |


    Note that there is no TC floored equal to zero or equal to minus one. The index is clearly +1 since from +1 the expected value is positive.

    Code:
    +----------+-------+-----+-----+------------+------------+----------------------+----------------------+
    |   Play   | Decks |  CR | IRC |  TC Index  |  RC Index  | Total EV >= TC Index | Total EV >= RC Index |
    +----------+-------+-----+-----+------------+------------+----------------------+----------------------+
    |    Ins   |   1   |   0 |  -4 |         1  |      1     |  0.08558354668387291 |  0.08558183737933568 |
    +----------+-------+-----+-----+------------+------------+----------------------+----------------------+


    The decimal index is +1.1

    Sincerely,
    Cac

    OK thank you. If I'm lucky I'll be able to get it.

    I still think best TC index(ins count) for +EV is greater than 0.00. I think you get >= 1.00?
    > 0.00 would work for any number of decks.

    k_c

  9. #59


    Did you find this post helpful? Yes | No
    OK thank you. If I'm lucky I'll be able to get it.

    I still think best TC index(ins count) for +EV is greater than 0.00. I think you get >= 1.00?
    > 0.00 would work for any number of decks.
    Remember that indices are generally evaluated by "greater than or equal" (>=). Also note that you could say TC >= -1 or TC >= 0 since these TCs do not exist.
    The correct thing in this case is TC >= +1.

    Sincerely,
    Cac

  10. #60


    Did you find this post helpful? Yes | No
    OK thank you. If I'm lucky I'll be able to get it.

    I still think best TC index(ins count) for +EV is greater than 0.00. I think you get >= 1.00?
    > 0.00 would work for any number of decks.

    k_c
    Sorry k_c, somehow a line didn't come out in my TC listing. The TC equal to zero does exist even though the expected value is zero. This is the line I accidentally leaked:

    Code:
    |         0 |  0.08558354668387287 |  0.00000000000000000 |


    Sorry again. Anyway the index is still +1 which is where the EV starts to be positive.

    Sincerely,
    Cac

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