Quote Originally Posted by k_c View Post
If the goal is to get the single most efficient TC index, my inclination to do this is to use a mid-shoe TC calculation as the index approximation. I wouldn't know the accuracy of this. I guess we'll see from Cac's sims.

Resulting TC insurance indexes for HiLo and true counted KO from mid-shoe:
Code:
          HiLo          KO

1 deck    1.33          -0.67
2 decks   2.41          -0.65
4 decks   2.86          -0.62
6 decks   3.02          -0.62
8 decks   3.10          -0.62
k_c
Why in the middle of the shoe? The goal is to find a single index that maximizes the expected value given the following parameters: number of decks, cards remaining, cards removed, and a card counting system. This index can be integer or decimal, floored or rounded. Below is the table that I calculated with my program for Hi-Lo and for TKO.
An important fact is that numbers for integer or decimal values with one digit of precision can be generated with the new version of CVDATA. Maybe Norman can help with the verification.

a) Hi-Lo

Code:
+----------+-------+-----+----------+-----------+-----+----------------------+
|   Play   | Decks |  CR | TC Index |  RC Index | IRC | Total EV >= TC Index |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   1   |  20 |      2   |      1    |   0 |  0.58171980020663483 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   2   |  26 |      2   |      3    |   0 |  0.97386472171957084 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   3   |  39 |      3   |      5    |   0 |  0.90293467695143381 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   4   |  52 |      3   |      6    |   0 |  0.83027321442020385 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   5   |  65 |      3   |      8    |   0 |  0.75983020092833753 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   6   |  78 |      3   |      9    |   0 |  0.69413408108466679 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   7   |  91 |      3   |     11    |   0 |  0.63388417844782019 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   8   | 104 |      3   |     13    |   0 |  0.57910212499303571 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|   Play   | Decks |  CR | TC Index |  RC Index | IRC | Total EV >= TC Index |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   1   |  20 |    1.4   |      1    |   0 |  0.58948461336093605 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   2   |  26 |    2.4   |      3    |   0 |  0.98281795951625006 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   3   |  39 |    2.7   |      5    |   0 |  0.90816953949120360 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   4   |  52 |    2.9   |      6    |   0 |  0.83159288103950568 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   5   |  65 |    3.0   |      8    |   0 |  0.75983020092833709 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   6   |  78 |    3.0   |      9    |   0 |  0.69413408108466634 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   7   |  91 |    3.1   |     11    |   0 |  0.63441572887679987 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   8   | 104 |    3.1   |     13    |   0 |  0.58054269141619064 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|   Play   | Decks |  CR | TC Index |  RC Index | IRC | Total EV >= TC Index |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   1   |  20 |   1.36   |      1    |   0 |  0.58949259373855689 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   2   |  26 |   2.40   |      3    |   0 |  0.98281795951624784 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   3   |  39 |   2.73   |      5    |   0 |  0.90817947158494905 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   4   |  52 |   2.88   |      6    |   0 |  0.83169540860503743 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   5   |  65 |   2.97   |      8    |   0 |  0.75994376091156390 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   6   |  78 |   3.03   |      9    |   0 |  0.69421662302300535 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   7   |  91 |   3.07   |     11    |   0 |  0.63455736758509551 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   8   | 104 |   3.10   |     13    |   0 |  0.58054269141618986 |
+----------+-------+-----+----------+-----------+-----+----------------------+
b) TKO

Code:
+----------+-------+-----+----------+-----------+-----+----------------------+
|   Play   | Decks |  CR | TC Index |  RC Index | IRC | Total EV >= TC Index |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   1   |  20 |     -3   |     -1    |  -4 |  0.62207920068091205 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   2   |  26 |     -2   |     -1    |  -8 |  1.03126899891434554 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   3   |  39 |     -1   |     -1    | -12 |  0.96589993725524714 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   4   |  52 |     -1   |     -1    | -16 |  0.89567516597613084 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   5   |  65 |     -1   |     -2    | -20 |  0.82406581226090381 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   6   |  78 |     -1   |     -2    | -24 |  0.75620947896421276 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   7   |  91 |     -1   |     -2    | -28 |  0.69325066039581429 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   8   | 104 |     -1   |     -2    | -32 |  0.63555057036254503 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|   Play   | Decks |  CR | TC Index |  RC Index | IRC | Total EV >= TC Index |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   1   |  20 |   -2.7   |     -1    |  -4 |  0.62411302793561507 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   2   |  26 |   -1.6   |     -1    |  -8 |  1.04217654345964661 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   3   |  39 |   -1.3   |     -1    | -12 |  0.97122453130055963 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   4   |  52 |   -1.1   |     -1    | -16 |  0.89657584952559255 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   5   |  65 |   -1.0   |     -2    | -20 |  0.82406581226090447 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   6   |  78 |   -0.9   |     -2    | -24 |  0.75632462454726679 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   7   |  91 |   -0.9   |     -2    | -28 |  0.69476873014568830 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   8   | 104 |   -0.9   |     -2    | -32 |  0.63837723117899026 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|   Play   | Decks |  CR | TC Index |  RC Index | IRC | Total EV >= TC Index |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   1   |  20 |  -2.67   |     -1    |  -4 |  0.62411302793561529 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   2   |  26 |  -1.60   |     -1    |  -8 |  1.04217654345964506 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   3   |  39 |  -1.26   |     -1    | -12 |  0.97135441954627266 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   4   |  52 |  -1.11   |     -1    | -16 |  0.89658797329402284 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   5   |  65 |  -1.01   |     -2    | -20 |  0.82407138460075480 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   6   |  78 |  -0.95   |     -2    | -24 |  0.75658940195274205 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   7   |  91 |  -0.90   |     -2    | -28 |  0.69476873014568685 |
+----------+-------+-----+----------+-----------+-----+----------------------+
|    Ins   |   8   | 104 |  -0.87   |     -2    | -32 |  0.63854885119060589 |
+----------+-------+-----+----------+-----------+-----+----------------------+


Sincerely,
Cac