Double Down on Soft 12

[Cacarulo]

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:

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:

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

 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

 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

[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:


2) UnbalancedTen

 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:

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

[Cacarulo]

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:

|       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.

+----------+-------+-----+-----+------------+------------+----------------------+----------------------+
|   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

[k_c]

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:

|       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.

+----------+-------+-----+-----+------------+------------+----------------------+----------------------+
|   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

[Cacarulo]

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

[Cacarulo]

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:

|         0 |  0.08558354668387287 |  0.00000000000000000 |

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

Sincerely,
Cac