# Thread: Cacarulo: The HALVES vs ZEN dispute

1. ## Cacarulo: ZEN Report II

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

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

Simulation started  on (MM/DD/YY): 03-16-2005 at 12:47:52
Simulation finished on (MM/DD/YY): 03-16-2005 at 15:04:37
Random seed = 1234567890

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

6 decks

Shufflepoint 260 cards, (83.33% penetration)

Face up game

System used is ZEN with indices table zen2

SBA floors when calculating the true count
Remaining decks estimated exactly for true count conversion
SBA divides running count by the number of 1/2 decks remaining

American rules - hole card game

Surrender is not allowed

Dealer stands on all 17

Doubling is allowed on any two cards

Doubling is allowed after splitting

Hand can be split 3 times, up to 4 hands

No resplit of aces

Only one card to split aces

Different tens can be split

Insurance is 1 half of a bet

Predefined variables:
INSURANCE  =   3    Buy insurance if true count >= INSURANCE
H7710      =  99    Hit 7,7 versus dealer's 10 if true count < H7710

No user defined variables

No leaving the shoe at any count

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

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

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

Player's bankroll is 100

Aim bankroll is 200

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

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

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

COUNT STATISTICS (PRIMARY):

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

-25   0.0000  -25   0.00000  0.000000  -8.182  13.8398  1.4515   1.4636
-24   0.0000  -24   0.00000  0.000000 -20.000   8.2368  1.2627   1.3277
-23   0.0000  -23   0.00001  0.000000 -20.000   5.4602  1.3025   1.2917
-22   0.0000  -22   0.00002  0.000000 -16.414   3.2850  1.3336   1.3004
-21   0.0000  -21   0.00004  0.000001 -21.404   2.0039  1.3209   1.2923
-20   0.0001  -20   0.00011  0.000001 -17.659   1.2462  1.3071   1.2845
-19   0.0003  -19   0.00026  0.000002 -16.763   0.8120  1.3001   1.2727
-18   0.0006  -18   0.00063  0.000003 -14.941   0.5120  1.2885   1.2623
-17   0.0013  -17   0.00132  0.000004 -14.894   0.3526  1.2811   1.2546
-16   0.0029  -16   0.00288  0.000005 -12.884   0.2370  1.2727   1.2449
-15   0.0059  -15   0.00585  0.000008 -11.393   0.1651  1.2631   1.2365
-14   0.0106  -14   0.01059  0.000010 -10.617   0.1219  1.2543   1.2284
-13   0.0248  -13   0.02483  0.000016  -9.345   0.0790  1.2455   1.2195
-12   0.0438  -12   0.04378  0.000021  -8.326   0.0591  1.2365   1.2106
-11   0.0790  -11   0.07905  0.000028  -7.432   0.0437  1.2275   1.2023
-10   0.1422  -10   0.14222  0.000038  -6.485   0.0323  1.2197   1.1949
-9   0.2512   -9   0.25119  0.000050  -5.625   0.0242  1.2117   1.1872
-8   0.4347   -8   0.43470  0.000066  -4.862   0.0183  1.2036   1.1797
-7   0.7361   -7   0.73607  0.000085  -4.117   0.0139  1.1957   1.1724
-6   1.2661   -6   1.26612  0.000112  -3.431   0.0106  1.1884   1.1655
-5   2.1314   -5   2.13144  0.000144  -2.798   0.0081  1.1812   1.1588
-4   3.7150   -4   3.71499  0.000189  -2.198   0.0061  1.1742   1.1523
-3   6.4992   -3   6.49919  0.000247  -1.652   0.0046  1.1676   1.1460
-2  11.9588   -2  11.95877  0.000324  -1.127   0.0034  1.1619   1.1399
-1  20.6934   -1  20.69340  0.000405  -0.616   0.0025  1.1568   1.1343
0  25.5236    0  25.52357  0.000436  -0.119   0.0023  1.1544   1.1310
1  11.5053    1  11.50530  0.000319   0.545   0.0034  1.1566   1.1317
2   6.3590    2   6.35905  0.000244   1.149   0.0046  1.1566   1.1354
3   3.5913    3   3.59132  0.000186   1.844   0.0061  1.1624   1.1633
4   2.0963    4   2.09628  0.000143   2.563   0.0081  1.1657   1.1817
5   1.2192    5   1.21924  0.000110   3.283   0.0107  1.1809   1.1964
6   0.7273    6   0.72733  0.000085   4.057   0.0138  1.1801   1.1954
7   0.4203    7   0.42026  0.000065   4.818   0.0181  1.1748   1.1917
8   0.2503    8   0.25029  0.000050   5.481   0.0234  1.1696   1.1881
9   0.1386    9   0.13863  0.000037   6.253   0.0313  1.1640   1.1844
10   0.0798   10   0.07979  0.000028   6.849   0.0410  1.1592   1.1810
11   0.0433   11   0.04333  0.000021   7.506   0.0554  1.1539   1.1776
12   0.0223   12   0.02230  0.000015   8.005   0.0770  1.1494   1.1745
13   0.0139   13   0.01395  0.000012   8.668   0.0970  1.1450   1.1717
14   0.0062   14   0.00619  0.000008   9.236   0.1446  1.1376   1.1676
15   0.0030   15   0.00302  0.000005  10.026   0.2065  1.1352   1.1665
16   0.0015   16   0.00145  0.000004  10.123   0.2961  1.1276   1.1606
17   0.0007   17   0.00071  0.000003  10.781   0.4227  1.1246   1.1590
18   0.0003   18   0.00030  0.000002  11.509   0.6498  1.1186   1.1575
19   0.0001   19   0.00013  0.000001  13.470   0.9873  1.1274   1.1631
20   0.0001   20   0.00005  0.000001  10.884   1.4782  1.0837   1.1427
21   0.0000   21   0.00002  0.000000  11.155   2.4097  1.0895   1.1448
22   0.0000   22   0.00001  0.000000  11.505   3.8769  1.0993   1.1331
23   0.0000   23   0.00000  0.000000  18.257   6.1770  1.0770   1.1480
24   0.0000   24   0.00000  0.000000  16.038  10.5801  1.0893   1.0943
25   0.0000   25   0.00000  0.000000  20.000  12.6396  1.0268   1.1212

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

PRIMARY STATISTICS:

Initial bet advantage (IBA):-0.29307%, St. Err. 0.001161%

Total bets advantage (TBA): -0.25690%

SCORE:                       0.00

Risk of Ruin:                100%

Estim. payoff per 100,000 rounds played is -293.07, with estim. std. 367.10

Average st. dev. per round:  1.16087

Av. std. per round per unit: 1.16087

Average bet per round:       1.00000

Average bet total:           1.14082

Insurance contribution:      0.02324%
Insurance contrib. to TBA:   0.02118%

Number of sessions won:      531116
Number of sessions lost:     827633
Total number of sessions:    1358749
Percentage of sessions won:  39.0886%, St. Err. 0.04186%
Surplus bank:                344490

Number of shoes played:      208638075

Number of rounds played:     10000000021

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

SECONDARY STATISTICS:

AC BLJACK  PUSH  HDOUBL SDOUBL  SPLIT SURREN  INSUR  INSADV  ACDIST

-10  2.789  9.310 12.959  2.323  3.519  0.000  0.000   0.000   0.149
-9  2.981  9.289 12.407  2.259  3.415  0.000  0.000   0.000   0.261
-8  3.174  9.266 11.849  2.199  3.324  0.000  0.000   0.000   0.450
-7  3.367  9.237 11.324  2.133  3.226  0.000  0.000   0.000   0.756
-6  3.566  9.227 10.825  2.070  3.137  0.000  0.000   0.000   1.294
-5  3.774  9.211 10.339  2.004  3.052  0.000  0.000   0.000   2.165
-4  3.983  9.202  9.869  1.938  2.970  0.000  0.000   0.000   3.752
-3  4.198  9.183  9.416  1.871  2.889  0.000  0.000   0.000   6.529
-2  4.419  9.118  8.978  1.804  2.811  0.000  0.000   0.000  11.949
-1  4.633  9.050  8.584  1.739  2.738  0.000  0.000   0.000  20.575
0  4.827  8.916  8.374  1.702  2.674  0.000  0.000   0.000  25.304
1  5.067  8.902  8.428  1.799  2.598  0.000  0.012   1.286  11.414
2  5.315  9.004  8.584  1.734  2.540  0.000  0.792   2.225   6.329
3  5.683  9.242  9.430  1.702  2.528  0.000  5.541   3.255   3.662
4  5.998  9.278  9.028  1.630  3.635  0.000  8.155   5.374   2.171
5  6.264  9.285  8.430  1.535  5.322  0.000  8.688   8.051   1.279
6  6.526  9.364  7.968  1.458  5.663  0.000  8.824  10.981   0.762
7  6.788  9.466  7.542  1.379  5.746  0.000  8.935  14.053   0.439
8  7.061  9.598  7.124  1.311  5.814  0.000  9.058  17.138   0.261
9  7.327  9.744  6.748  1.245  5.855  0.000  9.156  20.327   0.144
10  7.614  9.888  6.364  1.172  5.920  0.000  9.264  22.948   0.083

InsTC INSUR  INSADV  ST. ERR.

3   7.338   2.794   0.014
4   7.344   5.738   0.018
5   7.354   8.734   0.024
6   7.371  11.684   0.030
7   7.369  14.824   0.040
8   7.366  17.855   0.052
9   7.362  20.972   0.069
10   7.349  23.882   0.090

CUMULATIVE FREQUENCY OF OCCURRENCE:

Frequency of blackjack:      4.744%

Frequency of pushing:        9.021%

Frequency of hard doubling:  8.778%

Frequency of soft doubling:  1.760%

Frequency of splitting:      2.909%

Frequency of insurance:      0.658%

CORRELATION COEFFICIENTS:

AC   Correlation Coef.

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

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

Up card    17       18       19       20       21       BJ      Bust

2    13.9724  13.4446  13.0057  12.4035  11.8386     --    35.3350
3    13.4387  13.0618  12.5262  12.0822  11.4939     --    37.3972
4    13.0685  12.4154  12.1321  11.6457  11.1862     --    39.5521
5    12.1977  12.2563  11.7643  11.1822  10.7934     --    41.8062
6    16.5785  10.6314  10.6514  10.1593   9.7295     --    42.2500
7    36.8974  13.8030   7.8517   7.8736   7.3843     --    26.1900
8    12.8971  35.9774  12.8775   6.9278   6.9522     --    24.3680
9    12.0368  11.7394  35.1628  12.0428   6.0927     --    22.9255
10    11.1981  11.1720  11.1966  33.9772   3.4857   7.7156  21.2548
ace    13.0104  13.0901  13.0660  13.0908   5.3560  30.8421  11.5446

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

Cards:    2       3       4       5       6       7       8       9       10
Freq.: 45.4720 36.3746 14.8357  2.9487  0.3427  0.0251  0.0012  0.0000  0.0000

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

Card:    2      3      4      5      6      7      8      9      10     ace
Freq.: 7.6410 7.6481 7.6482 7.6547 7.6659 7.6939 7.7051 7.7100 30.9215 7.7116
```

2. ## Cacarulo: HALVES Report I

```

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

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

Simulation started  on (MM/DD/YY): 03-15-2005 at 22:15:34
Simulation finished on (MM/DD/YY): 03-16-2005 at  1:00:44
Random seed = 1234567890

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

6 decks

Shufflepoint 260 cards, (83.33% penetration)

Face up game

System used is HALVES with indices table halves_c22

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

American rules - hole card game

Surrender is not allowed

Dealer stands on all 17

Doubling is allowed on any two cards

Doubling is allowed after splitting

Hand can be split 3 times, up to 4 hands

No resplit of aces

Only one card to split aces

Different tens can be split

Insurance is 1 half of a bet

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

No user defined variables

No leaving the shoe at any count

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

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

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

Player's bankroll is 100

Aim bankroll is 200

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

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

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

COUNT STATISTICS (PRIMARY):

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

-25   0.1533  -25   0.15330  0.000039  -8.810   0.0315  1.2336   1.2085
-24   0.0467  -24   0.04668  0.000022  -7.131   0.0564  1.2195   1.1951
-23   0.0575  -23   0.05747  0.000024  -6.640   0.0507  1.2161   1.1918
-22   0.0724  -22   0.07240  0.000027  -6.286   0.0451  1.2131   1.1890
-21   0.0934  -21   0.09344  0.000031  -5.999   0.0396  1.2098   1.1859
-20   0.1195  -20   0.11948  0.000035  -5.617   0.0349  1.2064   1.1828
-19   0.1471  -19   0.14713  0.000038  -5.296   0.0314  1.2033   1.1799
-18   0.1962  -18   0.19622  0.000044  -4.997   0.0271  1.1999   1.1766
-17   0.2262  -17   0.22619  0.000048  -4.667   0.0252  1.1971   1.1739
-16   0.2972  -16   0.29721  0.000054  -4.363   0.0219  1.1940   1.1711
-15   0.3695  -15   0.36947  0.000061  -4.042   0.0196  1.1907   1.1680
-14   0.4311  -14   0.43109  0.000066  -3.765   0.0181  1.1881   1.1656
-13   0.6057  -13   0.60565  0.000078  -3.464   0.0152  1.1849   1.1627
-12   0.7369  -12   0.73691  0.000086  -3.201   0.0138  1.1820   1.1600
-11   0.9120  -11   0.91202  0.000095  -2.921   0.0123  1.1792   1.1574
-10   1.1527  -10   1.15273  0.000107  -2.632   0.0110  1.1764   1.1547
-9   1.4325   -9   1.43246  0.000119  -2.405   0.0098  1.1736   1.1521
-8   1.8628   -8   1.86281  0.000135  -2.124   0.0086  1.1709   1.1495
-7   2.3354   -7   2.33540  0.000151  -1.892   0.0076  1.1683   1.1470
-6   3.0160   -6   3.01600  0.000171  -1.660   0.0067  1.1659   1.1445
-5   3.8311   -5   3.83111  0.000192  -1.426   0.0059  1.1636   1.1420
-4   5.0898   -4   5.08982  0.000220  -1.185   0.0051  1.1615   1.1396
-3   6.5933   -3   6.59330  0.000248  -0.948   0.0045  1.1595   1.1373
-2   8.8894   -2   8.88945  0.000285  -0.710   0.0039  1.1573   1.1350
-1   9.6568   -1   9.65681  0.000295  -0.487   0.0037  1.1553   1.1329
0  14.3681    0  14.36813  0.000351  -0.259   0.0030  1.1544   1.1314
1   8.3994    1   8.39939  0.000277   0.040   0.0040  1.1567   1.1325
2   6.3760    2   6.37600  0.000244   0.320   0.0046  1.1579   1.1330
3   4.8252    3   4.82516  0.000214   0.580   0.0053  1.1577   1.1325
4   3.8007    4   3.80074  0.000191   0.860   0.0059  1.1560   1.1310
5   2.9091    5   2.90913  0.000168   1.111   0.0068  1.1563   1.1321
6   2.2983    6   2.29827  0.000150   1.385   0.0077  1.1611   1.1411
7   1.7822    7   1.78220  0.000132   1.661   0.0087  1.1655   1.1547
8   1.4484    8   1.44841  0.000119   1.952   0.0097  1.1643   1.1665
9   1.1197    9   1.11969  0.000105   2.262   0.0110  1.1621   1.1737
10   0.9017   10   0.90174  0.000095   2.554   0.0124  1.1743   1.1898
11   0.6993   11   0.69925  0.000083   2.893   0.0141  1.1817   1.1976
12   0.5430   12   0.54298  0.000073   3.190   0.0161  1.1839   1.2003
13   0.4847   13   0.48475  0.000069   3.568   0.0170  1.1828   1.1997
14   0.3644   14   0.36442  0.000060   3.892   0.0196  1.1810   1.1986
15   0.2799   15   0.27987  0.000053   4.191   0.0223  1.1786   1.1971
16   0.2287   16   0.22869  0.000048   4.504   0.0246  1.1763   1.1957
17   0.1883   17   0.18832  0.000043   4.774   0.0270  1.1737   1.1940
18   0.1440   18   0.14400  0.000038   5.150   0.0309  1.1713   1.1925
19   0.1112   19   0.11116  0.000033   5.455   0.0351  1.1686   1.1909
20   0.0935   20   0.09355  0.000031   5.762   0.0381  1.1663   1.1896
21   0.0685   21   0.06854  0.000026   6.033   0.0445  1.1639   1.1880
22   0.0555   22   0.05551  0.000024   6.311   0.0493  1.1614   1.1867
23   0.0428   23   0.04279  0.000021   6.629   0.0560  1.1589   1.1849
24   0.0337   24   0.03373  0.000018   6.953   0.0630  1.1564   1.1841
25   0.1091   25   0.10907  0.000033   7.948   0.0347  1.1474   1.1786

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

PRIMARY STATISTICS:

Initial bet advantage (IBA):-0.30923%, St. Err. 0.001161%

Total bets advantage (TBA): -0.27101%

SCORE:                       0.00

Risk of Ruin:                100%

Estim. payoff per 100,000 rounds played is -309.23, with estim. std. 367.20

Average st. dev. per round:  1.16120

Av. std. per round per unit: 1.16120

Average bet per round:       1.00000

Average bet total:           1.14100

Insurance contribution:      0.01608%
Insurance contrib. to TBA:   0.01489%

Number of sessions won:      524783
Number of sessions lost:     837439
Total number of sessions:    1362222
Percentage of sessions won:  38.5240%, St. Err. 0.04170%
Surplus bank:                342982.5

Number of shoes played:      208642697

Number of rounds played:     10000000035

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

SECONDARY STATISTICS:

AC BLJACK  PUSH  HDOUBL SDOUBL  SPLIT SURREN  INSUR  INSADV  ACDIST

-10  3.744  9.193 10.163  1.908  2.944  0.000  0.000   0.000   1.167
-9  3.841  9.196  9.963  1.888  2.915  0.000  0.000   0.000   1.446
-8  3.941  9.197  9.765  1.869  2.889  0.000  0.000   0.000   1.877
-7  4.043  9.193  9.570  1.848  2.859  0.000  0.000   0.000   2.348
-6  4.148  9.181  9.377  1.828  2.835  0.000  0.000   0.000   3.025
-5  4.252  9.154  9.189  1.807  2.808  0.000  0.000   0.000   3.835
-4  4.359  9.124  9.002  1.785  2.784  0.000  0.000   0.000   5.084
-3  4.467  9.088  8.823  1.764  2.760  0.000  0.000   0.000   6.572
-2  4.579  9.061  8.648  1.743  2.737  0.000  0.000   0.000   8.843
-1  4.684  9.040  8.489  1.723  2.715  0.000  0.000   0.000   9.588
0  4.779  8.943  8.390  1.704  2.693  0.000  0.000   0.000  14.247
1  4.899  8.891  8.451  1.775  2.668  0.000  0.000   0.000   8.337
2  5.005  8.903  8.518  1.787  2.645  0.000  0.000  -2.096   6.331
3  5.112  8.912  8.455  1.826  2.623  0.000  0.003  -1.052   4.789
4  5.222  8.927  8.344  1.804  2.602  0.000  0.027  -0.073   3.767
5  5.337  8.975  8.420  1.781  2.584  0.000  0.200   0.548   2.886
6  5.479  9.079  8.921  1.766  2.571  0.000  1.160   0.804   2.298
7  5.649  9.144  9.362  1.759  2.581  0.000  3.314   1.247   1.804
8  5.848  9.238  9.404  1.756  2.594  0.000  6.072   1.730   1.481
9  6.018  9.289  9.243  1.739  2.836  0.000  7.631   2.400   1.152
10  6.161  9.256  8.927  1.688  4.305  0.000  8.374   3.253   0.940

InsTC INSUR  INSADV  ST. ERR.

7   7.092   0.791   0.020
8   7.100   1.887   0.022
9   7.103   2.915   0.025
10   7.113   3.986   0.028

CUMULATIVE FREQUENCY OF OCCURRENCE:

Frequency of blackjack:      4.744%

Frequency of pushing:        9.024%

Frequency of hard doubling:  8.796%

Frequency of soft doubling:  1.765%

Frequency of splitting:      2.910%

Frequency of insurance:      0.642%

CORRELATION COEFFICIENTS:

AC   Correlation Coef.

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

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

Up card    17       18       19       20       21       BJ      Bust

2    13.9715  13.4466  13.0052  12.4032  11.8402     --    35.3334
3    13.4407  13.0625  12.5244  12.0833  11.4922     --    37.3969
4    13.0694  12.4157  12.1315  11.6447  11.1856     --    39.5531
5    12.1969  12.2563  11.7626  11.1824  10.7947     --    41.8070
6    16.5769  10.6320  10.6514  10.1578   9.7279     --    42.2540
7    36.8996  13.8029   7.8508   7.8747   7.3834     --    26.1886
8    12.8991  35.9747  12.8795   6.9279   6.9530     --    24.3658
9    12.0374  11.7381  35.1598  12.0435   6.0936     --    22.9277
10    11.1977  11.1723  11.1970  33.9754   3.4859   7.7168  21.2547
ace    13.0131  13.0899  13.0657  13.0908   5.3542  30.8404  11.5459

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

Cards:    2       3       4       5       6       7       8       9       10
Freq.: 45.4893 36.3655 14.8290  2.9473  0.3426  0.0251  0.0012  0.0000  0.0000

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

Card:    2      3      4      5      6      7      8      9      10     ace
Freq.: 7.6422 7.6435 7.6502 7.6515 7.6677 7.6945 7.7048 7.7159 30.9135 7.7162
```

3. ## Cacarulo: HALVES Report II

```

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

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

Simulation started  on (MM/DD/YY): 03-16-2005 at 15:11:00
Simulation finished on (MM/DD/YY): 03-16-2005 at 17:29:28
Random seed = 1234567890

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

6 decks

Shufflepoint 260 cards, (83.33% penetration)

Face up game

System used is HALVES with indices table halves2

SBA floors when calculating the true count
Remaining decks estimated exactly for true count conversion
SBA divides running count by the number of 1/2 decks remaining

American rules - hole card game

Surrender is not allowed

Dealer stands on all 17

Doubling is allowed on any two cards

Doubling is allowed after splitting

Hand can be split 3 times, up to 4 hands

No resplit of aces

Only one card to split aces

Different tens can be split

Insurance is 1 half of a bet

Predefined variables:
INSURANCE  =   3    Buy insurance if true count >= INSURANCE
H7710      =  99    Hit 7,7 versus dealer's 10 if true count < H7710

No user defined variables

No leaving the shoe at any count

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

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

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

Player's bankroll is 100

Aim bankroll is 200

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

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

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

COUNT STATISTICS (PRIMARY):

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

-25   0.0001  -25   0.00007  0.000001 -21.505   1.6418  1.3239   1.3063
-24   0.0001  -24   0.00007  0.000001 -19.929   1.5097  1.2944   1.2725
-23   0.0002  -23   0.00015  0.000001 -19.960   1.0398  1.2875   1.2680
-22   0.0003  -22   0.00031  0.000002 -16.208   0.7328  1.2873   1.2602
-21   0.0006  -21   0.00062  0.000002 -15.738   0.5169  1.2862   1.2590
-20   0.0012  -20   0.00120  0.000003 -14.643   0.3670  1.2739   1.2488
-19   0.0022  -19   0.00220  0.000005 -13.696   0.2702  1.2667   1.2417
-18   0.0043  -18   0.00428  0.000007 -12.394   0.1925  1.2595   1.2342
-17   0.0072  -17   0.00724  0.000009 -11.386   0.1472  1.2531   1.2271
-16   0.0130  -16   0.01303  0.000011 -10.137   0.1091  1.2455   1.2197
-15   0.0222  -15   0.02215  0.000015  -9.234   0.0832  1.2382   1.2128
-14   0.0342  -14   0.03418  0.000018  -8.479   0.0666  1.2313   1.2061
-13   0.0678  -13   0.06778  0.000026  -7.586   0.0470  1.2241   1.1995
-12   0.1041  -12   0.10412  0.000032  -6.831   0.0377  1.2177   1.1932
-11   0.1658  -11   0.16580  0.000041  -6.140   0.0297  1.2111   1.1872
-10   0.2667  -10   0.26670  0.000052  -5.451   0.0233  1.2047   1.1810
-9   0.4224   -9   0.42237  0.000065  -4.789   0.0184  1.1984   1.1753
-8   0.6670   -8   0.66701  0.000081  -4.161   0.0146  1.1921   1.1694
-7   1.0374   -7   1.03738  0.000101  -3.629   0.0116  1.1862   1.1639
-6   1.6496   -6   1.64964  0.000127  -3.030   0.0092  1.1804   1.1585
-5   2.5856   -5   2.58557  0.000159  -2.505   0.0073  1.1748   1.1532
-4   4.1993   -4   4.19927  0.000201  -2.004   0.0057  1.1695   1.1481
-3   6.8480   -3   6.84804  0.000253  -1.524   0.0045  1.1648   1.1431
-2  11.6894   -2  11.68941  0.000321  -1.048   0.0034  1.1604   1.1383
-1  18.5493   -1  18.54928  0.000389  -0.591   0.0027  1.1563   1.1339
0  22.7685    0  22.76852  0.000419  -0.151   0.0024  1.1549   1.1315
1  11.1955    1  11.19551  0.000315   0.427   0.0035  1.1580   1.1331
2   6.7097    2   6.70970  0.000250   0.964   0.0045  1.1546   1.1326
3   4.0703    3   4.07035  0.000198   1.504   0.0057  1.1568   1.1537
4   2.5688    4   2.56877  0.000158   2.090   0.0072  1.1597   1.1736
5   1.6022    5   1.60223  0.000126   2.707   0.0092  1.1696   1.1888
6   1.0276    6   1.02764  0.000101   3.363   0.0117  1.1818   1.1991
7   0.6443    7   0.64433  0.000080   4.014   0.0147  1.1798   1.1978
8   0.4169    8   0.41689  0.000064   4.656   0.0182  1.1750   1.1947
9   0.2552    9   0.25520  0.000050   5.268   0.0232  1.1700   1.1917
10   0.1621   10   0.16208  0.000040   5.882   0.0289  1.1655   1.1890
11   0.0982   11   0.09820  0.000031   6.472   0.0370  1.1603   1.1861
12   0.0566   12   0.05659  0.000024   7.041   0.0486  1.1555   1.1833
13   0.0398   13   0.03982  0.000020   7.518   0.0577  1.1507   1.1804
14   0.0207   14   0.02066  0.000014   8.110   0.0797  1.1462   1.1782
15   0.0116   15   0.01163  0.000011   8.602   0.1058  1.1411   1.1751
16   0.0065   16   0.00650  0.000008   9.282   0.1410  1.1367   1.1735
17   0.0037   17   0.00368  0.000006   9.857   0.1865  1.1313   1.1706
18   0.0019   18   0.00190  0.000004   9.921   0.2587  1.1274   1.1679
19   0.0010   19   0.00098  0.000003  10.509   0.3572  1.1183   1.1647
20   0.0005   20   0.00049  0.000002  10.809   0.5032  1.1185   1.1635
21   0.0002   21   0.00024  0.000002  11.579   0.7215  1.1103   1.1615
22   0.0001   22   0.00012  0.000001  12.107   1.0330  1.1163   1.1623
23   0.0001   23   0.00005  0.000001  12.635   1.5275  1.1103   1.1594
24   0.0000   24   0.00002  0.000000  12.123   2.2659  1.0987   1.1510
25   0.0000   25   0.00002  0.000000  11.399   2.4507  1.0863   1.1450

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

PRIMARY STATISTICS:

Initial bet advantage (IBA):-0.30958%, St. Err. 0.001161%

Total bets advantage (TBA): -0.27124%

SCORE:                       0.00

Risk of Ruin:                100%

Estim. payoff per 100,000 rounds played is -309.58, with estim. std. 367.00

Average st. dev. per round:  1.16055

Av. std. per round per unit: 1.16055

Average bet per round:       1.00000

Average bet total:           1.14133

Insurance contribution:      0.01582%
Insurance contrib. to TBA:   0.01488%

Number of sessions won:      523413
Number of sessions lost:     836420
Total number of sessions:    1359833
Percentage of sessions won:  38.4910%, St. Err. 0.04173%
Surplus bank:                342773

Number of shoes played:      208658952

Number of rounds played:     10000000011

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

SECONDARY STATISTICS:

AC BLJACK  PUSH  HDOUBL SDOUBL  SPLIT SURREN  INSUR  INSADV  ACDIST

-10  2.897  9.232 12.215  2.065  3.235  0.000  0.000   0.000   0.276
-9  3.060  9.224 11.759  2.036  3.175  0.000  0.000   0.000   0.435
-8  3.236  9.211 11.310  2.001  3.106  0.000  0.000   0.000   0.683
-7  3.411  9.204 10.875  1.970  3.046  0.000  0.000   0.000   1.058
-6  3.601  9.198 10.458  1.934  2.984  0.000  0.000   0.000   1.674
-5  3.797  9.192 10.048  1.897  2.926  0.000  0.000   0.000   2.612
-4  3.997  9.190  9.655  1.857  2.872  0.000  0.000   0.000   4.224
-3  4.206  9.152  9.271  1.817  2.819  0.000  0.000   0.000   6.859
-2  4.420  9.100  8.901  1.773  2.771  0.000  0.000   0.000  11.658
-1  4.634  9.050  8.565  1.732  2.726  0.000  0.000   0.000  18.428
0  4.824  8.926  8.410  1.706  2.684  0.000  0.000  -3.557  22.573
1  5.052  8.919  8.482  1.839  2.636  0.000  0.011  -0.200  11.115
2  5.285  8.962  8.280  1.797  2.600  0.000  0.564  -0.315   6.658
3  5.623  9.215  8.681  1.782  2.609  0.000  4.609   0.399   4.115
4  5.954  9.363  9.328  1.761  2.611  0.000  7.964   1.709   2.641
5  6.234  9.315  8.875  1.690  4.073  0.000  8.913   3.477   1.669
6  6.501  9.318  8.375  1.616  5.348  0.000  9.238   5.487   1.080
7  6.770  9.388  7.980  1.558  5.569  0.000  9.441   7.594   0.676
8  7.050  9.472  7.604  1.504  5.615  0.000  9.625   9.801   0.436
9  7.337  9.551  7.244  1.449  5.647  0.000  9.838  11.851   0.266
10  7.641  9.669  6.910  1.396  5.684  0.000 10.036  14.282   0.169

InsTC INSUR  INSADV  ST. ERR.

3   7.089   0.182   0.013
4   7.104   2.312   0.016
5   7.107   4.476   0.021
6   7.116   6.593   0.026
7   7.123   8.715   0.033
8   7.114  10.914   0.041
9   7.105  13.421   0.052
10   7.088  15.571   0.065

CUMULATIVE FREQUENCY OF OCCURRENCE:

Frequency of blackjack:      4.744%

Frequency of pushing:        9.025%

Frequency of hard doubling:  8.764%

Frequency of soft doubling:  1.764%

Frequency of splitting:      2.897%

Frequency of insurance:      0.806%

CORRELATION COEFFICIENTS:

AC   Correlation Coef.

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

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

Up card    17       18       19       20       21       BJ      Bust

2    13.9765  13.4457  13.0049  12.4033  11.8397     --    35.3300
3    13.4413  13.0606  12.5248  12.0825  11.4929     --    37.3980
4    13.0666  12.4162  12.1325  11.6466  11.1868     --    39.5512
5    12.1989  12.2543  11.7636  11.1825  10.7948     --    41.8059
6    16.5796  10.6325  10.6520  10.1606   9.7271     --    42.2482
7    36.8979  13.8017   7.8509   7.8738   7.3864     --    26.1893
8    12.9004  35.9720  12.8814   6.9286   6.9514     --    24.3661
9    12.0376  11.7393  35.1597  12.0416   6.0941     --    22.9278
10    11.1974  11.1729  11.1956  33.9764   3.4855   7.7171  21.2551
ace    13.0112  13.0923  13.0677  13.0931   5.3549  30.8379  11.5429

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

Cards:    2       3       4       5       6       7       8       9       10
Freq.: 45.5152 36.3475 14.8226  2.9459  0.3425  0.0251  0.0012  0.0000  0.0000

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

Card:    2      3      4      5      6      7      8      9      10     ace
Freq.: 7.6429 7.6446 7.6507 7.6518 7.6672 7.6950 7.7048 7.7150 30.9121 7.7159
```

4. ## Cacarulo: Re: Try running both sims again, . . .

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

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

That's exactly what I said in a thread below. The power of ZEN resides precisely in its insurance efficiency.
Don't need to run the sims because it is obvious that without Insurance HALVES must outperforms ZEN.

In any case, I've posted all the details of my sims just in case you or anyone wanted to verify the posted SCOREs.

Thanks.

Sincerely,
Cac

5. ## Cacarulo: Re: Sorry, can't agree

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

Haven't run sims with LS so I can't comment there.

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

The reasons could be many, namely less indices, different set of indices used, standard error (not too many rounds simmed), burned cards, more players at the table, etc.

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

That's why I posted SBA's input/output data.

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

Ahh, but BC isn't everything. You're underestimating the value of Insurance Shouldn't we use the SCORE to measure these things? :-)

Cac

6. ## JohnAuston: Re: Try running both sims again, . . .

>>Don't need to run the sims because it is obvious that without Insurance HALVES must outperforms ZEN.

Well, what say we just see, eh?

Some very smart people say it is obvious that HALVES outperforms ZEN even with Insurance.

Please. Re-run the sims that show Zen winning, but just disable the Insurance index for both Zen and Halves.

Then, if ALL the advantage goes away, we will know that that was it, and can debate whether or not that makes sense.

But if Zen still wins, then we will have learned something important that will let us continue further analysis into the "anomaly".

What would be the reason to NOT re-run the sims without Insurance?

7. ## Cacarulo: Re: Try running both sims again, . . .

> Well, what say we just see, eh?

> Some very smart people say it is obvious
> that HALVES outperforms ZEN even with
> Insurance.

> Please. Re-run the sims that show Zen
> winning, but just disable the Insurance
> index for both Zen and Halves.

> Then, if ALL the advantage goes away, we
> will know that that was it, and can debate
> whether or not that makes sense.

Seems fair.

> But if Zen still wins, then we will have
> learned something important that will let us
> continue further analysis into the
> "anomaly".

> What would be the reason to NOT re-run the
> sims without Insurance?

There's no problem, I'll do it.

Sincerely,
Cac

8. ## Zenfighter: Re: Full indexes from Norm's archived sims

From CVCX archives I?ve copied these two Norm?s reports:

```

PA Opt 1-16	Kb	Avg.Bet	%W/L	\$100 	SD/100	RoR	N0	DI	SCORE
Zen full ind.	793	34.68	1.35	46.95	706.49	13.5	21308	6.85	46.93
Halves full ind.797	33.78	1.38	46.52	706.88	13.5	21481	6.82	46.55

```

According to Norm the first one is Zen(?80), Heads up (2000 e09) and the second one Halves, Full indexes (2000 e09).

Skipping here the word ?Heads up? probably means with three other customers at the table, for the second one. Norm should clarify this. Heads up could be another story. Also 22 indexes only, too. But all in all Cacarulo has his chances being right here.

I will try to go for Catch 22.

A little of patience, please.

Zenfighter

9. ## Don Schlesinger: Too many questions

> From CVCX archives I?ve copied these two
> Norm?s reports:
>
> PA Opt 1-16 Kb Avg.Bet %W/L \$100 SD/100 RoR
> N0 DI SCORE
> Zen full ind. 793 34.68 1.35 46.95 706.49
> 13.5 21308 6.85 46.93
> Halves full ind.797 33.78 1.38 46.52 706.88
> 13.5 21481 6.82 46.55
> According to Norm the first one is
> Zen(?80), Heads up (2000 e09) and the second
> one Halves, Full indexes (2000 e09).
> Skipping here the word ?Heads up? probably
> means with three other customers at the
> table, for the second one. Norm should
> clarify this. Heads up could be another
> story. Also 22 indexes only, too. But all in
> all Cacarulo has his chances being right
> here.
> I will try to go for Catch 22.

"Full indexes" can't be an apples-to-apples comparison, because it means different things for different counts. The only way to compare is when the actual I18 (or Catch-22) are indicated, because then we know the same number of indexes, and the same plays were used for both sims.

Finally, once again, no one is addressing why the CVCX I18 sims for the two counts come out the way they do -- heavily in favor of Halves -- or why the SBA sims that John ran for BJA3 come out the same way.

Don

10. ## JohnAuston: I'm trying . . .

> Finally, once again, no one is addressing
> why the CVCX I18 sims for the two counts
> come out the way they do -- heavily in favor
> of Halves -- or why the SBA sims that John
> ran for BJA3 come out the same way.

. . . to help zero in on that ( see request to have the sims rerun, sans Insurance )

My thinking is , since the main edge Zen would have on Halves would be on Insurance, maybe the problem is there. SBA allows you set what ratio Insurance pays off at. Maybe that is accidentally set for a bigger Insurance payoff, playing to Zen?s edge?

Just guessing at this point.

John

Page 2 of 4 First 1234 Last

#### Posting Permissions

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