Hi to all,

The purpose of the following sims is to show accurately how much can be gained
by using OPP/SC?. I've also simulated KO and Hi-Lo under the same conditions
so you can compare OPP/SC? against them. I did the study using two different
strategies:

a) Generic BS (BS)
b) Counter BS (CBS)

Note: NO INDICES were used in any of the sims.

At the end you'll find some extra sims in which I added more players (only BS)
so you can see how they impact on each of the different systems.

Game analyzed: 6D,S17,DOA,DAS,SPA1,SPL3,NS,5/6 pen,5000 million rounds per sim

##################################################  #############################


1) KO + BS (heads up)

 play-all | rounds played = 100.00% 
spread ev/h sd/h ror% n0 di score ekb avb unit kelly
------------------------------------------------------------------------------
1 - 1 -0.428 11.542 100.00 0 0.00 0.00 10000.00 1.000 1.000 0.000
1 - 4 0.364 22.719 13.53 389866 1.60 2.56 1418.55 1.607 7.049 1.000
1 - 8 1.274 36.008 13.53 79822 3.54 12.53 1017.32 2.111 9.830 1.000
1 - 12 2.079 48.173 13.53 53669 4.32 18.63 1116.01 2.539 8.961 1.000
1 - 16 2.836 59.869 13.53 44553 4.74 22.45 1263.68 2.943 7.913 1.000
1 - 20 3.547 70.905 13.53 39955 5.00 25.03 1417.27 3.320 7.056 1.000


2) Hi-Lo + BS (heads up)

 play-all | rounds played = 100.00% 
spread ev/h sd/h ror% n0 di score ekb avb unit kelly
------------------------------------------------------------------------------
1 - 1 -0.428 11.542 100.00 0 0.00 0.00 10000.00 1.000 1.000 0.000
1 - 4 0.467 25.994 13.53 309605 1.80 3.23 1446.36 1.839 6.914 1.000
1 - 8 1.404 38.868 13.53 76679 3.61 13.04 1076.28 2.362 9.291 1.000
1 - 12 2.251 51.662 13.53 52661 4.36 18.99 1185.53 2.852 8.435 1.000
1 - 16 2.970 62.294 13.53 43994 4.77 22.73 1306.59 3.250 7.654 1.000
1 - 20 3.731 74.177 13.53 39525 5.03 25.30 1474.69 3.697 6.781 1.000


3) OPP + BS (heads up)

 play-all | rounds played = 100.00% 
spread ev/h sd/h ror% n0 di score ekb avb unit kelly
------------------------------------------------------------------------------
1 - 1 -0.428 11.542 100.00 0 0.00 0.00 10000.00 1.000 1.000 0.000
1 - 4 0.287 25.270 13.53 776469 1.13 1.29 2226.76 1.806 4.491 1.000
1 - 8 1.116 41.159 13.53 136006 2.71 7.35 1517.90 2.473 6.588 1.000
1 - 12 1.857 55.726 13.53 90027 3.33 11.11 1672.01 3.057 5.981 1.000
1 - 16 2.562 69.848 13.53 74312 3.67 13.46 1904.05 3.616 5.252 1.000
1 - 20 3.195 82.349 13.53 66415 3.88 15.06 2122.22 4.103 4.712 1.000


##################################################  #############################


1) KO + CBS (heads up)

 play-all | rounds played = 100.00% 
spread ev/h sd/h ror% n0 di score ekb avb unit kelly
------------------------------------------------------------------------------
1 - 1 -0.471 11.704 100.00 0 0.00 0.00 10000.00 1.000 1.000 0.000
1 - 4 0.425 22.975 13.53 292503 1.85 3.42 1242.56 1.604 8.048 1.000
1 - 8 1.452 36.359 13.53 62678 3.99 15.95 910.26 2.106 10.986 1.000
1 - 12 2.364 48.700 13.53 42447 4.85 23.56 1003.35 2.535 9.967 1.000
1 - 16 3.218 60.512 13.53 35350 5.32 28.29 1137.71 2.938 8.790 1.000
1 - 20 4.025 71.720 13.53 31759 5.61 31.49 1278.12 3.317 7.824 1.000


2) Hi-Lo + CBS (heads up)

 play-all | rounds played = 100.00% 
spread ev/h sd/h ror% n0 di score ekb avb unit kelly
------------------------------------------------------------------------------
1 - 1 -0.471 11.704 100.00 0 0.00 0.00 10000.00 1.000 1.000 0.000
1 - 4 0.539 26.334 13.53 238386 2.05 4.19 1285.76 1.839 7.777 1.000
1 - 8 1.592 39.289 13.53 60920 4.05 16.42 969.73 2.358 10.312 1.000
1 - 12 2.549 52.304 13.53 42091 4.87 23.76 1073.07 2.853 9.319 1.000
1 - 16 3.353 62.947 13.53 35242 5.33 28.38 1181.68 3.245 8.463 1.000
1 - 20 4.212 75.003 13.53 31705 5.62 31.54 1335.49 3.695 7.488 1.000


3) OPP + CBS (heads up)

 play-all | rounds played = 100.00% 
spread ev/h sd/h ror% n0 di score ekb avb unit kelly
------------------------------------------------------------------------------
1 - 1 -0.471 11.704 100.00 0 0.00 0.00 10000.00 1.000 1.000 0.000
1 - 4 0.341 26.100 13.53 587135 1.31 1.70 1999.90 1.824 5.000 1.000
1 - 8 1.279 42.180 13.53 108721 3.03 9.20 1390.79 2.500 7.190 1.000
1 - 12 2.116 57.022 13.53 72627 3.71 13.77 1536.70 3.090 6.507 1.000
1 - 16 2.884 70.763 13.53 60192 4.08 16.61 1736.11 3.626 5.760 1.000
1 - 20 3.645 84.652 13.53 53940 4.31 18.54 1966.04 4.166 5.086 1.000


##################################################  #############################


1) KO + BS (4 Players playing the same strategy - Seat #1)

 play-all | rounds played = 100.00% 
spread ev/h sd/h ror% n0 di score ekb avb unit kelly
------------------------------------------------------------------------------
1 - 1 -0.425 11.541 100.00 0 0.00 0.00 10000.00 1.000 1.000 0.000
1 - 4 0.357 22.518 13.53 397984 1.59 2.51 1420.55 1.595 7.040 1.000
1 - 8 1.261 35.862 13.53 80896 3.52 12.36 1020.00 2.099 9.804 1.000
1 - 12 2.065 48.160 13.53 54369 4.29 18.39 1122.95 2.531 8.905 1.000
1 - 16 2.804 59.553 13.53 45122 4.71 22.16 1265.01 2.921 7.905 1.000
1 - 20 3.517 70.730 13.53 40448 4.97 24.72 1422.50 3.304 7.030 1.000


2) Hi-Lo + BS (4 Players playing the same strategy - Seat #1)

 play-all | rounds played = 100.00% 
spread ev/h sd/h ror% n0 di score ekb avb unit kelly
------------------------------------------------------------------------------
1 - 1 -0.425 11.541 100.00 0 0.00 0.00 10000.00 1.000 1.000 0.000
1 - 4 0.462 25.859 13.53 313279 1.79 3.19 1447.36 1.828 6.909 1.000
1 - 8 1.399 38.908 13.53 77314 3.60 12.93 1081.84 2.357 9.244 1.000
1 - 12 2.236 51.536 13.53 53120 4.34 18.83 1187.78 2.840 8.419 1.000
1 - 16 2.955 62.263 13.53 44396 4.75 22.52 1311.91 3.240 7.622 1.000
1 - 20 3.708 74.051 13.53 39889 5.01 25.07 1478.97 3.682 6.761 1.000


3) OPP + BS (4 Players playing the same strategy - Seat #1)

 play-all | rounds played = 100.00% 
spread ev/h sd/h ror% n0 di score ekb avb unit kelly
------------------------------------------------------------------------------
1 - 1 -0.425 11.541 100.00 0 0.00 0.00 10000.00 1.000 1.000 0.000
1 - 4 0.233 25.240 13.53 1170552 0.92 0.85 2730.78 1.775 3.662 1.000
1 - 8 1.000 41.172 13.53 169435 2.43 5.90 1694.76 2.462 5.901 1.000
1 - 12 1.684 55.645 13.53 109238 3.03 9.15 1839.12 3.033 5.437 1.000
1 - 16 2.315 69.144 13.53 89196 3.35 11.21 2065.02 3.554 4.843 1.000
1 - 20 2.941 82.792 13.53 79232 3.55 12.62 2330.45 4.079 4.291 1.000


##################################################  #############################


From the above charts we can draw some interesting conclusions:

A) For a 1-16 spread OPP/SC captures from the other systems the following percents:

1) From KO    +  BS = 13.46/22.45*100 = 59.96% 
2) From Hi-Lo + BS = 13.46/22.73*100 = 59.22%
3) From KO + CBS = 16.61/28.29*100 = 58.71%
4) From Hi-Lo + CBS = 16.61/28.38*100 = 58.53%


B) Note that if we were to compare OPP/SC against KO or Hi-Lo with their corresponding
C22 indices we would have a terrible performance under the same spread. To wit:

1) KO    + C22 = $40.69 
2) Hi-Lo + C22 = $40.43


OPP + CBS would capture 16.61/40.69*100 = 40.82% from KO
and 16.61/40.43*100 = 41.08% from Hi-Lo.

C) Using more players makes OPP/SC's SCORE to deteriorate more than the other systems do.

Hope this helps.

Sincerely,
Cacarulo