Cacarulo: BC in terms of SCORE

[Cacarulo]

The idea of these sims is to show how is SCORE affected with a little change in BC. Say one system has a 0.977 and the other 0.984. How much does this "tiny" 0.07 (0.984-0.977) means in terms of SCORE?

In order to do the analysis we need to evaluate BC in its "pure" state. This is without playing variations - ONLY Basic Strategy -. We all know that playing variations affect BC.

Sims' conditions: 6D,S17,DOA,DAS,SPA1,SPL3,NS,5/6,BS,1 player,5000 million rounds.

1) System with 0.977 BC (TKO = -1 1 1 1 1 1 1 0 0 -1)

 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 -  2 -0.428 11.542 100.00       0  0.00   0.00 10000.00 1.000   1.000  0.000 

 1 -  3  0.098 17.705  13.53 3233475  0.56   0.31  3183.67 1.351   3.141  1.000 

 1 -  4  0.362 21.707  13.53  360083  1.67   2.78  1302.56 1.527   7.677  1.000 

 1 -  5  0.625 25.961  13.53  172527  2.41   5.80  1078.32 1.703   9.274  1.000 

 1 -  6  0.888 30.361  13.53  116824  2.93   8.56  1037.74 1.879   9.636  1.000 

 1 -  7  1.115 33.709  13.53   91389  3.31  10.94  1019.05 2.009   9.813  1.000 

 1 -  8  1.323 36.627  13.53   76620  3.61  13.05  1013.84 2.116   9.863  1.000 

 1 -  9  1.540 39.894  13.53   67139  3.86  14.89  1033.70 2.234   9.674  1.000 

 1 - 10  1.761 43.351  13.53   60625  4.06  16.49  1067.40 2.357   9.369  1.000 

 1 - 11  1.950 46.097  13.53   55876  4.23  17.90  1089.64 2.453   9.177  1.000 

 1 - 12  2.138 48.866  13.53   52228  4.38  19.15  1116.74 2.549   8.955  1.000 

 1 - 13  2.331 51.788  13.53   49354  4.50  20.26  1150.49 2.649   8.692  1.000 

 1 - 14  2.527 54.816  13.53   47040  4.61  21.26  1188.88 2.753   8.411  1.000 

 1 - 15  2.726 57.920  13.53   45143  4.71  22.15  1230.62 2.859   8.126  1.000 

 1 - 16  2.927 61.082  13.53   43562  4.79  22.96  1274.87 2.967   7.844  1.000 

 1 - 17  3.128 64.288  13.53   42227  4.87  23.68  1321.05 3.076   7.570  1.000 

 1 - 18  3.284 66.567  13.53   41078  4.93  24.34  1349.15 3.153   7.412  1.000 

 1 - 19  3.439 68.849  13.53   40069  5.00  24.96  1378.15 3.229   7.256  1.000 

 1 - 20  3.598 71.220  13.53   39178  5.05  25.52  1409.68 3.307   7.094  1.000 

2) System with 0.984 BC (Cac/7 = -2 2 2 2 2 2 1 0 0 -2)

 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 -  2 -0.428 11.542 100.00       0  0.00   0.00 10000.00 1.000   1.000  0.000 

 1 -  3  0.183 20.632  13.53 1273017  0.89   0.79  2327.85 1.565   4.296  1.000 

 1 -  4  0.467 24.749  13.53  281229  1.89   3.56  1312.46 1.771   7.619  1.000 

 1 -  5  0.732 28.508  13.53  151596  2.57   6.60  1109.95 1.934   9.009  1.000 

 1 -  6  0.992 32.376  13.53  106511  3.06   9.39  1056.63 2.095   9.464  1.000 

 1 -  7  1.222 35.524  13.53   84532  3.44  11.83  1032.84 2.220   9.682  1.000 

 1 -  8  1.457 39.000  13.53   71624  3.74  13.96  1043.74 2.358   9.581  1.000 

 1 -  9  1.668 41.944  13.53   63219  3.98  15.82  1054.61 2.471   9.482  1.000 

 1 - 10  1.886 45.157  13.53   57318  4.18  17.45  1081.10 2.595   9.250  1.000 

 1 - 11  2.091 48.130  13.53   52976  4.34  18.88  1107.78 2.709   9.027  1.000 

 1 - 12  2.291 51.038  13.53   49631  4.49  20.15  1137.01 2.819   8.795  1.000 

 1 - 13  2.496 54.104  13.53   46987  4.61  21.28  1172.78 2.935   8.527  1.000 

 1 - 14  2.692 57.020  13.53   44851  4.72  22.30  1207.56 3.046   8.281  1.000 

 1 - 15  2.880 59.771  13.53   43080  4.82  23.21  1240.57 3.149   8.061  1.000 

 1 - 16  3.071 62.627  13.53   41591  4.90  24.04  1277.20 3.256   7.830  1.000 

 1 - 17  3.265 65.564  13.53   40323  4.98  24.80  1316.55 3.367   7.596  1.000 

 1 - 18  3.438 68.099  13.53   39229  5.05  25.49  1348.79 3.462   7.414  1.000 

 1 - 19  3.615 70.720  13.53   38273  5.11  26.13  1383.51 3.559   7.228  1.000 

 1 - 20  3.794 73.408  13.53   37431  5.17  26.72  1420.23 3.660   7.041  1.000 

SCORE's percentages

1- 4 = 28.06% 

1- 8 =  6.97% 

1-12 =  5.22% 

1-20 =  4.70%

Note that many people say that both systems have virtually the same BC (~ 0.98). The above analysis proves that this is not true and that this tiny difference (0.07) is not so tiny after all.

Sincerely,
Cacarulo

[Don Schlesinger]

1. Why does the ev/h not change at all, going from a spread of 1-1 (flat betting) to a spread of 1-2? If we bet two units in all positive-EV situations, instead of flat-betting, how can that fail to raise our overall EV?

2. Why, if we're trying to exploit tiny BC differences, would not the larger spreads be most beneficial, rather than the smaller ones?

Don

[Cacarulo]

> 1. Why does the ev/h not change at all,
> going from a spread of 1-1 (flat betting) to
> a spread of 1-2? If we bet two units in all
> positive-EV situations, instead of
> flat-betting, how can that fail to raise our
> overall EV?

That's a little old bug that only occurs when the expectation can't be turned into positive territory. But you're right, the overall EV should be raised although it would still be negative. From 1-3 to 1-20 believe me that the answers are correct.
Whenever I get the time I will fix that bug.

> 2. Why, if we're trying to exploit tiny BC
> differences, would not the larger spreads be
> most beneficial, rather than the smaller
> ones?

I don't know the answer to this but it seems that not with optimal betting. Perhaps, if we used a fixed scheme for all spreads then the largest would be better but then ROR won't be the same.

Sincerely,
Cacarulo