Insurance Gain(%)By Betting One Extra Unit In Favorable Situations 

 

					 

Halves	       Efficiency       Cards 	  Zen           Efficiency 

                                Left 

					 

					 

0.000000	0.005748	286	0.000002	0.104264	 

0.000056	0.064655	260	0.000254	0.294273	 

0.000561	0.148474	234	0.001592	0.421542	 

0.002084	0.228834	208	0.004635	0.508829	 

0.005125	0.300274	182	0.009780	0.573058	 

0.010226	0.363429	156	0.017536	0.623248	 

0.018208	0.420096	130	0.028800	0.664490	 

0.030564	0.472202	104	0.045306	0.699949	 

0.050462	0.521726	78	0.070788	0.731872	 

0.086207	0.571145	52	0.115058	0.762295


Efficiency = gain achieved /gain from perfect insurance


Statistically inferences from the above data. 

 

 

Count	Mean	Median Variance  sd        1st Quart   3rd Quart Interquart     Skewness 

								 

								 

Halves	0.0204	0.0077	0.0008	0.0284	     0.0006	0.0306	  0.0300	0.4527 

								 

Zen	0.0294	0.0137	0.0014	0.0379	     0.0016	0.0453	  0.0437	0.4138


Blackjack translations.

Mean: average value of gains.

Median: middle value of gains.

Variance: average squared deviation of gains about its mean.

Sd: square root of variance (it?s been taken before truncating it)

1st Quartile: the median of the gains below the median

3rd Quartile: the median of the gains above the median

Interquartile: 3rd ? 1st

Skewness: average cubed deviation of gains about its mean divided by the sd. cubed.

(A Bell curve?skewness = 0. That is, perfectly symmetrical. Far from being the case here)

Here the skewness validates once more Thorp and Walden?s The Fundamental Theorem of Card Counting, and thus the curve appears shifted to the right.

Enjoy!

Zenfighter