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The effect of this stratification could thus be expected to be a reduction in the variance of the sample distributions proportional to the square of the Ten Count's correlation coefficients for the six situations examined. In addition to this reduction in variance of typically 40%, there would be the added bonus of saving computer time by not having to select the tenvalued cards using random numbers.
The results provide the continuum necessary to compare different card counting systems. Again, the following charts are best explained by example: with 10 cards left in the deck it
was proper to stand with twelve in .269 of the sample cases. The gain over basic strategy was 3.11 % in the sample, which compares with (3.16%) for the normal approximation. The Ten Count was 28% efficient, and a "special" system based on the density of the sevens, eights, and nines scored an impressive 78%.
The loss shown for the Ten counter playing a total of twelve with 21 cards left indicates the critical subsets with exactly 10 tens in them probably had an unduly large number of sevens, eights, and nines. A basic strategist (who always hits twelve) would have done better in this instance.