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Modern Blackjack nth Edition

SCOREs in Unbalanced Blackjack Counts — Is There a Flaw?

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Back in 2006, someone insisted that measuring results using the SCORE methodology was flawed when comparing unbalanced with balanced strategies. The point was that SCORE assumes the use of optimal betting ramps, and that with unbalanced strategies, the optimal betting ramps vary substantially by penetration. Therefore, since it is it unreasonable to believe that anyone would use a different betting ramp for every penetration, SCOREs suggest unbalanced strategies perform better than they actually do in a casino. Since my responding study never made it into my book, I will repeat it here.

Now it has been pointed out that the SCORE methodology requires optimal bet ramps and that optimal bet ramps vary by penetration. Let us look at this effect in KO. The below chart shows KO SCORE versus KO with a fixed betting ramp. The green line provides the SCOREs for KO (S17, DAS, 6D, 1-15.) For the red line, I calculated the optimal betting ramp for 4.75/6 penetration and then used that fixed betting ramp for all penetrations. As you can see, at 4.75/6 (65 cards) the two lines kiss. The farther you get from that point, the farther the two lines diverge as the betting ramp is farther from optimal.

For the second chart, I used exactly the same process for HiLo. Here you see the same effect; but it is less dramatic than in the KO chart. This is because a balanced strategy, by its nature, is a bit better at maintaining near optimal performance with a fixed betting schedule.

OK, Let’s put the data together. In the
third chart, I plotted KO fixed spread with HiLo fixed spread. This chart shows
KO and HiLo performing about the same at the typical penetrations (KO wins very
slightly) and HiLo beating KO at high and low penetrations. Of course you
shouldn’t play very poor penetrations and unfortunately no one will let you play
deep penetrations.

Now I picked 4.75/6 as my center point. This provides KO with 99% to 100.7% of HiLo performance from 44 to 90 cards cut off. You could pick a different center point if you tend to play different penetrations. Or, you could select two center points using two betting ramps to greatly broaden the range of penetrations at which KO and HiLo compare favorably. My point is that you do not need to memorize 100 different betting ramps. One or two is fine. If you want the best possible performance, generate a table of ideal betting ramps for every penetration and carry it with you. Hit the Betting Report button in CVCX and this is automatically created.

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Updated 04-24-2012 at 10:53 AM by Norm

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