What if I use a ramp calculated for the wrong depth?

It has been pointed out that the SCORE card counting strategy comparison methodology requires optimal bet ramps and that optimal bet ramps vary by penetration. That is, you would need to use a different betting schedule at every penetration to achieve the maximum benefit. But, do we really want to use a different betting schedule for every penetration? Let us look at the penalty if we choose to use one betting ramp at all penetrations.

First, we will look at this effect using REKO. In the below chart, the SCOREs are displayed for every penetration from 26 cards cut off to 132 cards cut off. Two sets of SCOREs are displayed: REKO SCOREs using a different optimal bet ramp for each penetration are displayed in blue. For the red line, I calculated the optimal betting ramp for one penetration (4.75 out of 6 decks) and then used that fixed betting ramp for all penetrations. As you can see, at 4.75/6 (65 cards) the two lines kiss. At this point, we are using the same ramp for both the red and blue lines. The farther you get from that point, the farther the two lines diverge, as the betting ramp is farther from optimal. The differences between the two lines are the penalties for not using the optimal betting ramp at each penetration.

The good news is that, as we should not be playing at very poor penetrations and can only rarely play at high penetrations, most of the time the penalty for using one spread is not that great.

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 © 2009 Norman Wattenberger