KO versus HiLo Strategy Comparison

It has taken some time for old-timers like myself to understand just how powerful the Knock-Out Blackjack Strategy is in comparison to True Counted Blackjack strategies. Since Peter Griffin's time, we have always believed that unbalanced card counting strategies cannot match the power of True Counted card counting. The common comparison is between the HiLo and KO strategies. It turns out that KO and Hilo when compared using SCORE methodology are essentially equal.

Now 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 should have a different betting schedule depending on the total penetration in a game. In theory, this should be more of a problem with unbalanced strategies as they are known to be weaker at very low and high penetrations. Let us look at this effect in KO. In the below chart, the SCOREs are displayed for every penetration from 26 cards cutoff to 132 cards cutoff. Two sets of SCOREs are displayed: KO SCORE (optimal bet ramp varying by penetration) 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.

This means that if you select one betting ramp for all penetrations; you will not be betting optimally at other penetrations and this will hurt your performance.

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 Blackjack strategy, by its nature, is a bit better at maintaining near optimal performance with a fixed betting schedule. But, it is not perfect.

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 card counters 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. 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.

Link to the Raw Data behind this chart – Chart 3

Now you could select two center points using two betting ramps to greatly broaden the range of penetrations at which KO and HiLo compare favorably. So let's take the next step. I created one betting ramp optimized at 97 card penetration and another at 58 cards. The idea is to use one for 4.5 deck penetration and above and one for below 4.5/6. To be absolutely fair, I did this for both KO and HiLo. Now, I calculated the c-SCOREs for every penetration for KO and HiLo using this scheme and plotted them below:

In summary, from a penetration of 41 cards to 124 cards (3.63/6 to 5.21/6) KO performance varies from 99.5% to 102% of HiLo. I believe this is all reasonable penetrations using one set of indexes and two betting ramps for both KO and HiLo at all penetrations. The conclusion is that the KO and HiLo card counting strategies are essentially equal in performance without the requirement for memorization of numerous betting ramps.

Link to Raw Data for – Both Charts