This calculator allows you to determine the Playing Efficiency (PE), Betting Correlation (BC) and Insurance Correlation (IC) of any card counting system.

Just plug in the tag values for each card rank and click Calculate.

**Playing Efficiency (PE)**: This is a measure of how effectively a counting system can be used to vary strategy. 0.70 is an approximate cap on the highest possible PE for a single parameter counting system.**Betting Correlation (BC)**: This is a measure of how effective a system is in detecting the player’s advantage based on the remaining cards. It is based on how closely the card counting tags match up with the effect of removal of each card rank. Good BC values can approach 1.00.**Insurance Correlation (IC)**: This is a measure of how well a counting system indicates correct insurance betting decisions.

For much more on the technical details of card counting system efficiencies, see Peter Griffin’s book The Theory of Blackjack: The Compleat Card Counter’s Guide to the Casino Game of 21

Hi

I am using Knockout counting system with a mild success.

In that book, there is a chart for basic strategy that is a little bit different than what I see everywhere else.

In KO, for a pair of 2 or 3 against the dealers 2 or 3, the decision is to HIT,

But I know that in almost all charts it is advised to split. what should I do here especially if I am playing win no-hole-card rule?

The difference is whether or not you are allowed to double after split. If yes, you should split 2s and 3s against a dealer 2 or 3. If no, then you should hit these hands instead. To get a specific chart for your exact game, see our Blackjack Basic Strategy Engine, and click Adjust the Rules.

That comment indicates you fundamentally don’t understand how it works to use a counting system to supplement basic strategy decisions. There is no counting system where you just break basic strategy in a consistent way for any reason that is not dependent on the count! For any balanced counting system, when the count is ZERO, then your decision table should match basic strategy exactly. That means you split 2’s and 3’s against a dealer’s 2 or 3, if the count is 0, and that’s why basic strategy says to do that, because on average the count WILL be 0. However, splitting 3’s against a dealer’s 2 IS the one which has its threshold pretty close to a count of 0. For instance, in the classic method known as hilo (I don’t know about knockout), where 2-6 get +1 and A and 10 get -1, the threshold is about -0.3. So you’d hit if the count divided by number of decks left goes under negative one third. If it’s 0, you split. If it’s positive, you split. A pair of 3’s against 3 and the threshold drops to -3.6. Against a 4 and it’s -6.8. A pair of 2’s against 2 and it’s -3.4, a pair of 2’s against 3 and it’s -6.1, a pair of 2 against a 6 and it’s -2.2, against a 3 and it’s -4.7. You can see why basic strategy is what it is because the basic strategy table tells you what you do when the count is 0, or more precisely, what the count would be on average by being dealt that hand. For instance, you double 9 against 2 when the count per remaining deck is more than 1.0, and that also demonstrates why you double on 9 against 2 in a 2-deck game, because just to get a 9 in the first place, you have to have gotten 2 low cards, and the dealer shows a low card, which means the count is 3, so in a 2-deck game, just by dealing a 9 against 2, the truecount is already 1.5, while in a 6-deck game the truecount is 0.5 since it’s a matter of dividing 3 by 2 or by 6, and so in the 2-deck game, basic strategy says double 9 against 2 because 1.5 is more than 1.0, while the 6-deck basic strategy says hit 9 against 2 because 0.5 is less than 1.0. But bottom line, if you’re varying strategy in accordance with ANY counting method, it will always be a function of the count. The decisions that hinge on a threshold that’s very close to 0 are the ones where it also won’t matter much on average if you do one thing or the other if you’re not counting and just using basic strategy. The decision thresholds that are closest to 0 are 16 against 10 hit/stand, 11 against A hit/double and soft 15 against 4 hit/double. Decisions that are kind of close to 0 are 3-3 against 2, soft 19 against 6, soft 18 against 2, and soft 13 against 5. In all of these, it won’t make a huge difference whether you do one action or the other if you’re not counting cards and you can just as well assume the decision thresholds are AT zero as to remember the exact numbers they are (11 against ace, the threshold is -.03, that’s super-super close, that means removing one high-card from a 30-deck shoe makes it no longer worthwhile to double 11 against ace).

How would I calculate a side count of aces effect?

Sorry, I don’t have a good answer for that. Perhaps you could estimate it by calculating the PE without the Ace included (prorate the other indexes to make it still balanced), and then do the BE with the Ace included. I have never used Ace side counts, as I found them difficult to implement accurately for the relatively small gain. As a result, I have always used counts with the Ace included (either Hi-Lo or Halves, depending on the game.)

I do not know what other people do, but for a side count I simply insert a letter in front of the running count in my head.

A-20, A-19, A-21 ect.

Strangely it works.

Thank you for the answer I am learning but know so little.

The more I read the less I know.

What about Speed Count and OPP and hand substraction ?

I cannot think of a convenient way to estimate the correlations for Speed Count. I’m not a fan anyway, as these counts are quite weak. I think the KO count is a better choice for an easy count.

Thank you.

I agree. I use ReKO. It was mainly to calculate how weak Speed Count is.

I’m not sure how much I can trust this calculator because it really ought to give some kind of error message if you give it an unbalanced system. Or at least come with some explanation of what it does for an unbalanced counting vector. This casts doubt on whether I can trust ANY of its results.

What I’m trying to do is find something which has a low correlation with hi-lo (dot product with the vector -1 1 1 1 1 1 0 0 0 -1, but with the last vector component counting 4 times as much since it’s 10 J Q or K, and then divide by the magnitudes of the 2 vectors) so that it’s undetectable to the people behind the eye in the sky the way they’re on the lookout for counters, but has a decent betting correlation. I’m playing around with 1 -1 -1 1 2 0 2 1 -1 -1 tentatively, which has a correlation of 0.3 with hi-low because A, 2 and 3 are reversed. But can I actually TRUST this thing’s results?

@observer just use hi-opt 1. It’s simpler, better, and ignoring aces and deuces helps reduce the correlation with hi-lo.