By Blackjack Rebel.
In my last article, High-Low (HL) count with 7m9c, I had suggested that Knock-Out (KO) is a better count for the shoe game than HL and I said I would not cover why in that article. So I am writing this article to explain why the KO is a better primary count for the shoe game than HL is. For the two deck game still use HL as the primary count but for the shoe game, KO is much better.1)EDITOR NOTE: This article was originally published on Oct 22, 2024. It has been republished here to simplify the presentation and make it easier to understand and use. The author is hopeful this new KO with TCRC article will draw interest and appreciates any comments or feedback.
This article will cover just the primary KO count along with a Table of Critical Running Counts (TCRC) for eight and six decks as an alternative to the High-Low (HL) for a shoe game. Some symbols used in this article are tc (or simply “t”) = true count, dp = decks played, dr = decks remaining, n = number of decks and crc = critical running count.
The KO is the HL with the sevens counted as +1 instead of 0 as in the HL. The HL is balanced at zero and so counting the sevens as +1 creates the unbalanced KO with an unbalance of four per deck. Similar to the balanced HL, start the KO at zero at the beginning of each shoe.
A major problem with switching from HL to KO was how to get accurate true counts with the unbalanced KO. This is solved with the Table of Critical Running Counts (TCRC). Use the following TCRC to get the KO true count from the KO running counts and decks played for playing strategy variations and also determine how many units to bet based using the KO running count and decks played. There is no need to do any true count calculations. Just memorized the TCRC and the betting table included in this article for the six and eight deck games which has a simple pattern. For example for a KO true count of one the crc increases by three for each deck played and for a KO true count of six the crc decreases by 2 for each deck played and they all converge to the pivot of 24 for six decks and 32 for eight decks as decks are played. The formula for six decks is crc(t) = 24 + (t – 4)*dr and for eight decks is crc(t) = 32 + (t – 4)*dr. If t = 0 then crc(t) = 4*n + (t – 4)*dr gives crc(0) = 4*n – 4*dr = 4*(n – dr) = 4*dp.
The KO indices for strategy variations are basically the HL indices. Three notable exceptions (all with a dealer up card of Ten) where the KO index is less than the HL index (see KO Risk Averse Indices chart) are: stand on hard 14 v T if KO ≥ crc(7), surrender hard 14 v T if KO ≥ crc(2) and surrender hard 13 v T if KO ≥ crc(6).
In addition to the ease of use of the KO count system where true counts can simply be looked up in a TCRC (instead of a true count calculation that is required with the HL), the KO true count at true counts of three or more where large bets are made and accuracy in true count calculations for betting and playing strategy variations is very important, are more accurate than the corresponding HL true counts.
HL has a pivot of a true count of zero and KO has a pivot of a true count of four. At a true count of six, for example, HL is six true count points away from its pivot and KO is two true count points away from its pivot and so KO true count of six using TCRC is three times more accurate than a HL true count calculation of six. In this situation, if HL true count where to obtain the same accuracy as the KO true count, decks would need to be estimated to the nearest third of a deck and HL true count calculations would need to be accurately divided by decks to the nearest third of a deck.
Consider the following example which demonstrates the accuracy of KO true count estimates as compared to HL true count estimates when the true count is close to the KO pivot of a true count of four. In the case of splitting T,T v 6 the expected value index is five but the risk averse index is six. So for six decks and estimated dr = 3 then using the risk averse index, split T,T v 6 if HL ≥ 6*dr = 6*3 = 18 and split T,T v 6 if KO ≥ crc(6) = 24 + 2*dr = 24 + 2*3 = 30. Now suppose the actual decks remaining were four and not three.
- Splitting T,T v 6 with HL = 18 is splitting T,T v 6 not a HL true count of six but at a HL true count of HL / actual decks remaining = 18 / 4 = 4.5 so T,T v 6 is actually being split below T,T v 6 expected value index of five even though the risk averse index of six was used.
- Splitting T,T v 6 with KO = 30 is splitting T,T v 6 not at a KO true count of six but at a KO true count, using tc(KO) = 4 + (KO – 4*n) / dr, of KO = 4 + (30 – 4*6) / 4 = 4 + 6 / 4 = 5.5. Thus even though the estimated decks remaining was off by a full deck to the actual decks remaining, the KO true count was at 5.5 and so was still above the KO expected value index of five for splitting T,T v 6.
Accuracy of tc(KO) to tc(HL) at tc = 3, 4, 5, 6 for n = 6 decks:
- KO = crc(3) = 24 – dr three times as accurate as HL = 3*dr
- KO = crc(4) = 24 exact as compared to HL = 4*dr
- KO = crc(5) = 24 + dr five times as accurate as HL = 5*dr
- KO = crc(6) = 24 + 2*dr three times as accurate as HL = 6*dr
Thus KO is superior to HL for the shoe game because:
- Power: KO is the theoretically most powerful level one count.
- Accuracy: KO is more accurate than the HL at true counts of three or more. KO estimation to the nearest deck is sufficient.
- Ease of use: KO with its TCRC or the simple formula crc(t) = 4*n + (t – 4)*dr is easier to use than HL true count calculations.
IMAGE CREDIT: Microsoft AI Copilot
INTRODUCTORY COMMENTS
EXAMPLES, CHARTS AND EXHIBITS
SCORE COMPARISON
TKO SIMULATIONS
Footnotes
| ↑1 | EDITOR NOTE: This article was originally published on Oct 22, 2024. It has been republished here to simplify the presentation and make it easier to understand and use. The author is hopeful this new KO with TCRC article will draw interest and appreciates any comments or feedback. |
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Received an email from Blackjack Rebel. Cacarulo has done the sims for TKO.
Blackjack Rebel replied “I showed that TKO and KO with TCRC both produce the same KO true counts. Thus the sim results for TKO also apply to KO with TCRC. The only difference is that TKO is very difficult to use while KO with TCRC is very easy to use. So these TKO sims shows that KO with TCRC should replace HL as the standard count for the shoe game since KO with TCRC is (1) theoretically more powerful than HL (2) has more accurate true counts than HL for true counts of 3 or more and (3) is easier to use than HL and if TCRC is memorized then it requires no true count calculations and if TCRC is not memorized critical running counts can be easily calculated with crc(t) = 4*n + (t – 4)*dr.“
I read the article about using the KO count with the Table of Critical Running Counts and found the explanation pretty intersting. Ive used High Low before so the idea of avoiding true count calculations caught my attention. Id definitely like to learn more about this approach….
Just finished reading about KO and the TCRC method. The part about accuracy around the pivot was especially interesting. It makes the system seem much easier to work with than I originally thought. I’m going to try going through the examples again.
I read the section about the KO pivot and critical running counts and found it surprisingly easy to follow. I had always thought an unbalanced count would be more complicated, but the TCRC seems to make it much more manageable. GOOD READ.
I came here after reading about the Knock out count for shoe games. I liked how the article explains the reasoning instead of just giving a table and leaving it at that. The tcrc approach seems quite practical.
I came across the press release on Times Business News and became interested in the blackjack techniques discussed, especially the KO count and TCRC approach. The way the system was explained made it seem much more practical and easier to understand than I expected. Definitely an interesting read.