By Blackjack Rebel.

In my final article, High-Low (HL) rely with 7m9c, I had advised that Knock-Out (KO) is a greater rely for the shoe sport than HL and I mentioned I’d not cowl why in that article. So I’m writing this text to elucidate why the KO is a greater major rely for the shoe sport than HL is. For the 2 deck sport nonetheless use HL as the first rely however for the shoe sport, KO is significantly better.

This article will cowl simply the first KO rely alongside with a Table of Critical Running Counts (TCRC) for eight and 6 decks as a substitute for the High-Low (HL) for a shoe sport. Some symbols used on this article are tc (or just “t”) = true rely, dp = decks performed, dr = decks remaining, n = quantity of decks, and crc = crucial operating rely. The linked PDF reveals the derivation of crc(t) = 4*n + (t – 4)*dr.

I understand that the HL is the usual for workforce play and this is the reason I wrote a separate ebook *HL with facet counts*. HL gamers usually don’t need to swap counting methods. But switching to the KO may be very straightforward to do and most KO taking part in technique variation indices are the identical because the HL indices. The few variations are proven within the linked PDF to this text.

My different books along with *HL with facet counts* that will probably be printed are *KO made easy* (which incorporates TCRC which is roofed on this article in addition to many extra particulars), *KO with facet counts*, *Spanish 21 with facet rely* and *Simple Plus/Minus facet counts.*

The KO is the HL with the sevens counted as +1 as an alternative of 0 as within the HL. The HL is balanced at zero and so counting the sevens as +1 creates the unbalanced KO with an unbalance of 4 per deck.

The HL is a balanced rely and so the HL pivot is a real rely of zero. At the HL pivot of zero when HL = 0, true rely HL is zero all over the place within the shoe and is unbiased of decks performed. The KO is unbalanced at 4 per deck and the KO pivot is at a real rely of 4. Similar to the HL which has a pivot at a real rely of zero being unbiased of decks performed at its pivot level, the KO rely can also be unbiased of decks performed at its pivot level which happens on the KO true rely of 4 which is a KO operating rely of 4*n. When KO is at its pivot level of KO = 4*n, the true rely KO is 4 all over the place within the shoe unbiased of decks performed. This is just like HL at its pivot of zero which has a real rely of zero all through the shoe unbiased of decks performed at its pivot level. KO having a pivot of a real rely of 4 makes all of the distinction in making KO a superior rely to the HL for the shoe sport the place true rely accuracy is paramount when bigger bets are made which happen at true counts of 3 or extra.

When dealing with the HL that you must continually estimate decks remaining and do true rely calculations. Your giant bets are out when the true rely is 3 or extra and that is the place you want accuracy within the true counts and that is the place the KO benefit is available in since its pivot is a real rely of 4.

Using a desk of crucial operating counts you now not must do true rely calculations however merely “look up” in your head the KO true rely based mostly on the KO operating rely and decks performed. Also estimating to the closest deck performed is greater than ample to calculate the KO true counts when KO true rely is three or bigger.

For true counts higher than two, the KO true rely desk lookup is extra correct than the HL true rely calculations because the KO true rely is much less delicate to errors in estimating decks performed for these greater true counts and there’s no division concerned in acquiring a real rely as with the HL which is one other potential supply of error. With KO only a easy desk lookup is required. At KO = 4*n, the true rely KO is 4 and is completely unbiased of decks performed or decks remaining as talked about above. At true rely KO of 5, the KO true rely is 5 occasions much less delicate to errors in estimating decks remaining because the HL is. So if a KO participant is estimating decks performed to the closest deck at a KO true rely of 5, a HL participant, to acquire comparable accuracy in his true rely calculation, must estimate decks remaining to the closest one-fifth of a deck. Also the HL participant would additionally have to do an correct division with the decks remaining to the closest one-fifth of a deck. The KO participant does no true rely calculations however merely makes use of the Table of Critical Running Counts to get his true rely. This is all coated with examples within the linked PDF.

The standalone KO is the strongest stage one major rely (no facet counts) and is extra highly effective than the standalone HL as confirmed by weighted CC (Correlation Coefficients) additionally proven within the linked PDF.

The KO with its unbalance of 4 per deck additionally makes for very straightforward calculations of some facet bets. For instance, Lucky Ladies (LL) with payouts of 4, 10, 25, 200 and 1000 to 1 for any twenty, suited twenty, suited and matched twenty, QHQH no vendor blackjack and QHQH vendor blackjack has an very simple rule of when to begin betting LL. Bet LL for six decks each time KO is bigger than or equal to 27. This easy rule robotically adjusts for greater KO true rely wanted as decks remaining decreases. There isn’t any true rely calculations or changes, merely examine KO to 27 and play if LL if KO is bigger than or equal to 27 for the six deck sport. This can also be defined within the linked PDF.

If passing by a blackjack shoe that already has a number of decks within the discard tray and also you discover many small playing cards on the desk, begin counting that shoe with the KO and use KO for desk entry. Even if many low playing cards are usually not seen, begin counting that desk for 3 or 4 rounds, roughly one deck. If tc after counting one deck is at the least one, then enter the desk. So, after counting one deck in an eight deck shoe, if KO ≥ 11, then sit down and begin taking part in.

For the eight-deck sport tc = 1 when KO = 11, 14, 17 and tc = 2 when KO = 18, 20, 22 when dp = 1, 2, 3, respectively, the place dp = decks performed or decks counted if not getting into the sport because the starting of the shoe.

An benefit of the KO over the HL is that for six decks if KO = 24 or eight decks if KO = 32 then tc(KO) = 4 all over the place within the shoe and so is unbiased of decks performed. You do not need to fret concerning the decks you counted or didn’t rely nor any true rely calculations. Therefore, a big wager on every of two fingers might be made when KO ≥ 24 for six decks or KO ≥ 32 for eight decks regardless of the quantity of uncounted decks earlier than getting into the shoe.

Finally the KO is a significantly better major rely so as to add plus/minus facet counts to and produces a extra highly effective rely system than including plus/minus facet counts to HL.

Why swap from High-Low to KO for the shoe sport?

I wish to clarify why I select for blackjack the unbalanced KO rely as the first rely as an alternative of the ever present balanced HL.

First, the KO rely is barely extra highly effective than the HL with the next taking part in effectivity as will probably be proven later on this ebook by evaluating the WACCs. But extra importantly, the KO rely with a pivot of a real rely of 4 is good for the six-and-eight deck video games. For the shoe sport, a pivot at a real rely of 4 is extra helpful than a pivot at a real rely of zero for a balanced rely, as will probably be defined beneath. A TCRC for the KO will probably be developed, which may be very straightforward to memorize since there are patterns to the development of the TCRC. Once the TCRC is memorized, the operating counts similar to a desired KO true rely and decks performed can simply be retrieved from reminiscence with no division or different math concerned.

Although the first KO rely is unbalanced with a pivot of a real rely of 4, all facet counts are balanced plus/minus counts and so are straightforward to rely and hold monitor of with the help of chips that will probably be described in different books. It is to be famous that if a balanced rely is added to or subtracted from an unbalanced rely, the ensuing derived rely can also be unbalanced with the identical unbalance as the unique unbalanced rely. Thus, when plus/minus balanced facet counts are added to or subtracted from the KO rely, for instance, the ensuing derived rely can also be unbalanced with an unbalance of 4 per deck, the identical unbalance because the KO rely.

I recommend the next three standards in figuring out the first and facet counts to make use of that are defined intimately in my different books. I selected the phrases beneath on this description and can describe what I imply by these phrases.

First, the rely have to be **highly effective**, (also referred to as

*precision*or

*exact*), as measured by betting correlation of the rely for betting effectivity and by WACC (Weighted Average Correlation Coefficient) for enjoying effectivity that are in contrast between the assorted counts into account. CC (Correlation Coefficients) between the tag values of the first rely or any of its derived counts (DC), which for the KO is DC = KO + okay*(XmYc), are calculated for the assorted taking part in technique conditions and a weighted common of these CCs is calculated giving the WACC for that rely.

XmYc = X minus Y rely with X and Y being a card rank, EoR = Effect of Removal for every strategic taking part in technique choice and ‘k’ is an actual quantity fixed (‘k’ is usually rounded to an integer or half integer). The DC, just like the KO rely, has an unbalance of 4 per deck and the worth of ‘k’ is chosen for any given specific taking part in technique scenario to maximise absolutely the worth of the infinite deck CC between the tag values of the DC and the EoR for the given taking part in technique scenario. The precise method will probably be defined extra absolutely in my different books. Here I can’t be utilizing any facet counts and can solely cowl the stand-alone KO rely.

Second, the rely have to be **correct** for true counts of 2, 3, 4, 5, and 6. The KO is an unbalanced rely with a pivot at a real rely of 4 so the KO is unbiased of decks performed at its pivot level and so is precise at a real rely of 4. At true counts of 3 and 5 the gap from the pivot is one true rely level, so true counts of 3 and 5 are much less delicate to errors in estimating decks performed at these true counts than is a balanced level rely system, which has a pivot level which is a real rely of zero, that’s three true rely factors away from a real rely of 3 and 5 true rely factors away from a real rely of 5, making the balanced rely very delicate to errors in estimating the decks performed at these greater true counts when the utmost wager is out and so accuracy is most vital. And at true counts of 2 and 6, the gap from the KO pivot level is 2 true rely factors. Note {that a} true rely of 2 can also be two true rely factors away from a balanced rely which has a pivot of a real rely of zero however a real rely of 6 is six true rely factors away from a balanced rely with a pivot of zero however solely two true rely factors away from KO + okay*(XmYc) which has a pivot of a real rely of 4. Accuracy in true rely calculations for enjoying technique departure at a real rely of 6 the place the utmost wager is out is rather more vital than accuracy in taking part in technique at a real rely of 2 with a comparatively small wager out. So the KO + okay*(XmYc) continues to be comparatively insensitive to errors in estimating decks performed at true counts of 2 and 6. It can also be to be famous that, as defined earlier, if a balanced rely is added to an unbalanced rely with an unbalance of ‘u’ per deck, the ensuing derived rely can also be unbalanced with an unbalance of ‘u’ per deck. Since the KO is unbalanced with an unbalance of 4 per deck and so has pivot at a real rely of 4, then all KO + okay*(XmYc) derived counts are additionally unbalanced with an unbalance of 4 per deck and they also all even have a pivot at a real rely of 4.

The last standards utilized in deciding on the first and secondary facet counts are **simplicity **aka

**. Note that the KO is a level-one rely and the facet rely, (XmYc) can also be a level-one plus/minus rely which counts solely two playing cards. This makes retaining each counts easy and simple to make use of. However, KO is less complicated to make use of than HL as a result of HL requires true rely calculations and correct estimation of decks performed whereas for true counts higher than three KO is extra correct than HL and KO simply requires a fast psychological lookup within the TCRC and estimation to the closest full deck is greater than ample for true counts higher than 3.**

__ease of use__*So the KO + okay*(XmYc) meets all three standards giving excessive marks in energy as measured by the CC for each taking part in effectivity and betting effectivity, accuracy at true counts of 2, 3, 4, 5, and 6 and ease of use in a on line casino atmosphere and beats the HL in all three classes.*

Using Correlation Coefficients to match energy between numerous rely methods

Note that utilizing the CCs of the tag values of every counting system with the EoR for every scenario offers outcomes, versus simulations, which have zero variance. The solely query within the use of CCs to measure relative taking part in effectivity energy between numerous counts is the choice of the weights. Using my chosen weights, the outcomes of the taking part in effectivity energy of numerous major counts is proven in WACC of every rely and the betting effectivity is proven within the betting correlation coefficient of every rely.

*HL vs KO, S17*the place particular person CC for the HL and KO are in contrast towards one another. For betting there is only one CC so there isn’t any weighting concerned and so BCC is similar as betting effectivity. For the CC for particular person technique adjustments what I did was calculate a WACC to summarize the CC between the assorted counts. Referring to

*HL vs KO, S17*chart once more you will note 33 technique change included in WACC calculation. WACC is just not technically taking part in effectivity however is a proxy for enjoying effectivity since as WACC will increase, the taking part in effectivity will increase and SCORE additionally will increase.

In the above chart solely WACC is proven. Looking once more on the exhibit labeled *HL vs KO, S17 *on web page 20 of the linked PDF you will note that I spotted I ought to have added extra technique adjustments to WACC so what I did was calculate OCCC (Other Cases CC) the place I put 12 further technique adjustments simply to be full. So each WACC and OCCC needs to be used to match relative taking part in effectivity between numerous rely methods. But for simplicity right here I reference solely WACC which is usually adequate to match taking part in effectivity between numerous rely methods. Also a have a look at the exhibit labeled *HL vs KO, S17 *on web page 20 of the linked PDF you will note LSCC (Late Surrender CC) so when LS is obtainable, the facility of LS taking part in effectivity between numerous counts might be in contrast.

In the chart above I’ll take into account solely WACC to match taking part in effectivity between numerous primacy counts with no facet counts. As described beforehand betting effectivity is instantly in contrast utilizing simply BCC for S17, DAS, LS and S17, DAS, no LS. Note that utilizing my chosen weights, the WACC of the Hi-Opt 2, aka, HO2, comes out on high, as anticipated. So, for major counts, power-ranking counts for enjoying effectivity utilizing WACC with my chosen weights reveals HO2 with the very best taking part in effectivity. These outcomes agree with simulations, which provides confidence to my chosen weights and the method of utilizing WACCs to measure relative taking part in effectivity between counts. Also, not like simulations, the WACC methodology used to measure relative taking part in effectivity between totally different counts has zero variance and might be completed in a matter of minutes and doesn’t require any indices or betting ramps.

Disadvantages of Simulations:

- Takes a very long time to run and are tedious to arrange.
- Requires the calculation of indices for every taking part in technique (one other potential supply of error) for every of the counts being in contrast.
- There can also be the issue of variance with simulations which is lowered by rising the quantity of fingers simulated.
- The optimum wager for every given rely must be calculated and considered.

Advantages of Correlation Coefficients:

- WACC and BCC might be completed in a matter of minutes.
- WACC and BCC are precise with zero variance.
- WACC and BCC used to match numerous counts require no indices.
- Same judgmental weights for the CC of every technique change is utilized to each rely analyzed so there isn’t any bias within the calculation of WACC between totally different counts. All counts use the identical judgmental weights.
- No worries about numerous betting ramps for numerous counts and the way variations in betting ramps have an effect on the betting is not directly thought-about in selecting the judgmental weights of the assorted counts based mostly on frequency of the technique change and the estimated common quantity wager on that scenario.

Correlation Coefficients are calculated with the tag values of the rely being analyzed and the EoR. EoR are LSL estimates, in order that they assume that blackjack is linear. Simulations don’t have any assumptions on blackjack being linear. With lower than one deck remaining, non-linearity kicks in.

Finally in simulations all taking part in technique and betting adjustments are lumped collectively into one last end result. If there’s a downside with a selected technique change it’s masked within the last end result. Correlation Coefficients however supply surgical precision the place every technique change is individually analyzed.

**IMAGE CREDIT: Microsoft AI Copilot**

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