Request for sim of KO with TCRC vs HL

Just to remind you, your TC number accuracy at TC= +0 and +1 will be a lot worse than that of HiLo. I'm still not certain if the accuracy at +6, +7 and +8 will be worse or not.
 

Furthermore, all your argument is based on the assumption that you can keep the KO count perfectly correct at the end of the shoe.  Not off even by one point

KO or KO with TCRC should be used for the back counted shoe game so you really do not even care about KO true counts of zero or one.  Use TKO or KO with TCRC for the back counted shoe game, estimate decks remaining to the nearest full deck and use risk averse indices for doubles, splits and late surrender.

For true counts less than 2 HL true count is more accurate than KO true count.

For true count of 2 HL and KO have the same accuracy.

For true counts of 3, 4, 5, 6, 7, 8 KO true count is more accurate than HL true count.

Accuracy of tc(KO) to tc(HL) at tc = 2, 3, 4, 5, 6, 7, 8 for n = 6 decks:

1. KO = crc(2) = 24 – 2*dr sane accuracy as HL = 2*dr
2. KO = crc(3) = 24 – dr three times as accurate as HL = 3*dr
3. KO = crc(4) = 24 exact as compared to HL = 4*dr
4. KO = crc(5) = 24 + dr five times as accurate as HL = 5*dr
5. KO = crc(6) = 24 + 2*dr three times as accurate as HL = 6*dr
6. KO = crc(7) = 24 + 3*dr (7/3) times as accurate as HL = 7*dr
7. KO = crc(8) = 24 + 4*dr two times as accurate as HL = 8*dr

KO pivot is a true count of four and HL pivot is a true count of zero.

At t = 0 or 1 the true count is closer to the HL pivot of a true count of zero than the KO pivot of a true count of 4.  So HL is more accurate than KO at t = 0 or 1, but who cares. At t = 0 or 1 you are either betting table minimum or a small bet and you are using for the most part basic strategy.

And I would like to comment on your statement “your argument is based on the assumption that you can keep the KO count perfectly correct at the end of the shoe.  Not off even by one point”

Keeping KO running count accurately is no different than the requirement of blackjack teams using HL that their players keep the HL running count accurately. KO like HL is a simple level one count system and yes, you need to keep both HL and KO correctly. HL teams have their counters practice counting down a deck accurately in less than a minute and they have training sessions where you fail if you make mistakes in the HL running count too frequently. KO and HL are simple level one counts and you need to practice to keep the running counts of both accurately.

I started to understand your proposal. Basically, you back count about 95% of the time. You Wong in at the end of the shoe and when your running count is greater than 22. You bet $100/$200/$300/$400/$500 at RC=+23/+24/+25/+26/+27, respectively. 
 

This has nothing to do with 1/4, 1/2, and 1 deck estimates for the remaining deck number. Right?

That is not what you do at all. With KO with TCRC you play blackjack just as you do with HL  At HL = dr or KO = crc(1) you have a  true count of one for a neutral game and that is when you can start increasing your bets.  When I say back count I mean you leave the table when HL < (-2)*dr or KO < crc(-2).

Read and read carefully the articles I gave you before and which I will include again below and  you will understand.

https://www.blackjackreview.com/wp/2025/09/14/ko-with-table-of-critical-running-counts-2/                                                                                                                                                                                                                                                       

https://static.bjrnet.com/pdf/KO_WithCriticalRunningCounts/KOwithTCRCexhibits.pdf 

 . 

Actually, I'm interested in another terminology you have been frequently using, that is, Risk Averse Index.  What is it? I've never used it myself. 

Here is the deal. If you can make me understand Risk Averse Index, I will provide the SCORE numbers for you. As far as I can tell, you know something I don't know. 

Here you have the sims:

A) Rules: 6D,S17,DOA,DAS,SPA1,SPL3,LS,5/6,R22+FAB4 indices,50 billion rounds

             1-12(PA)    1-16(PA)    1-4(BC)
-------------------------------------------
TKO-H       54.79        62.21        90.41
TKO-F        54.54        61.92        89.84
HILO-H      53.10         60.27        87.45
HILO-F       52.39        59.38        85.84
KO               51.63        58.91        86.09
-------------------------------------------
 

B) Rules: 6D,S17,DOA,DAS,SPA1,SPL3,NS,5/6,R22 indices,50 billion rounds

             1-12(PA)    1-16(PA)    1-4(BC)
-------------------------------------------
TKO-H       37.03        42.94        66.96
TKO-F        36.81        42.71        66.55
KO              35.20        41.03        64.19
HILO-H     35.19         40.81        63.94
HILO-F      34.64        40.16        62.51
-------------------------------------------

Sincerely,
Cac

This above is quality research, but one line is missing, that is, the SCORE value when exact deck number is used for true count calculation. Great work! 

Cac did an excellent job!  Thank you very much Cac.

Cacs sims show exactly what I predicted. For true counts of 3 or more KO with TCRC or TKO true counts are very accurate and for the back counted shoe game there is very little to gain by using more accurate estimate of decks renaming for TKO. 

But HL true counts compared to TKO is much more sensitive to errors in estimating decks remaining for true counts of 3 or more than TKO is. Thus the increase in the score from going from F (decks remaining estimated to the nearest full deck) to H (decks estimated to the nearest half deck) is much greater for HL than it is for KO. 

Thus for TKO or KO with TCRC, estimating of deck remaining to the nearest full deck is more than adequate. Also Colin Jone’s sims showed that the major gain in HL true count accuracy occurs in going from F to H estimation of decks remaining. Going from H to quarter or exact estimate of decks remaining will give very little extra advantage.

Oh  I neglected to answer Aceside's question on RA (risk averse) indices. I did not make up and I would never take credit for RA indices. They have been around for a long time. Google risk averse blackjack indices and you will see many articles.. In my KO with TCRC article listed a chart with the RA indices I used for KO with TCRC.

Here is a history of RA indices that I found on the web:

Risk averse indices in blackjack are strategies designed to optimize a player's utility by minimizing variance while maximizing expected value (EV), allowing for more aggressive betting without significantly increasing risk.

What are Risk Averse Indices?

Risk averse indices are a set of strategies used in blackjack that focus on reducing the variance of specific decisions while still capturing a significant portion of the expected value. These indices were first introduced by Joel Friedman in 1980 and have since become a part of mainstream blackjack theory. They allow players to make more informed decisions about when to increase their bets, particularly in high-stakes situations.

You definitely know a lot about risk averse indices. Still, I’d like to use a real example to demonstrate how a risk averse index is calculated.
 

For example, the 10 vs. 10 HiLo Double-down EV max deviation index is at TC=+4. Is there a risk averse index for this decision? How to minimize variance while maximize expected value (EV)? What is the math formula here? Please help!

I know Don and Gronbog discussed this a lot, but I really haven’t paid very much attention to this part. 

I am not an expert on RA indices and we are getting away from the purpose of this post which was to do simulations on KO with TCRC or TKO and compare it with HL to show TKO or KO with TCRC is the better count system. 

You just have to know how to se RA indices. 

For doubling hard 10 v T, the expected value index for both KO and HL is around 4. The risk averse HL index for this play
is 7 but I judgmentally chose the risk averse KO index as 6. This is because for this play, CC(HL) = 81.1 % but CC(KO) = 90.9%.

Don't get bogged down in details. Just switch to KO with TCRC for the shoe game and use the RA indices I put in a table on my KO with TCRC article.

Cac's sims prove what I was saying all along. He proved my predictions correct.

KO with TCRC with decks estimated to the nearest full deck and using the simple critical running count formulas or memorizing TCRC is easier to use that HL and calculation of HL true counts, requires less computation and so less errors, can be played quicker with less mental fatigue than HL and is a stronger system than HL and so KO with TCRC should replace HL as the industry standard for the shoe game.

I do not buy your conclusion, because it relies heavily on other people’s random work. To convince me, you must show your math step-by-step right here.

Also, based on the few posts you have presented so far, I judge you do not understand SCORE.  This terminology was created by Don, but he is right here. I’d like to hear what he may say about this. 

See  BJA3, pp. 370-377. Everything you could possibly want to know about r-a indices, with all the math is there.

Don

Why is the difference for estimating to half decks vs full decks so much larger in Hi Lo vs TKO? The differences are 2.5 to almost 3 times as large. 
 

Wondering why these counts would be effected so differently by deck estimation method.

Thanks,

Phil

I am going to use your simulator to get the SCORE numbers with exact remaining deck numbers. These numbers above mean nothing. They also could be wrong. 

The Hi-Lo RA index for 10 vs T is +7. Find the paper by Joel Friedman or read about them in BJA3. There is no formula. They are computed by iterative simulation.

Aceside wants to see the TKO and HL SCORE with decks estimated exactly. That is a total waste of time.

Refer to Colin Jones' sims of HL with decks estimated to the nearest full deck, nearest half deck and nearest quarter deck.

https://www.blackjackapprenticeship.com/bja-guide-to-deck-estimation/ 

Scenario: 6 Deck Game (4.5 of 6 decks dealt): S17, DAS, RSA*

Bet Spread: 1-12 Spread, wong-out at True -2

EV with Full-Deck Divisor: $39.80/hr; N0: 343 hours

EV with Half-Deck Divisor: $42.14/hr; N0: 331 hours (6% more than Full Deck)

EV with Quarter-Deck Divisor: $42.50/hr; N0: 329 (7% more than Full Deck)

Practical Considerations

More complex isn’t always better.

First off, more complex can mean more room for error. Most of us can, with a little practice, divide our

running count by any whole number. But dividing by half-decks is a bit more of mental gymnastics. And

dividing by quarter-decks takes even more brain power.

The more mental energy it takes to do your true count conversion, the more room there is for making

mistakes. And mistakes will cost you MUCH more than the 5-10% increase in EV you might get for using a

more complicated divisor.

What you are going up against is the law of diminishing returns. Going for the HL going from full deck to half deck estimation is where you get most of your gain which Colin put at increasing EV by 6%. Going to quarter deck your EV is increased 7%, only an additional 1% increase. And if you sim exact true counted to the exact number of decks remaining I would assume your increase would also be pitiful additional 1% or less. Stop trying to get HL SCORE for estimated decks past half deck – something that is very difficult for humans to do and produces almost no additional gain. For KO even improving from full deck estimation to half deck estimating is pitiful and gong to quarter or exact is a total waste to time.

You are must better off using KO with TCRC estimated to the nearest full deck and either doing simple crc calculations or memorizing TCRC so you do not even have to both doing any calculations at all and just mentally look up the required crc in a fraction of a second.

So as I said before for KO with TCRC just estimated decks to the nearest full deck and you will be fine. And if you want additional improvements use RA indices and even add a simple plus/minus side count such as 5m7c to KO but do not waste your time and energy in trying to estimate decks less than to the nearest full deck for KO with TCRC or to less than half deck for HL.

To answer the question 

Why is the difference for estimating to half decks vs full decks so much larger in Hi Lo vs TKO? The differences are 2.5 to almost 3 times as large.

Refer to my previous post on Oct 30, 2025, 9:39:54 AM

KO with its pivot at a true four of four, for true counts around 4 where large bets are made KO gives extremely accurate true counts and are not effected much by errors in estimating decks remaining and it is the KO accuracy at these true counts with large bets out which has the great impact on the SCORE. So KO is already accurate around it pivot of a true count of 4 and so increasing deck reaming accuracy does not help KO much. This is what I predicted before I got Cac's sims to prove that I was correct.

But HL pivot is at a true count of zero so for true count of 4 where large best are made, HL is much more sensitive to errors in estimating decks remaining that KO is and that is why increasing the accuracy of decks remaining helps improve HL SCORE much more than it improves KO SCORE.