Request for sim of KO with TCRC vs HL

Your statement “KO with TCRC … involves no true count calculations at all” is false.  You must learn to be more logical. 
 

About a year ago, I compared KO, Hi-Lo, TKO on double-deck games. These results were posted here.
 

For 6-deck games, I can post the SCORE numbers, but I need Gronbog or Cacarulo to say something first. 

In my simulator https://www.blackjack-hack.com/blackjack-hack.php for true count you can divide by the number of decks remaining or the number of half decks remaining. 
 

It has approximate or exact number of decks or half decks remaining. Approximate is to the nearest 1/2 deck, exact is the exact number of decks remaining (to several decimal points as exact as the processor does it). 
 

Thanks,

Phil

If using an unbalanced count then running count should be selected in my simulator. I am not certain that true counts are calculated correctly for unbalanced counts. It just divides running count by decks remaining, same as it would for a balanced count. Which I guess is not correct for unbalanced counts.

Phil

In a previous thread I showed:

TKO produces correct KO true counts just like KO with TCRC.

The base KO true count formula where all other KO critical running count and true counts formulas are derived as well KO true count formulas for TKO is:

tc(KO) = t = (KO – 4*dp) / dr where KO is started at zero

KO is unbalanced at four per deck. Thus, If dp = 1 then EV KO = 4, if dp = 2 then EV KO = 8 and if “dp” decks are played then EV KO = 4*dp. Thus (KO – EV KO) = (KO – 4*dp) is the deviation of KO from its expected value and it is this difference which is divided by the decks remaining to get tc(KO). 

Please read carefully the following links

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

You can use either TKO or KO with TCRC to get accurate KO true counts. Either works fine but using KO with TCRC does not require true count calculations. Instead you do very simple critical running count calculations or simply memorize TCRC and you do not have to do any calculations at all and you estimate decks to the nearest full deck which is more than adequate for KO with TCRC.

IF you need to know KO true count derivations to do your sims refer to the following previous threads:

Derivation of various KO with TCRC true count formulas.
Blackjack Rebel
Posts count: 31
Topics count: 3
Oct 20, 2025, 10:33:41 PM

Derivation of TKO true count formula:

Blackjack Rebel
Posts count: 31
Topics count: 3
Oct 22, 2025, 11:41:30 PM

I was looking through some previous threads on this post and it looks like Cac gave TKO vs HL sims and basiicallyi answered my questions. 

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        54.79       62.21       90.41
HILO      53.10       60.27       87.45
-------------------------------------------

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        37.03       42.94       66.96
HILO      35.19       40.81       63.94
-------------------------------------------

HL and TKO true counts were both calculated using decks estimated to the nearest full deck. So TKO handily beats HL. If HL were estimated to the nearest quarter deck, HL SCORE would increase closer to TKO SCORE estimated to the nearest full deck. So TKO estimated to the nearest full deck is equal to HL estimated to the nearest quarter deck.

So Cac sim proves the superiority of TKO over HL and since KO with TCRC produces KO true counts like TKO does then KO with TCRC is also superior to HL and is easier to use than HL and requires that decks be estimated only to the nearest full deck so KO with TCRC should replace HL.

 Cac sims answers all of these questions.  I want to thank Cac for his sims.

Phil the creator clears up the confusion! I always used the exact deck number for simulation purposes because I didn’t need a rough 1/2 deck resolution. Actually, I hope you can add an exact true count (TC) option too.  I’m a theorist, so I really don’t care about these round/floor/truncate complications. 

You need to read carefully what Cac says “the remaining deck estimate is rounded to the nearest half deck.” Although you are a dedicated researcher, you do not read into other people’s work. 

My simulator doesn’t have 1/4 deck resolutions.

Phil

What is the extra True Count option?

Thanks,

Phil

I want this option:  the exact TC number, which is the exact running count divided by the exact remaining deck number.

Thank you for your work!

That’s right. You did it correctly. We should not have any 1/4 deck resolution consideration, because the card thickness itself has a 25% uncertainty, to begin with.

I do divide the running count by the exact number of decks remaining to get true count if the exact method is chosen. But I then round the true count with the rounding method selected. So all it ever uses is an integer true count number even if exact is selected.

I don't know if people of play with fractional counts. If you divide by the number of half decks remaining that possibly is more resolution?

Phil

I thought about this again. The current round/floor/truncate options are good. You don’t need to add anything for now. This is a minor effect. 

I want to thank Cacarulo, Aceside, Phil and others for sharing the simulations and SCORE results of TKO vs HL. This is exactly what I wanted.

And I did notice Cacarulo said “For TKO and Hi-Lo, the indices are floored, the division is by full decks, and the remaining deck estimate is rounded to the nearest half deck.”  Not sure if this means true counts are calculated with full decks or half deck estimates since he first says he divides by full decks so I thought true counts were calculated using full deck estimates and then he says the remaining decks are rounded to the nearest half deck. So I am totally confused but this is a minor point.

The major point is that the SCORE of TKO is significantly higher than the HL SCORE. This is what my analysis showed all along but without sims I was not able to prove it. Now it has been proven.

So TKO is the strongest level one count for blackjack. But the reason TKO has not replaced HL as the standard blackjack count is that, in my opinion, it is a bit difficult to use.

But KO with TCRC gives the exact same KO true counts as TKO so KO with TCRC SCOREs are the exact same as TKO SCORES and so KO with TCRC significantly outperforms HL just like TKO does.

But not only does KO with TCRC significantly outperform HL, KO with TCRC is easier to use that HL.

KO with TCRC is an easier and simpler count system to use than the HL, a stronger count system than the HL and using KO with TCRC, true count calculations (which can be a complex if decks are estimated to the nearest half or quarter deck) are avoided and replaced with critical running counts, either calculated with simple formulas or mentally looked up for immediate access if TCRC is memorized. With KO with TCRC decks are estimated to the nearest full deck which is more than sufficient. Thus using KO with TCRC there is less likelihood of making betting or playing strategy errors as compared with using HL and KO with TCRC is also easier to use and stronger than HL. Furthermore, KO makes a better primary count to add plus/minus side counts to than HL.

Thus based on this analysis, for the shoe game, the industry standard of HL should be replaced with KO with TCRC which is the strongest, simplest and easiest to use level one blackjack card counting system.

I’m glad you thank aceside. Regarding the conclusion, I’m still reserved. I believe Hi-Lo running count is the strongest level one count, but KO might/could be stronger. 

Look at Cac sims of TKO, Ignore his KO entries which I assume do not correctly adjust for KO true counts. TKO gives correct KO true counts and that is what you need to look at.

Cac says 50 billion round sims and the SCORE of TKO handily beats HL in every sim.. KO should be used only for the shoe game. Use HL for the two deck game. 

So if KO true counts are calculated correctly as in TKO and KO with TCRC then KO is stronger than HL.

I always say something opposite to yours. For double-decks, you should use KO, but for multiple-decks, you should use Hi-Lo. Why? Because counting the card 7 as a low tag does not matter very much in multiple-deck shoe games. 

The amount of unadulterated bullshit and outright disinformation in this thread is, frankly, quite astounding. I caution new readers to the site to take with a grain of salt anything you read here that isn't posted by Gronbog, Cacarulo, and me.

And, just for fun, I'll hazard an over/under for the amount of times Blackjack Rebel tells us that his system is superior to Hi-Lo at 50, before the thread mercifully ends. He apparently thinks that the more times you say the same thing, the more people will listen to you. In my lifetime (probably more than double his), I've found exactly the opposite to be true.

Don

I have not run any simulations for TKO vs. HL or obtained any SCORE results.

Thanks,

Phil