Request for sim of KO with TCRC vs HL

Neither did aceside.

There are several ways to calculate a TC, for which we only need to know the RC and the decks remaining (DR).
First, let’s determine the different ways in which the remaining decks can be estimated in a six-deck game:

1. Decks rounded to the nearest whole deck:
   In this case, the possible denominators for the division will be: 6, 5, 4, 3, 2, and 1
   This is the easiest way to estimate, although it’s also the least precise.

2. Decks rounded to the nearest half deck:
   Here, the possible denominators for the division will be: 6, 5.5, 5, 4.5, 4, 3.5, 3, 2.5, 2, 1.5, 1, and 0.5
   This is the method most players I know tend to use.

3. Decks rounded to the nearest quarter deck:
   Possible denominators: 6, 5.75, 5.50, 5.25, 5, 4.75, 4.50, 4.25, 4, 3.75, 3.50, 3.25, 3, 2.75, 2.50, 2.25, 2, 1.75, 1.50, 1.25, 1, 0.75, 0.50, and 0.25

4. Decks to the exact card:
   This method is used in simulators for greater precision but is impossible to perform in practice.
   Example: If there are 91 cards remaining, the decks remaining are calculated as 91 / 52 = 1.75.

The next step is to define the division.
If we divide the RC by any of the DR values calculated above, we are dividing by full decks.
Examples: +10 / 1.75, –5 / 3.5, +1 / 4
If instead of dividing by whole decks we divided by half-decks, in the six-deck example we would have twelve half-decks: 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1

Finally, we must define how we’re going to round the result of the RC / DR division. Here, we can choose between floored (the most commonly used), rounded, or truncated.

Hope this helps.

Sincerely,
Cac

If anyone is interested in testing all these methods, comparing different systems, and calculating SCOREs, the best thing you can do is get CVData.
I find it hard to understand how there are people who play blackjack seriously and still don’t have it. It’s essential.

Sincerely,
Cac

Also, folks who develop their own software should have it in order to confirm the correctness of their work.

Let me just say this. I intended to do a comparison simulation between Hi-Lo and TKO, but OP and I could not agree on our terms. I wanted to do a sim on a 6-deck 4.5/6 Pen game, but OP insisted on a game of 5/6 Pen. That meant no deal.

Each sim takes, what, three minutes????? What a joke. Who gives a damn if you set it to 4.5 decks or 5? Do them both, for God's sake.

Don

OP also wanted to do a sim on back-counted bet spread of 1-8, but this part will take me several hours, so I didn’t want to do it. If someone requests an easier sim of play-all 1-12 bet spread, I will do it. 

What are you using, an abacus??

Don

I did a sim on a 6-deck S17 LS 4.5/6 Pen game with Hi-Lo several weeks ago, and I saved the records. For TKO, all I need to do is amend it with TKO. This part is easy.  When I have Wi-Fi, I will do it. Another thing worrisome is I may get different numbers from Cac’s. 

Once you have CVData and can run all the simulations you want, then we can start discussing the differences.
For now, I don’t think it’s possible to do it accurately with the tools you currently have — I’m talking about calculating a SCORE and everything that comes with it.

Sincerely,
Cac

I have tried this sim but haven't reached a good result. I will ask Phil to fix the problem. 

Cac ran the sims. Phil and Aceside just commented. Sorry for the confusion of who did what. 

I do not require any more sims. Cac's sims gave the answer that I was looking for.

There really is no need to get into any more detail. Cac’s sims showed what I want to know for sure and that is KO, when the KO true count is calculated correctly such as with TKO or with KO with TCRC, is a stronger count system than HL. In every case Cac tested, TKO SCOREs are significantly greater than HL SCOREs.

Cac sims showed that in every case, PA 1 to 12, PA 1 to 16 and BC 1 to 4, that TKO SCORE was significantly greater than HL SCORE.  Here were the sim results he gave in a previous thread. There really is nothing else to say. TKO is a stronger count system than HL.

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
-------------------------------------------

In previous threads in this post, I derived the TKO true count formula that Cac used and I also showed derivations of KO true count formulas for my KO with TCRC. I derived both formulas from the same base KO true count formula: tc(KO) = t = (KO – 4*dp) / dr where KO starts at zero. Both TKO and KO with TCRC produce the exact same correct KO true counts.

So if TKO is stronger than HL then so is KO with TCRC and that is what I wanted to know.

I have no other questions

Wait a second! Your KO with TCRC is inferior than TKO, because TKO has almost continuous TC values but your stuff has large-gapped discrete TC values. That's why you said your system has a higher accuracy at +3 and above TCs, at a cost of lower TC ones.
 

For theoretical investigations, I said they were the same, but they are not even close in use.

I need to look at it but I don’t think my simulator correctly calculates true counts for unbalanced counts. Will look at it and should be able to fix it.
 

Thank you,

Phil

Increasing the accuracy of decks remaining helps with the HL SCORE as it increases the accuracy of the HL true count but has minimal help with the TKO or KO with TCRC SCORE since for KO true counts of three or more with decks estimated to the nearest full deck are already accurate. For TKO or KO with TCRC you do not need to estimate decks any more accurately than to the nearest full deck.

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

1. KO = crc(3) = 24 – dr three times as accurate as HL = 3*dr

2. KO = crc(4) = 24 exact as compared to HL = 4*dr

3. KO = crc(5) = 24 + dr five times as accurate as HL = 5*dr

4. KO = crc(6) = 24 + 2*dr three times as accurate as HL = 6*dr

That is why I said for KO true counts of three or more, KO with TCRC with decks estimated to the nearest full deck is equivalent to HL with decks estimated to the nearest quarter deck.

For negative true counts, critical running counts of KO with TCRC are terrible but who cares as your minimum bet is being played or you are not playing at all if back counting.

If you have TKO SCORE with decks estimated to the nearest full deck and with decks estimated exactly, then check these SCOREs and should see hardly any difference. However, if you compare the SCORE of HL with decks estimated to the nearest full deck with decks estimated exactly you will, according to Colin Jones’ sims, show an increase in EV of 7% or more. That is my prediction and I stand by my prediction.

If you want to increase your SCORE use Risk Averse indices instead of Expected Value indices. For TKO or KO with TCRC estimating decks to the nearest full deck is more than adequate. 

For TKO do you start the running count at -4 multiplied by the number of decks? I know you can start it wherever you like but what would be normal for TKO?

For unbalanced counts is a true count calculation still just the running count divided by the number of decks remaining?

Or is the true count calculation the deviation between where the running count is vs where the running count would be expected to be given the number of decks played then divided by the number of decks remaining? 
 

I would like to implement a correct true count for TKO and also for any unbalanced count. But starting with TKO, I am not familiar with how true count is calculated in TKO. 
 

Gronhog, CAC it sounds like you have implemented this already, how do you do the true count calculation for TKO?

(I do understand all the details about number of decks remaining estimated or exact and also using number of half decks and the use of the rounding modes)
 

Thank you,

Phil

For TKO, you simply start the RC at -4 × nd (number of decks) and then divide by the remaining decks. That’s all there is to it. The only difference compared to Hi-Lo is that in this case, you start the RC at 0.

Sincerely,
Cac

Yes, this is correct. Yes, you can start with any Initial Running Count (IRC).  In your program, you just change “Begin Count at” to “IRC”, and then the true count (TC) becomes,
 

TC = (IRC + sum of removed card tags) / (decks remaining).

For the TKO simulation, I want to wager $10/$25/$50/$75/$100/$125 at TC=-4/-3/-2/-1/0/+1, respectively, and insure at TC=-1. 

You have cited this part a dozen times. I’m tired of hearing this. I’ve already explained to you: this is misleading! 
 

Your statement of TKO has a higher TC accuracy at TC of +3 or above is false. At deep penetrations, HiLo has a higher TC accuracy, because its TC zero error centers at TC=0, which is most frequent, while in TKO, although TC zero error centers at TC=0 too, it is a much rarer event.