NEW Card Counting System! (CAC2 + CAC2 Enhanced)

[boneuphtoner]

I would like to clarify some points regarding the calculation of TC since there are several ways to do it.

There are three things to consider when performing the calculation:

1) Divisor of the TC: This means you can divide the RC by whole decks, half decks, or quarter decks. In CAC2, the division is done by whole decks.
2) How the remaining decks are estimated: It can be estimated to the nearest full deck, to the nearest half deck, to the nearest quarter deck, or to the exact card.
CAC2 estimates the remaining decks to the nearest half deck: 6, 5.5, 5, 4.5, 4, 3.5, 3, 2.5, 2, 1.5, 1.
3) How the division is rounded: floored, truncated, rounded. CAC2 uses floored

First off, many congrats on developing such a wonderful system! I have bought it myself and am looking forward to start using it, but I’d like to clarify this point above. I have been using Norm's excellent FELT count, and I have always estimated remaining shoe games to the whole deck level with whole deck resolution - and I use flooring. The system was designed this way. In CAC2 do I have to estimate whole decks with half deck resolution in shoe games? I ask this as I have never been confident at estimating shoe games, especially 8 deckers, at half deck resolution.

In Norm's excellent Modern Blackjack book, he did an excellent sim estimating errors in deck estimation, and the conclusion I took away is you can be 10% wrong all the time with FELT and it makes a very small difference. If CAC2 absolutely requires half deck resolution for shoes to realize the increase in performance, I would like to know this. Would appreciate hearing your thoughts on this matter.

Thanks in advance for your help!

[Cacarulo]

First off, many congrats on developing such a wonderful system! I have bought it myself and am looking forward to start using it, but I’d like to clarify this point above. I have been using Norm's excellent FELT count, and I have always estimated remaining shoe games to the whole deck level with whole deck resolution - and I use flooring. The system was designed this way. In CAC2 do I have to estimate whole decks with half deck resolution in shoe games? I ask this as I have never been confident at estimating shoe games, especially 8 deckers, at half deck resolution.

In Norm's excellent Modern Blackjack book, he did an excellent sim estimating errors in deck estimation, and the conclusion I took away is you can be 10% wrong all the time with FELT and it makes a very small difference. If CAC2 absolutely requires half deck resolution for shoes to realize the increase in performance, I would like to know this. Would appreciate hearing your thoughts on this matter.

Thanks in advance for your help!

You're welcome.
Yours is a very interesting question that I know confuses many people, so I will try to be as clear as possible.
All the figures computed in the PDF are based on estimating the remaining decks to the nearest half. However, this isn't meant to be rigid.
Over time, as our eyesight may decline, our estimates may become less precise.
Nonetheless, to gain a better understanding of the effects of using different estimations, simulations are invaluable.

In this instance, I created a set of 22 indices (R22) using "full decks" as the TC divisor and estimation of decks remaining "to the nearest full deck",
with division rounding set to "floored".
The analyzed game was 6D,S17,DOA,DAS,SPA1,SPL3,NS,4.5/6, with 100 billion rounds for each simulation.

The same set was used in all simulations. For the four possible estimations using a spread of 1-16, these were the obtained SCORES:

1. Exact card estimation: 27.59
   
2. Nearest quarter deck estimation: 27.56
   
3. Nearest half deck estimation: 27.49
   
4. Nearest full deck estimation: 26.96
   

CAC2 uses option 3), but if one wants to use option 4), the penalty would be 1.96% in terms of SCORE.

Hope this helps.

Sincerely,
Cac

[boneuphtoner]

Thanks so much Cac! Exactly the info I was looking for! And you also nailed one reason why I’m not confident estimating shoe games at half deck resolution - my eyesight is not what it once was!

[boneuphtoner]

Hey Guys - I just wanted to report that CAC2 is the real deal. I’ve done a few sims in CVCX and I made a few simplifications to the system to suit my needs and abilities. First, in calculating the true count, I use whole deck resolution for estimating shoes and half deck for pitch. Secondly, I rounded CAC2 full indices very slightly. I’ve never not used rounded indices, having spent a bulk of my time on using KO preferred or Norm’s FELT. But this time I used more granular rounding, and have groups of indices in +2, +7, etc. Like Cac says above, there is a penalty in using whole deck resolution compared to the original half deck - however, with my rounded full indices and full deck resolution, it does edge out the original CAC2/R22 with half deck resolution.

But how does it compare with the other strategies with similar rounding, etc? Please see below for the SCORE comparisons. CAC2’s superiority carries through here as well.

CVCX Sims (Rounded Full Indices with Whole Deck Shoe Resolution etc.)

6D, S17 DAS RSA, 82%, 1-6, Play-All
CAC2-Ultimate	25.07
Halves-CAC2	24.90
Zen-CAC2	24.21
FELT-CAC2	24.01

DD, S17 DAS RSA, 64%, 1-4, Play-All
CAC2-Ultimate	45.75
Zen-CAC2	45.60
Halves-CAC2	45.44
FELT-CAC2	44.79

And I am making progress at increasing my speed and learning the indices. I’ve never learned such a large index set before having always done something close to the Catch 22 - but using CV index tests, it really accelerates your learning.

[Cacarulo]

Hey Guys - I just wanted to report that CAC2 is the real deal. I’ve done a few sims in CVCX and I made a few simplifications to the system to suit my needs and abilities. First, in calculating the true count, I use whole deck resolution for estimating shoes and half deck for pitch. Secondly, I rounded CAC2 full indices very slightly. I’ve never not used rounded indices, having spent a bulk of my time on using KO preferred or Norm’s FELT. But this time I used more granular rounding, and have groups of indices in +2, +7, etc. Like Cac says above, there is a penalty in using whole deck resolution compared to the original half deck - however, with my rounded full indices and full deck resolution, it does edge out the original CAC2/R22 with half deck resolution.

But how does it compare with the other strategies with similar rounding, etc? Please see below for the SCORE comparisons. CAC2’s superiority carries through here as well.

CVCX Sims (Rounded Full Indices with Whole Deck Shoe Resolution etc.)

6D, S17 DAS RSA, 82%, 1-6, Play-All
CAC2-Ultimate	25.07
Halves-CAC2	24.90
Zen-CAC2	24.21
FELT-CAC2	24.01

DD, S17 DAS RSA, 64%, 1-4, Play-All
CAC2-Ultimate	45.75
Zen-CAC2	45.60
Halves-CAC2	45.44
FELT-CAC2	44.79

And I am making progress at increasing my speed and learning the indices. I’ve never learned such a large index set before having always done something close to the Catch 22 - but using CV index tests, it really accelerates your learning.

Wow, surprising! It never would have occurred to me to use a matrix of rounded indices or grouped indices in CAC2.
The mere fact of losing performance would have made me discard the idea. But, with this post, it's shown that sometimes
ideas need to be tested (simulated) before dismissing them.

Good job and thank you!

Sincerely,
Cac

[BJGenius007]

Hey Guys - I just wanted to report that CAC2 is the real deal. I’ve done a few sims in CVCX and I made a few simplifications to the system to suit my needs and abilities. First, in calculating the true count, I use whole deck resolution for estimating shoes and half deck for pitch. Secondly, I rounded CAC2 full indices very slightly. I’ve never not used rounded indices, having spent a bulk of my time on using KO preferred or Norm’s FELT. But this time I used more granular rounding, and have groups of indices in +2, +7, etc. Like Cac says above, there is a penalty in using whole deck resolution compared to the original half deck - however, with my rounded full indices and full deck resolution, it does edge out the original CAC2/R22 with half deck resolution.

But how does it compare with the other strategies with similar rounding, etc? Please see below for the SCORE comparisons. CAC2’s superiority carries through here as well.

CVCX Sims (Rounded Full Indices with Whole Deck Shoe Resolution etc.)

6D, S17 DAS RSA, 82%, 1-6, Play-All
CAC2-Ultimate	25.07
Halves-CAC2	24.90
Zen-CAC2	24.21
FELT-CAC2	24.01

DD, S17 DAS RSA, 64%, 1-4, Play-All
CAC2-Ultimate	45.75
Zen-CAC2	45.60
Halves-CAC2	45.44
FELT-CAC2	44.79

And I am making progress at increasing my speed and learning the indices. I’ve never learned such a large index set before having always done something close to the Catch 22 - but using CV index tests, it really accelerates your learning.

I would like to see SCORE on RSA is not allowed. I never saw any casino let players re-split aces nowadays. I think casinos force people to stand on soft 2 is the worst thing ever happened to BJ players next to 6:5 Blackjack. In the old days, the most money I made is when I split aces, then double on the soft hands. In the lucky day, I can split three times and double and made 8X my max bets in one hand. But those days are gone.

[Cacarulo]

I would like to see SCORE on RSA is not allowed. I never saw any casino let players re-split aces nowadays. I think casinos force people to stand on soft 2 is the worst thing ever happened to BJ players next to 6:5 Blackjack. In the old days, the most money I made is when I split aces, then double on the soft hands. In the lucky day, I can split three times and double and made 8X my max bets in one hand. But those days are gone.

I don't quite understand what you're referring to. In this particular case, "boneuphtoner" made a comparison of different systems with that particular rule. Evidently, where he plays, RSA is allowed.
For the case where RSA is not allowed, there is a comparative analysis at the beginning of this thread (6D,S17,DOA,DAS,SPA1,SPL3,NS,4.5/6).

Let's consider that RSA means that aces can be split more than once (SPA2 or SPA3). Not being allowed to split aces (SPA0) would indeed be horrible.
In that case, the basic strategy would be to double down on AAv6 and hit in all other cases.
Let's see the effect on BS for the different options:

6D,S17,DOA,DAS,SPA1,SPL3,NS ==> BS-EV = -0.4022 
6D,S17,DOA,DAS,SPA2,SPL3,NS ==> BS-EV = -0.3409
6D,S17,DOA,DAS,SPA3,SPL3,NS ==> BS-EV = -0.3326
6D,S17,DOA,DAS,SPA0,SPL3,NS ==> BS-EV = -0.5819

Sincerely,
Cac

[BJGenius007]

I don't quite understand what you're referring to. In this particular case, "boneuphtoner" made a comparison of different systems with that particular rule. Evidently, where he plays, RSA is allowed.
For the case where RSA is not allowed, there is a comparative analysis at the beginning of this thread (6D,S17,DOA,DAS,SPA1,SPL3,NS,4.5/6).

Let's consider that RSA means that aces can be split more than once (SPA2 or SPA3). Not being allowed to split aces (SPA0) would indeed be horrible.
In that case, the basic strategy would be to double down on AAv6 and hit in all other cases.
Let's see the effect on BS for the different options:

6D,S17,DOA,DAS,SPA1,SPL3,NS ==> BS-EV = -0.4022 
6D,S17,DOA,DAS,SPA2,SPL3,NS ==> BS-EV = -0.3409
6D,S17,DOA,DAS,SPA3,SPL3,NS ==> BS-EV = -0.3326
6D,S17,DOA,DAS,SPA0,SPL3,NS ==> BS-EV = -0.5819

Sincerely,
Cac

I mean in all casinos I visited in the past ten years, they allow me to split ace pair only once and I cannot split again if I got another ace. And for each ace after split, each hand can get only one card even it ends up with soft 2, 3, 4, 5, 6. I can only win that hand on dealer bust. That totally destroyed the value of players getting ace. When this rule was invented, it is the biggest nerf ever invented until the casinos invented 6:5 Blackjack. It is the reality of the current BJ condition. Those SCORES benefiting from unlimited ace actions are unrealistically high if re-split aces is not allowed and double after splitting ace is not allowed. To make comparison on different systems, I think you should use the most likely rule set.

[Norm]

RSA is not that unusual. Go to https://www.qfit.com/maps.shtml and scroll down. You will see the percentages at the bottom right of the various games in CBJN this month. Click on a state and then a number of decks and you will see the percentages for that combo.

[Cacarulo]

I mean in all casinos I visited in the past ten years, they allow me to split ace pair only once and I cannot split again if I got another ace. And for each ace after split, each hand can get only one card even it ends up with soft 2, 3, 4, 5, 6. I can only win that hand on dealer bust. That totally destroyed the value of players getting ace. When this rule was invented, it is the biggest nerf ever invented until the casinos invented 6:5 Blackjack. It is the reality of the current BJ condition. Those SCORES benefiting from unlimited ace actions are unrealistically high if re-split aces is not allowed and double after splitting ace is not allowed.

The general rule has always been SPA1, which means that aces can be split only once. Additionally, only one card can be received on each hand,
without the obvious possibility of doubling down. RSA (usually SPA3) exists in some casinos but functions like the previous one.
There is also another rule (HSA) that allows you to request more cards on each of the split aces always without the possibility of doubling down.

I just to make comparison on different systems, you should use the most likely rules casinos set.

Perhaps you should read the document to see that that's actually what I do.
And as I said earlier, I wasn't the one who made the comparisons with RSA.

Sincerely,
Cac

[Freightman]

RSA is not that unusual. Go to https://www.qfit.com/maps.shtml and scroll down. You will see the percentages at the bottom right of the various games in CBJN this month. Click on a state and then a number of decks and you will see the percentages for that combo.

This is right. My standard game includes RSA and ES10 and I’m aware of this in multiple jurisdictions.

[boneuphtoner]

Edit - sorry guys, I meant eliminating RSA, not DAS

Hey Guys - I haven’t had a chance to export the results yet, but getting rid of RSA doesn’t hurt my rounded CAC2 in the least in comparison to the other strategies like Halves, Zen, and FELT-F (all with similar rounding to be fair). But as I mentioned previously, I only rounded very slightly and have many more groups than I ever had - for example, for TC of 0-10, I have groups of 0, +2, +5, +7, and +10 - I never used a system with that kind of index granularity before. I hurt the performance of the system far more by deciding to use whole deck resolution for shoes - but I know my abilities. It took me using a full rounded index set to just barely overtake CAC2 with the standard R22 and half deck resolution.

[BJGenius007]

Edit - sorry guys, I meant eliminating RSA, not DAS

Hey Guys - I haven’t had a chance to export the results yet, but getting rid of RSA doesn’t hurt my rounded CAC2 in the least in comparison to the other strategies like Halves, Zen, and FELT-F (all with similar rounding to be fair). But as I mentioned previously, I only rounded very slightly and have many more groups than I ever had - for example, for TC of 0-10, I have groups of 0, +2, +5, +7, and +10 - I never used a system with that kind of index granularity before. I hurt the performance of the system far more by deciding to use whole deck resolution for shoes - but I know my abilities. It took me using a full rounded index set to just barely overtake CAC2 with the standard R22 and half deck resolution.

For me, SPA1 is not the problem. The nHSA (no hit soft ace) hurts SCORE the most.