ITS OFFICIAL PART 3
- Thread starter ZenKinG
- Start date
It is not my system. Other very successful APs used it first. Like I said you are giving up EV and SCORE for leaving behind wide swings away from EV. If you are looking for SCORE of EV improvements, there isn't any. If you are looking to live above EV to have infrequent corrections that bring you back to EV rather than living below EV waiting for the rarer good runs to bring you up to EV then losing smaller amounts and losing less frequently while winning more frequently is the ticket. I know of many ways to do this. They all start by getting away from reducing everything to a number on a number line and trying to isolate more specific deck compositions within TC groups to reduce the bets for those over bet situations.
Like I said SCORE and EV will increase if you use the same technique to raise under bet bets within the TC bin but volatility will also go up. I doubt the user will find that an improvement in practice despite being a statistical improvement for long term stats. Large buy-ins and large wins and losses are a big red flag besides being more stressful on the bettor. It is better to have reduced buy-ins and more steady BR growth by having smaller land less frequent losses and more frequent wins. As you can probably guess larger and more frequent losses tend to produce a short term downward trend that waits for big wins to get back to EV. But smaller and less frequent losses tend to have you above EV waiting for you to spin wheels breaking even for a while to drop back to EV. It is all a matter of how the sessions are likely to add up in the short term. They head to more or less the same long term. One generates more heat and stress while the other is comfortable and easily more tolerated by the casino. As you know in todays AP BJ getting the EV is not the problem, being allowed to play is. This approach is a big help toward being tolerated. Too many people worry about EV. Today's battle is to have the EV but be tolerated not maximize EV.
Like I said SCORE and EV will increase if you use the same technique to raise under bet bets within the TC bin but volatility will also go up. I doubt the user will find that an improvement in practice despite being a statistical improvement for long term stats. Large buy-ins and large wins and losses are a big red flag besides being more stressful on the bettor. It is better to have reduced buy-ins and more steady BR growth by having smaller land less frequent losses and more frequent wins. As you can probably guess larger and more frequent losses tend to produce a short term downward trend that waits for big wins to get back to EV. But smaller and less frequent losses tend to have you above EV waiting for you to spin wheels breaking even for a while to drop back to EV. It is all a matter of how the sessions are likely to add up in the short term. They head to more or less the same long term. One generates more heat and stress while the other is comfortable and easily more tolerated by the casino. As you know in todays AP BJ getting the EV is not the problem, being allowed to play is. This approach is a big help toward being tolerated. Too many people worry about EV. Today's battle is to have the EV but be tolerated not maximize EV.
I keep telling you this is not my system. Someone else adapted my concepts to BJ using different criterion to divide things into more specific related deck compositions. What I have been talking about is trading some EV and SCORE for more predictable winning results. Long term stats don't show the short term. That is why you give up EV. You could use the concept to gain EV but that would be a step in the wrong direction in casino play. On a computer it would look great. But in a casino your results would have increased buy-ins, and more severe swings which makes them take notice of you, all for a small increase in EV. This is about being tolerated, which is much more likely if your buy-ins are smaller and your results are less extreme while winning almost as much in the long run. In casino play the main thing is being allowed to play, not generating the highest EV or SCORE. The EV will more than even out with the extra play you get before you get banned. Some of these illiterates act like I am saying this generates more EV or better long term stats. The entire time I have been saying the opposite. That trading a little EV for more frequent wins and less frequent and less severe losses is what it is about. I am not sure we could even agree on a way to show that using stats. Long term stats don't even hint about what happens in the short term. But if you have played a long time both ways the difference is quickly apparent if you keep detailed records.
More handwaving, fanciful unsupported claims, hot air, and again nothing whatsoever of substance.
From your summary, it sounds like you're giving up EV and SCORE for a reduced variance. Well, no problem there, if that's your bag, and exactly the same thing can be accomplished with a reduced spread. But how much, exactly, are you giving up, and how much is variance reduced? Who analyzed it and what were the results? How do these results compare to the same spread for some other regular counting system? How do you know you're even playing at an advantage?
"I am not sure we could even agree on a way to show that using stats. Long term stats don't even hint about what happens in the short term."
Of course there is. Provide objective data on EV, variance, and SCORE, using well defined spreads and games. Show a plot of real results, a la QFIT's graphs. Surely you studied simulation results carefully to ensure you have an actual advantage, before putting your money on the line. You wouldn't ever think of placing a bet based on a hunch, would you?
This is not a complicated thing, and is trivial to simulate. The field of statistics is designed for exactly this purpose.
(Reminds me of that old JSTAT 10-count nonsense from years back.)
From your summary, it sounds like you're giving up EV and SCORE for a reduced variance. Well, no problem there, if that's your bag, and exactly the same thing can be accomplished with a reduced spread. But how much, exactly, are you giving up, and how much is variance reduced? Who analyzed it and what were the results? How do these results compare to the same spread for some other regular counting system? How do you know you're even playing at an advantage?
"I am not sure we could even agree on a way to show that using stats. Long term stats don't even hint about what happens in the short term."
Of course there is. Provide objective data on EV, variance, and SCORE, using well defined spreads and games. Show a plot of real results, a la QFIT's graphs. Surely you studied simulation results carefully to ensure you have an actual advantage, before putting your money on the line. You wouldn't ever think of placing a bet based on a hunch, would you?
This is not a complicated thing, and is trivial to simulate. The field of statistics is designed for exactly this purpose.
(Reminds me of that old JSTAT 10-count nonsense from years back.)
Dummy, I’m still very confused by your super duper system. It looks like it’s giving up EV in the long run to somehow help variance in the short run. If I have a big bankroll and only care about the long run, why would I ever use it?
Personally, I don’t care about smoothening out the variance. I’m only interested in EV and winning as much money as possible in the long run.
Is there something else I’m missing with your system?
Personally, I don’t care about smoothening out the variance. I’m only interested in EV and winning as much money as possible in the long run.
Is there something else I’m missing with your system?
BJgenius, I replied to your above quote because I`m curious as to your opinion on keeping side counts of neutral cards (well, neutral in other systems) since your count tracks all of them. If you haven`t seen yet, Dummy has been saying in above posts that doing so can have a dramatically positive effect on win percentage rate. So since you`re the only other person I know of who does this (aside from Tarzan), I wanted to ask you how much better you think the performance is when doing that... Where did you get AccuZen from anyway, I`ve never heard of it. Did you create it? Do you track 8s and 9s together, or separately? I`m guessing the latter, but I suppose they could be tracked together into one side count...
Dummy, it`s hard to motivate anyone to do their own research like you`re suggesting with neutral card side-counts, because, as johndoe mentioned, you`re not really giving us any hard data/stats on exactly how effective it is... I can see what you`re talking about with over-betting in situations where there`s too high a density of neutral cards left to play vs. high cards... But the question is, just how much better are results if you do this in shoe games? As ZK mentioned, with the frequency distribution in a shoe game (especially 8 deck!), I just don`t see how it could make all that much of a difference. I dunno about anyone else, but I`ve mulled over changing counts before, and unless it`s a dramatic difference in performance I really can`t afford the time involved with learning a new system.
Dummy, it`s hard to motivate anyone to do their own research like you`re suggesting with neutral card side-counts, because, as johndoe mentioned, you`re not really giving us any hard data/stats on exactly how effective it is... I can see what you`re talking about with over-betting in situations where there`s too high a density of neutral cards left to play vs. high cards... But the question is, just how much better are results if you do this in shoe games? As ZK mentioned, with the frequency distribution in a shoe game (especially 8 deck!), I just don`t see how it could make all that much of a difference. I dunno about anyone else, but I`ve mulled over changing counts before, and unless it`s a dramatic difference in performance I really can`t afford the time involved with learning a new system.
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We've tried to point out, on many occasions, that the reason everyone has trouble wrapping his head around the claims is that they're not for blackjack!! They're for SP21, which is dissimilar enough to call it a completely different game! So, when you read Three's/Dummy's analyses, understand that they do NOT apply to the game of blackjack as you know it.
Don
Don
The SP21 system doesn't even track neutral cards. The SP21 system is an entirely different thing that I wouldn't discuss to begin with. This is for BJ. There are two keys to getting the swing control in order to have more easily tolerated results and more certain growth of your BR (reduced swings). One is you use the information differently than traditional methods of side counting and the other you account for all the neutral cards. The neutral cards are considered insignificant for betting. For the traditional method of side count adjustments for betting that is true. But the density of neutral cards within a TC affect high card density which affects your advantage a lot. It affects your results for doubles and splits and the frequency of BJ's. The traditional method of using neutral card info doesn't factor in their effect on high card density.
Variance and short term swings are two very different things. Variance is a long term stat. Changes in short term swings don't show up in long term stats including variance. Anyway just by betting less in general, as suggested in a previous post, you are reducing under bet deck compositions, properly bet deck compositions, and over bet deck compositions. The idea is to reduce bets but only a subset of the over bet deck compositions. Combine that with waiting for slightly more EV to risk more money on weaker doubles or splits and your results don't give up much EV but are much more user friendly in the way of swings on the way to the long run and the threat level your actions seem to the casino (buy-ins and results). I will drop this because short term swings are an area of research that has no statistics that define them and are generally not researched. The mantra is all that matters is EV and variance. If that is the narrow perspective people have they will never be aware of short term swings from stats but they will feel it in their actual results.
Variance and short term swings are two very different things. Variance is a long term stat. Changes in short term swings don't show up in long term stats including variance. Anyway just by betting less in general, as suggested in a previous post, you are reducing under bet deck compositions, properly bet deck compositions, and over bet deck compositions. The idea is to reduce bets but only a subset of the over bet deck compositions. Combine that with waiting for slightly more EV to risk more money on weaker doubles or splits and your results don't give up much EV but are much more user friendly in the way of swings on the way to the long run and the threat level your actions seem to the casino (buy-ins and results). I will drop this because short term swings are an area of research that has no statistics that define them and are generally not researched. The mantra is all that matters is EV and variance. If that is the narrow perspective people have they will never be aware of short term swings from stats but they will feel it in their actual results.
I'm all for thinking outside the box like Tthree does rather than just be given a formula and run with it. Naturally, my whole life I was always one to try and think of different ways to do things. The problem with Tthree's approach though is it doesn't even pass the sniff test for me to get interested and it's all because of a very basic understanding of the game and frequency distribution. In a highly dealt pitch game, it's a different story, so something like Tarzan's count or Tthree's count can be very beneficial especially since you'll be able to play longer with less scrutiny from the pit and surveillance by keeping your spread even lower. BUT in a SHOE GAME I just don't see how tracking certain denomination cards can be any what beneficial to the player and this is because of the dilution of cards in a shoe game. In a 6 deck game there are 312 cards and in an 8 deck game 416 cards, so the chance of one certain card denomination to be in a huge surplus or deficit in the LONG RUN to help you make a lot more accurate play decisions is completely negligible; negligible enough to not warrant any increase in a player's hourly rate, if ANY.
Just look at what happened when they finally ran sims on Tarzan's count. I told everyone for years Tarzan's count wouldn't make any worthwhile increase in EV for a SHOE GAME and guess what? I was right. Go look up the simulations done on his count. If I remember correctly, there wasn't any EV increase, and if there was it was a very negligible difference that even the EV purists would say is not worth it.
Just look at what happened when they finally ran sims on Tarzan's count. I told everyone for years Tarzan's count wouldn't make any worthwhile increase in EV for a SHOE GAME and guess what? I was right. Go look up the simulations done on his count. If I remember correctly, there wasn't any EV increase, and if there was it was a very negligible difference that even the EV purists would say is not worth it.
FWIW, I entirely agree with you. And, I'm surprised to read what Three wrote above, because, in private correspondence, he always led me to believe that none of this had anything to do with regular blackjack and even that it absolutely wouldn't apply to regular blackjack.
So, I don't know where the above is coming from.
Don
So, I don't know where the above is coming from.
Don
I am not sure I explained this very well. It is the expected neutral card deck compositions that get their bets reduced for Hilo. That is why I said to do your own research. This varies by count system. And things don't do what you might expect.
Here is a CDA program link:
http://www.bjstrat.net/cgi-bin/cdca.cgi
Let's say you use Hilo. You have a TC that has the same number of cards of each rank for the lows and highs that has a TC of +2 (average advantage for an 8 deck game 1.5 decks cut off is 1.06%) with 5 decks left (to make adjustments to neutral cards easy, that is a RC of +12. If the 7 through 9 ranks are at expectation you have a deck composition that looks like this (cards remaining 2-A) for S17, DAS, LS, noRSA, SP4:
1) Neutral TC +2 with 5 decks left (260 cards): ( 19,19,19,19,19,20,20,20,84,21) advantage .8095%
2) Two less of each counted card at TC +2 with 5 decks left(260 cards): (17,17,17,17,17,27,27,26,76,19) advantage 1.069%
3) Two more of each counted card at TC +2 with 5 decks left(260 cards): (21,21,21,21,21,13,13,14,92,23) advantage 1.038%
So as you see it is the normal distributions of neutral cards that get reduced bets with 5 decks left and a TC of +2. That is most of the TC bins frequency.
For 2.5 decks left at TC +2:
1) Neutral TC +2 with 2.5 decks left (130 cards): ( 10,9,10,9,9,10,11,10,42,10) advantage .9697%
2) One less of each counted card at TC +2 with 2.5 decks left(130 cards): (9,8,9,8,8,14,14,13,38,9) advantage 1.220%
3) One more of each counted card at TC +2 with 2.5 decks left(130 cards): (11,10,11,10,10,7,7,7,46,11) advantage 1.110%
Again, as you can see the most frequent deck compositions where the neutral cards are at expectation are what get reduced bets. So ZK argument that the dilution to have most neutral card densities in shoe games close to expectation is exactly when you would be reducing bets. Like I have said so many times, there is value to knowing the neutral cards are at expectation. And as I have repeatedly said linear adjustments for neutral cards for betting are useless (As is indicated by increased advantage for both surplus and deficit neutral cards and significantly reduced advantage for neutral cards at expectation. Experts say floating advantage only happens at very deep penetration but as is indicated even as many as 5 decks left show a much more significant discrepancy in advantage than at 2.5 decks left. So much for what experts know about different ways to use information. It helps if you don't speak from ignorance on a new way of using information) but using a different method to use neutral cards to assess advantage reveals an opportunity that is overlooked. All anyone had to do was do the slightest effort with their own initiative and they would have seen I was right. I said play around with the CDA and you would get it. But all the supposed experts that never looked into other ways to use information are ignorant on what happens when you use information in new ways.
Here is a CDA program link:
http://www.bjstrat.net/cgi-bin/cdca.cgi
Let's say you use Hilo. You have a TC that has the same number of cards of each rank for the lows and highs that has a TC of +2 (average advantage for an 8 deck game 1.5 decks cut off is 1.06%) with 5 decks left (to make adjustments to neutral cards easy, that is a RC of +12. If the 7 through 9 ranks are at expectation you have a deck composition that looks like this (cards remaining 2-A) for S17, DAS, LS, noRSA, SP4:
1) Neutral TC +2 with 5 decks left (260 cards): ( 19,19,19,19,19,20,20,20,84,21) advantage .8095%
2) Two less of each counted card at TC +2 with 5 decks left(260 cards): (17,17,17,17,17,27,27,26,76,19) advantage 1.069%
3) Two more of each counted card at TC +2 with 5 decks left(260 cards): (21,21,21,21,21,13,13,14,92,23) advantage 1.038%
So as you see it is the normal distributions of neutral cards that get reduced bets with 5 decks left and a TC of +2. That is most of the TC bins frequency.
For 2.5 decks left at TC +2:
1) Neutral TC +2 with 2.5 decks left (130 cards): ( 10,9,10,9,9,10,11,10,42,10) advantage .9697%
2) One less of each counted card at TC +2 with 2.5 decks left(130 cards): (9,8,9,8,8,14,14,13,38,9) advantage 1.220%
3) One more of each counted card at TC +2 with 2.5 decks left(130 cards): (11,10,11,10,10,7,7,7,46,11) advantage 1.110%
Again, as you can see the most frequent deck compositions where the neutral cards are at expectation are what get reduced bets. So ZK argument that the dilution to have most neutral card densities in shoe games close to expectation is exactly when you would be reducing bets. Like I have said so many times, there is value to knowing the neutral cards are at expectation. And as I have repeatedly said linear adjustments for neutral cards for betting are useless (As is indicated by increased advantage for both surplus and deficit neutral cards and significantly reduced advantage for neutral cards at expectation. Experts say floating advantage only happens at very deep penetration but as is indicated even as many as 5 decks left show a much more significant discrepancy in advantage than at 2.5 decks left. So much for what experts know about different ways to use information. It helps if you don't speak from ignorance on a new way of using information) but using a different method to use neutral cards to assess advantage reveals an opportunity that is overlooked. All anyone had to do was do the slightest effort with their own initiative and they would have seen I was right. I said play around with the CDA and you would get it. But all the supposed experts that never looked into other ways to use information are ignorant on what happens when you use information in new ways.
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These are two entirely different ways to accomplish reducing loss frequency and size. When I say I am talkingg about BJ I know I am talking about BJ. You shouldn't listen to all the people that can't know what I am talking about and say I am talking about SP21 because their expertise is limited to the traditional way of using information so they don't understand revolutionary new ways of doing things. Don you know my strange thoughts on SP21 and why they would work the way they do. You may be skeptical but you get the concept. I have outlined above how this works and you can see it is a totally different concept whose only similarity is finding a way to sub-divide betting groups into related deck composition subsets of the main betting bin rather than unrelated deck composition subsets of the main betting bin. Using information this way allows for stratification of stats. You never know if they will lead to anything useful until you do the research.
I have said enough. My case is proven by the stats. If people don't understand how even the weakest count in terms of collecting deck composition specific bins shows the stratification I have been speaking of i the exact manner I have been saying I can't teach them why. To understand the new way to use information you have to abandon reducing everything to a number on a number line and see deck compositions as a complicated multi-dimensional landscape when thinking about things. Reducing deck compositions to a single dimension is like looking at a beautiful landscape with the wrong prescription glasses that are so scratched and fogged up that you just see a fuzzy image. I probably shouldn't talk about the new innovations to counting because so many are experts at living in a one dimension landscape in a multi-dimensional landscape that they just can't see all the other dimensions that exist and the opportunities that can be found there.
I have said enough. My case is proven by the stats. If people don't understand how even the weakest count in terms of collecting deck composition specific bins shows the stratification I have been speaking of i the exact manner I have been saying I can't teach them why. To understand the new way to use information you have to abandon reducing everything to a number on a number line and see deck compositions as a complicated multi-dimensional landscape when thinking about things. Reducing deck compositions to a single dimension is like looking at a beautiful landscape with the wrong prescription glasses that are so scratched and fogged up that you just see a fuzzy image. I probably shouldn't talk about the new innovations to counting because so many are experts at living in a one dimension landscape in a multi-dimensional landscape that they just can't see all the other dimensions that exist and the opportunities that can be found there.
Does anyone else feel like they are re-watching a really bad movie? 
I though we had resolved all this BS, including complete debunking and even acknowledgement that this person mislead everyone by not acknowledging he was talking about sp21 the first go around. Now he is back rehashing the same exact BS and insisting it about regular BJ this time around.
Dummy, or whatever handle you want to go by...on whatever site you happen to be on, there is something seriously wrong with you. It is like you have this obsession to try to prove to how smart you are to everyone. Some sort of insecurity where you seek approval or something. JUST STOP!
I though we had resolved all this BS, including complete debunking and even acknowledgement that this person mislead everyone by not acknowledging he was talking about sp21 the first go around. Now he is back rehashing the same exact BS and insisting it about regular BJ this time around.
Dummy, or whatever handle you want to go by...on whatever site you happen to be on, there is something seriously wrong with you. It is like you have this obsession to try to prove to how smart you are to everyone. Some sort of insecurity where you seek approval or something. JUST STOP!
I think it is funny that you say I have to prove how smart I am when this is not even something that I came up with. I was collaborating with another AP concerning searching for new opportunities from using information in a different way. This is something he came up with. I only described what to look for in the way of short term results to see swing control and what he must do to get different results from finer bins. We were collaborating back and forth but this is his baby. I didn't talk about anything too specific until I got his permission. I used Hilo in my example because it is simple and the gain from using information in this way is directly proportional too how tight the advantage bell curve is around the betting bin average, and Hilo has a very wide bell curve which indicates it is poor when it comes to betting accurately despite a respectable BC. You can imagine the gain from starting with a count that is much more accurate at assessing specific deck compositions. I know quite a few AP's that are doing this. The big power is when your bets get larger. All I do is try to help people think outside the box in order to find much better ways of doing things. Every time people get pissed at me when speaking from their ignorance about new ways of doing things. They have absolutely no experience with the new techniques and have no idea what to expect but act like they are experts about it. Now who is trying to show everyone how smart they are by speaking from ignorance about cutting edge ideas, and who is trying to help people think of new and better ways to do things by pointing out the important things that must happen in order to get more accuracy from sub-bin groupings rather than a random cross-section of the bin or bins the deck compositions came from.
I have said my peace. Those experts can keep denying what I say from absolutely no research into it, even one of them pointed out the swing control can be done by reducing bets across the board rather than targeting over bet deck compositions, or they can understand that just from the weakest count for using this type of approach, due to the lack of sorting things well by advantage to begin with from its simplicity, and see what happens at high frequency for any advantage TC bin and understand that by reducing the bets so they aren't over bet will do just what I have said in the way of short term swings without the large reduction in EV an across the board reduction would have.
Don't expect me to share any other innovations. There are a lot more and I am researching even more things I think will prove quite valuable for any game. Rather than doing research and learning from it or finding data to refute what I say, the experts on traditional ways of using information just get critical without anything to base their criticism on. In my book people who think their expertise in one area in a any way makes them experts in a completely different line of study are the ones that are trying to act smart about what they know nothing about. A smart person would do some research before speaking on a subject that doesn't exist in the area of their expertise. All it would have taken was just a little tinkering on a CDA to see that most of the comments refuting me were wrong and usually exactly the opposite of what the CDA shows. You don't hear the rushing out to refute me once data for the a count that would show the least gain from using the technique. The data showed that all their assumptions about what they expected to see was not only wrong but expecting the exact opposite of what actually happens. This is not a one-dimensional technique. Details that are totally lost in when reducing everything to a number on a number-line come to light.
Just imagine what occurs when you add this technique to a count that is good at assessing advantage for specific deck compositions like halves or Hiopt2/ASC. People don't side count shoes because using traditional techniques they see the effort as valuable only when the side counted cards are not near expectation and only use the information for playing decisions. In shoes betting accurately is far more important than playing accurately. I have shown that when trying to reduce bets for some over bet situations that is totally flipped. It is the neutral cards near expectation that has value and the information is used for bet sizing in addition to playing decisions , and the value is higher early in the shoe than it is late in the shoe. All of that is the exact opposite of reality of using the same information gathered linearly.
I have said my peace. Those experts can keep denying what I say from absolutely no research into it, even one of them pointed out the swing control can be done by reducing bets across the board rather than targeting over bet deck compositions, or they can understand that just from the weakest count for using this type of approach, due to the lack of sorting things well by advantage to begin with from its simplicity, and see what happens at high frequency for any advantage TC bin and understand that by reducing the bets so they aren't over bet will do just what I have said in the way of short term swings without the large reduction in EV an across the board reduction would have.
Don't expect me to share any other innovations. There are a lot more and I am researching even more things I think will prove quite valuable for any game. Rather than doing research and learning from it or finding data to refute what I say, the experts on traditional ways of using information just get critical without anything to base their criticism on. In my book people who think their expertise in one area in a any way makes them experts in a completely different line of study are the ones that are trying to act smart about what they know nothing about. A smart person would do some research before speaking on a subject that doesn't exist in the area of their expertise. All it would have taken was just a little tinkering on a CDA to see that most of the comments refuting me were wrong and usually exactly the opposite of what the CDA shows. You don't hear the rushing out to refute me once data for the a count that would show the least gain from using the technique. The data showed that all their assumptions about what they expected to see was not only wrong but expecting the exact opposite of what actually happens. This is not a one-dimensional technique. Details that are totally lost in when reducing everything to a number on a number-line come to light.
Just imagine what occurs when you add this technique to a count that is good at assessing advantage for specific deck compositions like halves or Hiopt2/ASC. People don't side count shoes because using traditional techniques they see the effort as valuable only when the side counted cards are not near expectation and only use the information for playing decisions. In shoes betting accurately is far more important than playing accurately. I have shown that when trying to reduce bets for some over bet situations that is totally flipped. It is the neutral cards near expectation that has value and the information is used for bet sizing in addition to playing decisions , and the value is higher early in the shoe than it is late in the shoe. All of that is the exact opposite of reality of using the same information gathered linearly.
Three, I do appreciate you taking the time to go through this system in detail. I liked your Hilo plus 2 example. It helped me better understand where you’re coming from. I’m not saying I will use it, but I now know what you’re taking about. Before it was all in some type of code that didn’t make any sense. It’s something new I haven’t seen in books. I’ll need to reread your posts several more times to get a better grasp of it. Thanks!
The neutral cards 7-9 do run into surplus or deficit just like other cards. You need to realize that in this group 7 behaves as a small card and 9 behaves as a large card. You are making the assumption that the surplus or deficit is equally distributed among the three cards, which is incorrect. The surplus of this group due to more 7 or more 9 will change your advantage in opposite directions. So your calculations have a lot of error. I say estimation with large error is no better than not counting them. No matter how you say it, you will be unable to tell if any surplus/deficit is caused by 7s or 9s.