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"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
First I want to thank Gronbog for all of his help and for his simulations. They were very enlightening and I am sure that everyone appreciates his hard work.
Also I would like to explain my comment on BC. I realize that betting is very important for the shoe game. But what I was surprised at was just a 2% increase in BC of HO2 w ASC over HL made such a big difference. Gronbog's last simulation quantifies how the increase in BC effected the sim results since the only thing changed in the last simulation was using HL + (1/3)*(5m6c) for betting instead of using HL for betting which increase BC by around 0.9% but was still over 1% below HO2 - 2*(Adef) for betting. Please refer to the attached file for details.
Also I would like to comment that simulations show POWER. There were five components I looked at when choosing a count system.
1. Ease of Use
2. Power as measured by simulations and indirectly by CC of individual plays and Betting Correlation (BC)
3. Accuracy. Accuracy of True count calculations when tc > 3 which I have shown the KO gives very accurate true counts when tc > 3 as possosed to a balance system. Also the KO side counts are +/- which are EXACT whereas a side count of Aces is APPROXIMATE since you are estimating dr.
4. Camouflage - strange plays may be made which look like a mistake to the casino when your large bets are out. This may help you play longer such as hitting hard 12 v 6 at KO true count of 4 for example. The formula is hit hard 12 v 6 if KO + 1.5*(AA89mTc) <= crc(-1) which simplifies to hit (I showed this derivation in a previous chart posted of KO with AA89mTc with chips in the chart) hard 12 v 6 if AA89mTc < (2/3)*(-1 - t)*dr where t = tc(KO). So if tc(KO) = 4 then hit hard 12 v 6 if AA89mTc < (2/3)*(-1 - 4)*dr or approximately hit hard 12 v 6 if AA89mTc < (-3)*dr. SO you are making the right play here but you are going against basic strategy and hitting hard 12 v 6 when KO true count is plus 4 and you have a large bet out. This may add camouflage as well as not taking insurance when tc(KO) = 6 for example as long as AA89mTc < (-2)*dr and a few other plays.
5. Side Bets. AA89mTc and 5m7c may be used for some side bets if offered by the casino which the HO2 with ASC cannot. For example for the Lucky Ladies bet use LLc = Tc = KO + AA89mTc and for Super 4 bet use S4c = super 4 count = KO - (1/2)*(AA89mTc) or if Blazing 7's if offered, use 5m7c to help bet the Blazing 7's.
So again, simulations show only POWER which is number 2 on my list. But KO with AA89mTc and 5m7c also have advantages 3, 4, and 5 which is not addressed by simulations. Also it should be noted ,which I will point out again below, that KO with AA89mTc and 5m7c was NEVER simulated.
KO with AA89mTc and 5m7c was always my recommended count combination for blackjack shoe game. And I have never changed my mind!
The HL with AA78mTc and 5m6c was used as a proxy to see if my calculations were correct because it was much simpler to simulate the HL system than the KO system.
Based on CC of individual plays and on BC, these would indicate the KO with AA89mTc and 5m7c will beat the HO2 with ASC for S17, DAS and no LS and if late surrender is offered (Gronbog did not simulation LS) then KO with AA89mTc and 5m7c definitely will. Remember that all of my predications came true based on CC of individual plays and on BC and that each time additional changes were added, the SCORE improved. This indicates that my calculations are correct and using these same calculations show that KO with AA89mTC and 5m7c will beat the HO2 with ASC most likely for the no LS game and definitely for the LS game.
And again, simulations only take into account POWER and does not address the other 4 points I mentioned in choosing a system which the KO system does a good job with.
So below I will discuss this in more detail and go over Gronbog's latest sim results.
Again, KO with AA89mTc and 5m7c was NEVER simulated as so you cannot say that this KO system would not outperform the HO2 with ASC.
The results were exactly as I predicted. Don asked me for my prediction and I told him the gap would be closed but HL with AA78mTc and 5m6c would still be below the HO2 with ASC because the BC even with 5m6c added is still just over 1% below the HO2 - 2*(Adef) BC.
Attached is a file that shows that I had predicted that the gap would have been decreased 44%. Ignoring the play all simulations, the gap was actually decreased around 30%. My prediction was off a little but is was based on my assumption that the gap remaining was totally due to betting and that the gap would be closed linearly with BC.
In my last book HL with + - side counts, I never considered 5m6c as a 2nd side count to add to HL with AA78mTc. I had suggested 5m9c as a 2nd side count to improve betting. If 5m9c were used as a second side count the BC of HL + (1/2)*(5m9c) would have been much closer to HO2 – 2*(Adef) and there would have been some additional playing strategy changes as well. The results of HL with AA78mTc and 5m9c would have been even closer.
I got involved with 5m6c because I looked at the improvement in hard 16 v T hit/stand decision which is the 2nd most important strategy deviation. But that improvement was not enough, at least for the shoe game, to offset the inferior BC.
It should be pointed out that every prediction I made came true and that when more changes were added the SCORE improved. That means that my calculations are correct. But my efforts were like trying to put a band aid on a pig (the pig being the HL with AA78mTc and 5m6c which was NEVER my recommended count and never even a count combination I ever considered with the HL in my 4th book HL with + - side counts). In the end the HL with AA78mTc and 5m6c underperformed the HO2 with ASC.
I had emailed my Index Generator Excel program to Gronbog. This program was checked by ETFAN in 2011, the resident mathematician for Arnold Synder. I came up with the LSL (Least Squares Line) technique which ETFAN was unfamiliar with. ETFAN knew Peter Griffin's PD (Proportional Deflection) technique and taught it to me. I programmed in the PD into my spreadsheet and the results obtained with my LSL technique exactly matched the PD techniques. So two independent methods that produced the exact same results. Gronbog’s simulations further show that my calculations are correct as the indices and values of k1 and k2 of HL with AA78mTc and 5m6c generated from my LSL technique were entered into the sim program. If my LSL technique were incorrect the SCORES would not have improved each time a new set of changes were added from the output of my LSL program.
I told Gronbog to feel free to share my LSL Index Generator program I emailed him with either Norman or Don Schlesinger if they are interested.
As I had mentioned earlier, HL with AA78mTc and 5m6c is NOT and NEVER was my recommended system. It was chosen because it was simpler to simulate that the KO count and KO system.
My recommended count from day one has always been KO with AA89mTc and 5m7c and I have not changed my mind. Please review some of my previous posts on the forum where I describe KO with AA89mTc and 5m7c.
Please also review the list of 8 advantages that I posted for using the KO with XmYc side counts over the HO2 w ASC for the shoe game, the main advantaged being true count accuracy for true counts > 3 and EXACT XmYc side counts,
The side counts may also come in handy for various side counts. For example, as I posted earlier, I use LLc = Lucky Ladies count = Tc = Ten count = KO + AA89mTc for the Lucky Ladies bet. And if Blazing 7’s were offer, then the 5m7c could be used for the Blazing 7’s bet. Also if Super 4 bet is offered, use S4c = super 4 count = KO – (1/2)*(AA89mTc) for the Super 4 bet. To be fair, since a side count as Aces is used with HO2, that side count of Ace would also come in handy for the Super 4 bet. So HO2 with ASC helps with the Super 4 bet there is no additional HO2 side count help with the LLc or Blazing 7’s.
I would like to review again here where I got AA89mTc and 5m7c as side counts to the KO. They just did not come out of thin air. I chose the KO count as my primary count because it is a simple level one count and also because I liked the KO unbalanced counts for the shoe game because of the true count accuracy calculations for true counts > 3 as compared to a balanced count which I also explained earlier in this forum.
First I wanted to find the side count which when used with the KO increased the BC the most. So I first chose 45m79c to add to the KO system using brc = betting running count = KO + (1/2)*(45m79c) for betting. Although that increase KO betting for the S17, DAS, LS game to 99.6%, unless you are keeping only one side count, keeping 45m79c along with AA89mTc is very difficult. So once I decided to add AA89mTc as my second side count, which I will describe below, for a very slight decrease in BC, I chose to switch 45m79c with 5m7c since 5m7c is much easier to keep if AA89mTc is also used with the KO. Using brc = betting running count = KO + (1/2)*(5m7c) give a BC of 99.0% for S17, DAS, LS game so BC decreased by 0.6% for the LS game. Also 5m7c adds some strategy gains which you get for free. However, 45m79c adds even more strategy gains so there is also a loss in playing strategy when 5m7c is used instead of 45m79c when AA89mTc is also used. However, the slight loss in BE and PE when 5m7c is used instead of 45m79c is acceptable because the 5m7c is much easier and practical to use with the AA89mTc. So for ease of use with only a small decrease in BE and PE use 5m7c instead of 45m79c when AA89mTc is also used as a side count.
My third book is entitled KO with 45m79c and AA89mTc which is the best two side count card combination as it has both the highest BC and also is better for more playing strategy decisions than using KO with 5m7c and AA89mTc as described above. However, keeping both the 45m79c with AA89mTc is just too difficult to use so, as I described above, I gave up a little in BE and PE and switched from 45m79c to 5m7c to use with KO and AA89mTc.
So after I chose 45m79c or 5m7c as my side count to add to the primary KO count, my next goal was to increase playing efficiency. The most important playing strategy change is insurance. So I wanted to find a side count that maximized the insurance decision. Adding AA89mTc to KO gives Tc = Ten count = KO + AA89mTc which give perfect insurance. Thus AA89mTc was me selected second side count to add to KO with 45m79c or KO with 5m7c. Then other strategy changes with AA89mTc added to OK just fell in place as a bonus.
Si although direct simulation of KO with 5m7c and AA89mTc was never done, the simulations of HL with AA78mTc and 5m6c shoes that my calculations and predictions were correct. This same procedure I used for KO with 5m7c and AA89mTc so if it worked for HL with AA78mTc and 5m6c then it should also work for KO with AA89mTc and 5m7c.
My case for the KO with 5m7c and AA89mTc
In the absence of direct simulations of KO with 5m7c and AA89mTc I would like to put forth my case for this KO system for the shoe game based on what I have and summarized and what I have listed in previous blogs on this forum below.
S17, DAS, No LS:
In previous posted I had listed, sorted by CC, the CC of HO2 w ASC against the KO with AA89mTc and 5m7c for the I18, and also for an expanded list of 49 playing strategy changes and then the BC of each system for the no LS game.
The numbers I am listing below are from memory. Look at my previous posts for exact numbers
If you looked at the I18 CC comparison and if you consider an absolute value CC difference of less than 3% as a tie, then you would see that the KO system outperformed the HO2 system in 8 of the I18, there were 8 ties and the HO2 system beat the KO system in only two of the I18. Also the maximum "loss" of the KO system was significantly below the maximum "gains" of the KO systems where loss and gains were differences in CC. When the expanded list of 49 playing strategy changes were consider and considering CC difference of less than 2.5% as ties, then the KO system beat the HO2 system in 25 situations, tied 14 and lost 10. The point I am making here is that these comparisons of CC show that the PE of KO with AA89mTc and 5m7c beats HO2 with ASC and KO + (1/2)*(5m7c) has a LS BC = 99.1% whereas HO2 – 2*(Adef) BC = 98.5%.
Thus KO with AA89mTc and 5m7c beats HO2 with ASC in both PE and BE and so the KO system must beat the HO2 system.
S17, DAS, LS:
This situation got only worse for HO2 with ASC when LS is offered.
If LS is offered, the HO2 system does even worse when compared to my KO system. My KO system beats that HO2 system in EVERY SINGLE LS decision. In addition when LS EoR are used, the BC of KO + (1/2)*(5m7c) outperforms that HO2 with ASC now by over 1% from the 0.6% for the no LS EoR.
So now simulations have proven that my calculations are correct and every single prediction that I made using my LSL program was correct then this last prediction of my KO system must also be correct. The KO with AA89mTc and 5m7c MUST beat the HO2 with ASC.
Last edited by bjanalyst; 02-05-2019 at 11:00 AM.
Just one note on index generation. IMO, indices for human use cannot be generated algorithmically as accurately as by simulation as humans do not estimate remaining cards exactly. Indeed, many humans don’t even calculate estimated decks to the same accuracy in the early and late depths and several methods of true count calculation are used. I also don’t believe algorithmic methods accurately calculate split indices. There are simply too many nonlinear aspects to blackjack.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
You are correct about blackjack being non-linear. But linear approximations work really well especialliy if decks remaining are greater than one. If you are less than one deck remaining then from what i read non-linearliy may have a bigger impact. But linear approximates are the best a human and do and they work very well. Don said as much in his BJA3 where LSL approximations were used for EoR. And I used infinite deck approximations I gave to Gronbog for indices and values of k1 and k2 in HL with AA78mTc and 5m6c and you can see that simulations showed that they did work well as the SCORE improved with each addition of changes that I gave to Gronbog.Originally Posted by Norm
It should also be noted that as CC increases the difference in indices between various numbers of decks decrease and they all approach the infinite deck index for any given situation as CC approaches one. So my goal was to maximize the CC of each individual playing strategy variation and with increased CC coefficients the difference in indices between different number of decks decreases so you do not have to memorize as many index changes for different number of decks - another advantage o my system.
I had emailed Gronbog my LSL index generator Excel file and I emailed him that he can forward it to you or to Don if you wish to review it. As I stated earlier, ETFAN of Arnold Synder helped me with some mistakes I had made with this program and also showed me PD technique which gave the same results as the LSL technique that I developed. So feel free to review that LSL index generator Excel file to lend even more credibility to my results.
Again, the jury is out on KO with AA89mTc and 5m7c because it was NEVER simulated but I already gave you my predictions above based on CC of individual plays and based on BC for both no LS and LS games. ALL of my other predictions came true about HL with AA78mTc and 5m6c based on CC of individual plays and based on BC so I would expect my predictions of KO with AA89mTc and 5m7c will also come true.
Again my prediction is that KO with AA89mTc and 5m7c will probably beat HO2 with ASC for S17, DAS, no LS and will most certainly beat HO2 with ASC for S17, DAS, LS. With LS offered KO with AA89mTc and 5m7c has to beat HO2 with ASC.
PS: Another reason for using unbalance KO for the shoe game. You statedhumans do not estimate remaining cards exactly.
Perfect point of why you want ot use KO count. I showed in previous attachments that the KO count is much more accurate than any balanced count when tc > 3. Also linear combinations of balanced counts with an unbalanced count also yield an unbalanced count with the same unbalance as the original unbalance counts. Thus KO + k1*(5m7c) + k2*(AA89mTc) is also unbalanced with a pivot of true count of 4 for every value of k1 and k2.
There is no need for extremely accurate estimate of dr when KO is used. Look at my first book KO with Table of Critical Running Count. and you will see this in more detail. Also look at an exhibit I posted earlier with errors in estimating true counts from errors in decks remaining. There I showed that the farther from the pivot the more sensitive errors in estimating decks remaining have in calculation true counts and at the pivot the true count independent of decks remaining. So at true count of 5 for example, the HL is 5 true count points away from its pivot of a true count of 0 but KO is only 1 true count point away from its pivot of a true count of 4. So the KO is five times more accurate in true count calculations at a true count of 5 than the HL is. And accurate true count calculations are very important when your big bets are out such as true counts > 3 which the KO count does an excellent job with. So with the KO count estimating to the nearest deck remaining is more than accurate.
Also I showed the XmYc is EXACT as opposed to ASC being an estimate since you are estimating dr for ASC and you just admitted humans cannot estimate dr accurately.
So this was my point #3 which was ACCURACY which is another reason KO with AA89mTc and 5m7c should be used instead of HO2w with ASC for the shoe game.
Last edited by bjanalyst; 02-05-2019 at 11:35 AM.
One of the best methods available to humans -- but certainly not the best a computer can use. Also, if ETFan helped you with coding, I strongly suggest you find someone else to help in future.
Note: Poor indices most often improve SCORE over no indices. An improvement does not mean the index is "correct". This is the reason that compromise indices work.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
I have not used ETFAN since 2011. He helpd me initially with understanding some CC nuanance and such and taught me PD. THE LSL techinique was all my idea and doing linear combaintions of counts to get a derived count which I then maximize the CC to EoR with was also all my idea. And I have given ETFAN and Arnold Snyder credit in the credit ssctions of the introduciotn to each of my books saying atht ehty helped me initially with my calcluations. BUt my Excel program is now proven and it works fine as simluations of Gronbog showed. I do not need any more help. I just needed some help at the beginning but now I know what to do and do not need help. My Excel program is correct as ETFAN had reviewed my program and said it was fine. Ask Gronbog to email you a copy that I sent to him and you can review it yourself.
[QUOTE=Norm;264777
Note: Poor indices most often improve SCORE over no indices. An improvement does not mean the index is "correct". This is the reason that compromise indices work.[/QUOTE]
Remember that Griffin said that if a situation is borderline it is best to stick to basic strategy than depart from basic strategy early as you will lose more money by departing from basis strategy early than you would from waiting until you are definitely over the index to make the playing strategy play.
The formula I use is pa(t) = AACpTCp*(t - Idx) where pa(t) = player's advantage at true count "t", AACpTCp = Average Advantage Change per True count point and Idx = index. Note if t = Idx then pa(Idx) = 0 and if t = Idx + 1 then pa(t) = AACpTCp. I put together in my books a chart of pa's for various true counts for some splitting and doubling situations. My suggestion was to wait at least one true count point over the index before doubling or splitting. When you are at the index your advantage of doubling or splitting over not doubling or splitting is zero - it is even and from an expected value point of view it does not matter. But from a risk point of view it matters a lot. Why would you double of spilt and risk more money for virtually not EV gain. So wait until the double or splitting index is at least one true count point over the Idx to double or split.
Also I have shown that as CC increases the difference in indices between various numbers of decks decreases and approach the infinite deck index. And my goal was to increase CC so these increased CC also increase the accuracy of my indices.
I have not made any mistakes and no one has shown any mistakes that I have made. My calculations are correct.
Last edited by bjanalyst; 02-05-2019 at 11:50 AM.
It depends on the index and strategy decision. An index can be off by +/-4 and still improve results. Just not improve them as much as is possible. Also, I don't understand why anyone would consider using infinite deck calculations. Further, I've never heard of anyone using algorithmic techniques to calculate risk averse indices. RA indices improve SCORE.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
I did not use algorithms to calculate risk averse indices. I just made a simple logical observation to wait until the true count is at least one true count point over the index to make strategy changes, otherwise stick to basic strategy. This goes especially for doubles or splits were more money is put on the table. However, for LS I would suggest rounding down the index where you might surrender a little early as that would reduce risk since if you surrender you know you lost one-half. So I have rounded down the surrender indices to the nearest integer. But round up to double or split indices and you can use the exact indices for hit/stand. Another consideration in borderline hit/sand or double split decision is how close you are to the cut card. If you stand or do not double or split in borderline situations that you probably will get an extra round of play before the cut card comes out. And this is another advantage of surrendering and rounding down the surrender index. Besides reducing risk you also are not using up cards in a high count situation and may get an extra round of play before the cut card comes out.
For the six deck game the infinite deck indices worked fine. Also remember that I have increased the CC for many of these plays so the difference in indices between various number of decks also decreases and approached the infinite deck index. Simulations show that the calculated infinite deck indices worked fine.
For insurance for example, the index if 4 with CC = 100%, that is insure if KO + AA89mTc >= crc(4) = 4*n and it totally independent of number of decks used and since the index it at the pivot point of the KO count is also independent of decks remaining. This is the most important playing strategy change and the index is exact for all number of decks and is independent of decks remaining.
And I am glad that SCORE takes into account RA indices. So player just needs to add one to doubling or splitting indices or use the LS which I have already rounded down to the nearest integer and if borderline hit/stand use basic strategy and also stand I marginal sudations and do not double when the count is high so you get an extra round before cut card by not using up high cards in a large positive count by hitting or doubling and splitting.
I am not home so I do not have my files with me but in my books I have charts of players advantage by doubling or splitting at various true counts for various doubles or splits. If AACpTCp is kind of low then you may want to wait two true count points before doubling or splitting.
I have read that doubling hard 10 v T is very risky. The analysis was done using the HL count which is to double hard 10 v T whenever tc(HL) >= 4. It was suggested to wait until tc(HL) = 6 to double as a risk averse index. It should be noted that HL has a hard 10 v T CC of only 81% whereas KO has a hard 10 v T CC of 91% so doubling hard 10 v T when KO >= crc(4) = 4*n is safer than doubling hard 10 v T when HL >= 4*dr. Also the KO index is 4 for doubling hard 10 v T which is EXACT and totally independent of decks played or decks remaining. The HL pivot of a true count of zero is four true count points away from the index of 4 for hard 10 v T so it also subject to error in estimating decks remaining.
The only way you are going to get definitive answers to your questions is if simulations were done on the KO with AA89mTc and 5m7c. My indices worked fine for HL with AA78mTc and 5m6c so using the same techniques with KO with AA89mTC and 5m7c I am sure that my indices and values of k1 and k2 will also work fine.
Last edited by bjanalyst; 02-05-2019 at 12:20 PM.
Instead of performing accurate RA index calculations, you perform complex calculations and then just add one? 10v10 you add 3 with a single level count. The majority of indices you add zero.
If I had known you just add one, it would have saved me a ton of code.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
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