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Thread: Add 7m9c to HL to improve betting and surrender

  1. #118


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    Quote Originally Posted by dogman_1234 View Post
    There seems to be a lack of understanding on your part of what you are trying to do here.

    The foundation of your understanding of blackjack is poor. The subtle nuances that the games offers can be easily found in many a literature. The main ones are The Theory Of Blackjack by Peter Griffin, and Blackjack Attack by Don Schlesinger. Both are a requite read for any 21 AP researcher!

    Now, to better educate you on your lack of understanding concerning 21 itself, let us take a tour of the game (at its current face.) First, we need to have the numerical values to determine what it is we are to expect from 21. From there, we find the difference in these expectations for each rank removed from a full pack/shoe. We therefore have a beginning foundational understanding by way of the Effect of Removals:


    https://web.archive.org/web/20090826...or/beor1ds.htm
    https://web.archive.org/web/20090106...or/peor1ds.htm

    From here, we will then ask ourselves, "What is the 'best' way to articulate these values to be human-usable?" When someone invokes a sense of "best", we must think in terms of mathematical optimization!

    Once you have read both books, and used the above data to compute new point values, you will be able to understand why many here deride your new "system". Simply put: the amount of work needed to gain the give EV of your system is negligible! You will then understand why some prefer to use a level 2 system, compromised systems, side counts, and secondary counts based on the given EOR's listed. You will understand better where your gains will be based on EXPECTED VALUES and *NOT ON CC!*

    You can have a system as complex as Tarzan, but if it is as complex as Tarzan's and pails in comparison with respect to expectation, don't be surprised when others can't take you seriously over your claims. As baseless as many of your claims have been.

    I have been *MORE* than nice to you for this post. Please take time to re-read it, digest everything, purchase the above books, and seriously consider going a different route.

    If don't want to build/program a simulator, consider building a Combinatorial Analyser! A great academic exercise as well as an invaluable tool to have and modify as needed!

    Been there, done that. You are not telling me anything that I do not already know.

    My EXCEL program calculates indices for any number or decks and any count, balanced or unbalanced, but I concentered on the infinite deck approximation.

    And if I used two counts, I used Excel Solver to find the values of k1 and k2, for example, KO + k1*(5m7c) + k2*(AA89mTc) that maximized the absolute value of the CC between the tag values of the derived count an the EoR from BJA which EoR were calculated to four or five digits using combinatorial analysis.

    I developed the LSL technique ETFAN was using Proportional Deflection (PD). ETFAN vefifid that my Excel file was correct. We tested each on several examples and LSL and PD produced identical results, adding more credibility that I did things correctly. Also indices generated from my Excel program for the HL for example, corresponded to the HL indices published. So another indication that things were done correctly. And also my formulas for playing strategy changes make logical sense also.

    As another level of proof that I have done things correctly, every time I gave Gronbog a new set of strategy changes with values of "k" and a new index, the SCORE improved, every single time. For HL with AA78mTc I gave Gronbog some very crazy and insignificant soft doubling indices with new values of "k" and indices. And the SCORE improved, very slightly as expected, but it did improve. If i had made an error, the simluations would have shown in and the SCORE woudl not have increased. But the SCORE increased EVERY time I gave Gronbog new indices and values of "k".

    I also tested my LSL linear combination of counts tecnhique against examples that Griffin used in his Therooy of Blackjack with his complicaed correlation coefficient matrix and I got the same results. My calcluations are CORRECT.

    I have a book published in 2016 called Blackjack KO with Table of Critical Running Counts which I am redoing along with redoing KO with 5m7c and AA89mTc to make them easier to read. But in that book I covered what you mentioned above and much, much more including more formulas and relationships between infinite deck indices that I derived.

    So here is how I described what I did in a footnote in my book Blackjack KO with Table of Critical Running Counts.

    The multiple linear regression method used in this paper consists of defining a new count, X2 = X0 + k*(X1), and finding the value of ‘k’ that maximizes the absolute value of the infinite deck correlation coefficient between the tag values of X2 and Y = Effects of Removal, EoR. m = Slope(EoR, X2) = Slope(Y, X2) is the same whether X2 is balanced or not, that is, it is not necessary to convert X2 to a balanced count before calculating the infinite deck index. Once the value of ‘k’ is determined so that X2 is now defined, then the slope of the least squares line (LSL) between Y = EoR and X2 is calculated, i.e., m = slope of LSL = AAC (Average Advantage Change) in EV for X2 increasing by one and for 51 cards remaining. This is because Y = EoR is given for a single deck and so EoR(c) = EoR for card ‘c’ removed from a single deck = EV(51 cards remaining after removing card ‘c’) – EV(full deck) so 51 cards are remaining. See Effects of Removal Definition exhibit under Derivations in the Appendix. But AAC in EV for 52 cards remaining is required, i.e., AACpTCp = AAC per True Count point is required. So AACpTCp is calculated as AACpTCp = (51/52)*(AAC) = (51/52)*(slope). Then infinite deck index is calculated as Idx = FDHA / AACpTCp. Griffin used a slightly different (and more complicated and abstract, in my opinion) procedure where he constructs a 3 x 3 correlation coefficient matrix of X0, X1 and Y. The multiple linear regression method has intuitive appeal since as ‘k’ varies, X0 + k*(X1) can be seen to represent a series of various derived counts to choose from, each with its own correlation coefficient with EoR. The value of ‘k’ giving the best count is the value of ‘k’ that maximizes the absolute value of the correlation coefficient of the tag values of the derived count, X2, and EoR for the given playing strategy situation under consideration. See the exhibits under Calculation of KO Index for Standing on hard 15 v T in the Appendix for an example of these calculations. I used this technique to find the value of ‘k’ in KO + k*(5m7c) that maximized the absolute value of the infinite deck correlation coefficient between the tag values of KO + k*(5m7c) counts for each given situation’s EoR. Once the value of ‘k’ had been determined, then a LSL was fitted to the KO + k*(5m7c) count and the EoR and the index calculated. As a check, the proportional displacement (PD) technique was also used to calculate the index of KO + k*(5m7c) count. Both LSL and PD techniques produced identical indices.



  2. #119


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    Quote Originally Posted by bjanalyst View Post

    Been there, done that. You are not telling me anything that I do not already know.
    Why did you deviate from the procedure than?

    Quote Originally Posted by bjanalyst View Post


    I have a book published in 2016 called Blackjack KO with Table of Critical Running Counts which I am redoing along with redoing KO with 5m7c and AA89mTc to make them easier to read. But in that book I covered what you mentioned above and much, much more including more formulas and relationships between infinite deck indices that I derived.

    So here is how I described what I did in a footnote in my book Blackjack KO with Table of Critical Running Counts.

    It is a shame that KO with 5m7c and AA89mTc doesn't even perform close to the "Gordon Count" with all the side counts and you have to side count two components.

  3. #120


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    Quote Originally Posted by bjanalyst View Post

    Been there, done that. You are not telling me anything that I do not already know.

    My EXCEL program calculates indices for any number or decks and any count, balanced or unbalanced, but I concentered on the infinite deck approximation.

    And if I used two counts, I used Excel Solver to find the values of k1 and k2, for example, KO + k1*(5m7c) + k2*(AA89mTc) that maximized the absolute value of the CC between the tag values of the derived count an the EoR from BJA which EoR were calculated to four or five digits using combinatorial analysis.

    I developed the LSL technique ETFAN was using Proportional Deflection (PD). ETFAN vefifid that my Excel file was correct. We tested each on several examples and LSL and PD produced identical results, adding more credibility that I did things correctly. Also indices generated from my Excel program for the HL for example, corresponded to the HL indices published. So another indication that things were done correctly. And also my formulas for playing strategy changes make logical sense also.

    As another level of proof that I have done things correctly, every time I gave Gronbog a new set of strategy changes with values of "k" and a new index, the SCORE improved, every single time. For HL with AA78mTc I gave Gronbog some very crazy and insignificant soft doubling indices with new values of "k" and indices. And the SCORE improved, very slightly as expected, but it did improve. If i had made an error, the simluations would have shown in and the SCORE woudl not have increased. But the SCORE increased EVERY time I gave Gronbog new indices and values of "k".

    I also tested my LSL linear combination of counts tecnhique against examples that Griffin used in his Therooy of Blackjack with his complicaed correlation coefficient matrix and I got the same results. My calcluations are CORRECT.

    I have a book published in 2016 called Blackjack KO with Table of Critical Running Counts which I am redoing along with redoing KO with 5m7c and AA89mTc to make them easier to read. But in that book I covered what you mentioned above and much, much more including more formulas and relationships between infinite deck indices that I derived.

    So here is how I described what I did in a footnote in my book Blackjack KO with Table of Critical Running Counts.

    The multiple linear regression method used in this paper consists of defining a new count, X2 = X0 + k*(X1), and finding the value of ‘k’ that maximizes the absolute value of the infinite deck correlation coefficient between the tag values of X2 and Y = Effects of Removal, EoR. m = Slope(EoR, X2) = Slope(Y, X2) is the same whether X2 is balanced or not, that is, it is not necessary to convert X2 to a balanced count before calculating the infinite deck index. Once the value of ‘k’ is determined so that X2 is now defined, then the slope of the least squares line (LSL) between Y = EoR and X2 is calculated, i.e., m = slope of LSL = AAC (Average Advantage Change) in EV for X2 increasing by one and for 51 cards remaining. This is because Y = EoR is given for a single deck and so EoR(c) = EoR for card ‘c’ removed from a single deck = EV(51 cards remaining after removing card ‘c’) – EV(full deck) so 51 cards are remaining. See Effects of Removal Definition exhibit under Derivations in the Appendix. But AAC in EV for 52 cards remaining is required, i.e., AACpTCp = AAC per True Count point is required. So AACpTCp is calculated as AACpTCp = (51/52)*(AAC) = (51/52)*(slope). Then infinite deck index is calculated as Idx = FDHA / AACpTCp. Griffin used a slightly different (and more complicated and abstract, in my opinion) procedure where he constructs a 3 x 3 correlation coefficient matrix of X0, X1 and Y. The multiple linear regression method has intuitive appeal since as ‘k’ varies, X0 + k*(X1) can be seen to represent a series of various derived counts to choose from, each with its own correlation coefficient with EoR. The value of ‘k’ giving the best count is the value of ‘k’ that maximizes the absolute value of the correlation coefficient of the tag values of the derived count, X2, and EoR for the given playing strategy situation under consideration. See the exhibits under Calculation of KO Index for Standing on hard 15 v T in the Appendix for an example of these calculations. I used this technique to find the value of ‘k’ in KO + k*(5m7c) that maximized the absolute value of the infinite deck correlation coefficient between the tag values of KO + k*(5m7c) counts for each given situation’s EoR. Once the value of ‘k’ had been determined, then a LSL was fitted to the KO + k*(5m7c) count and the EoR and the index calculated. As a check, the proportional displacement (PD) technique was also used to calculate the index of KO + k*(5m7c) count. Both LSL and PD techniques produced identical indices.


    I told you guys he will never stop lol. It's like someone who does not have the ability to hear what others are saying.
    See, he still thinks that his KO project was a success.
    He does NOT UNDERSTAND anything that Don, Tarzan and others have said. He "knows that he is right" and that is all that matters to him.
    Let's see how long it takes for him not to reply to this thread again.
    It's all the same as his KO system in the past...he just wants to keep adding things.
    And he brings it to the forum desperately trying to make it seem like we are waiting for the results lol.
    How many members have said they are waiting for the results bjanalyst? None.
    Last edited by Counting_Is_Fun; 12-05-2019 at 12:39 AM.

  4. #121


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    Quote Originally Posted by Counting_Is_Fun View Post
    I told you guys he will never stop lol. It's like someone who does not have the ability to hear what others are saying.
    See, he still thinks that his KO project was a success.
    He does NOT UNDERSTAND anything that Don, Tarzan and others have said. He "knows that he is right" and that is all that matters to him.
    Let's see how long it takes for him not to reply to this thread again.
    It's all the same as his KO system in the past...he just wants to keep adding things.
    And he brings it to the forum desperately trying to make it seem like we are waiting for the results lol.
    How many members have said they are waiting for the results bjanalyst? None.

    It is you and the readers of this forum who do not stop.

    Ask yourself why you are not stopping adding posts with ridiculous and unfounded statements and questions prodding me to respond instead of patiently waiting for the sim results. And then when I respond to your crazy quesiotns you blame me for not stopping. BLAME YOURSELVES for continuing to ask crazy questions.

    I was content on waiting till the sim results came in but readers of this forum could not wait. They continued to prod me with questions and more questions which is why there are so many posts.

    So if you want this to stop then STOP asking me ridicolus quesiotns and STOP criticizing me and just wait for the sim reuslts.

    You state that I am so sure that I am correct.

    I will just reply to that based on my record. Ever time I added new indices and counts with different "k" values the sim results showed an increase in the SCORE. So obvioulsy I must be dong something right.

    So my prediction for HL w 7m9c with LS is that the HL will be improved substantially with a simple plus/minus level one side count counting only two ranks, 7m9c added to the HL.

    And I also stated that the results when compared to the HO2 w ASC are up in the air.

    I am not sure how close the HL w 7m9c will come to the HO2 w ASC. And that is because, as I stated earlier, BEs are the same, HO2 w ASC beats HL w 7m9c for regular blackjack and HL w 7m9c beats HO2 w ASC for surrender.

    So I predict a significant improvement in HL with adding 7m9c but I am NOT predicting whether it will beat HO2 w ASC.

    So if you want to keep the posts down then wait for sim results before positng any more quesitons.

  5. #122


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    Quote Originally Posted by bjanalyst View Post

    It is you and the readers of this forum who do not stop.

    Ask yourself why you are not stopping adding posts with ridiculous and unfounded statements and questions prodding me to respond instead of patiently waiting for the sim results. And then when I respond to your crazy quesiotns you blame me for not stopping. BLAME YOURSELVES for continuing to ask crazy questions.

    I was content on waiting till the sim results came in but readers of this forum could not wait. They continued to prod me with questions and more questions which is why there are so many posts.

    So if you want this to stop then STOP asking me ridicolus quesiotns and STOP criticizing me and just wait for the sim reuslts.

    You state that I am so sure that I am correct.

    I will just reply to that based on my record. Ever time I added new indices and counts with different "k" values the sim results showed an increase in the SCORE. So obvioulsy I must be dong something right.

    So my prediction for HL w 7m9c with LS is that the HL will be improved substantially with a simple plus/minus level one side count counting only two ranks, 7m9c added to the HL.

    And I also stated that the results when compared to the HO2 w ASC are up in the air.

    I am not sure how close the HL w 7m9c will come to the HO2 w ASC. And that is because, as I stated earlier, BEs are the same, HO2 w ASC beats HL w 7m9c for regular blackjack and HL w 7m9c beats HO2 w ASC for surrender.

    So I predict a significant improvement in HL with adding 7m9c but I am NOT predicting whether it will beat HO2 w ASC.

    So if you want to keep the posts down then wait for sim results before positng any more quesitons.
    My post only had one question..."How many members have said they are waiting for the results bjanalyst?"
    And I definitely didn't ask you to post more of your expectations again, uggg.

  6. #123
    Senior Member Tarzan's Avatar
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    Quote Originally Posted by DSchles View Post
    Nice post. Nice to hear from you again. And, of course, what you write is 100% accurate.

    Happy Holidays, my friend.

    Don
    I've been busy with personal issues and projects, some major things going on, all quite positive but not without a lot of effort, so unable to spend as much time on the forum as I'd like. Happy holidays to you also, and everyone here for that matter.

  7. #124


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    I wouidl ike to double check the top 6 HL w 7m9c indices that I am using.

    I am attaching them as a PDF to this post.

    I think there are index generator programs that can calculated indices if you add the tag value of the count you are considering.

    The two counts I am considering in my top 6 are HL + 2*(7m9c) and HL + 3*(7m9c).

    psrc1 = HL + 2*(7m9c) has tag values of 1, 1, 1, 1, 1, 2, 0 , -2, -1, -1 for ranks 2, 3, 4, 5, 6, 7, 8, 9, T, A respectively.
    psrc2 = HL + 3*(7m9c) has tag values of 1, 1, 1, 1, 1, 3, 0 , -3, -1, -1 for ranks 2, 3, 4, 5, 6, 7, 8, 9, T, A respectively.

    psrc1 is used for surrendering 8,8 v T DAS, hard 14 v 9, Hard 14 v T, hard 14 v A and Hard 13 v T.
    psrc2 is used for standing on hard 14 v T.

    The top 6 HL w 7m9c with indices I calculated are:

    surrender 8,8 v T DAS if psrc1 >= 2*dr
    surrender hard 14 v 9 if psrc1 >= 6*dr
    surrender hard 14 v T if psrc1 >= 3*dr
    surrender hard 14 v A if psrc1 >= 6*dr
    surrender hard 13 v T if psrc1 >= 8*dr

    And stand on hard 14 v T if psrc2 >= 9*dr

    See attached PDF for more details on these indices.

    I want to make sure that these six indices are correct.

    So what needs to be done is to put in the tag values of psrc1 for the five surrender plays and the tag values of psrc2 for standing on hard 14 v T.

    See the indices that are generated for these six plays.

    I would like to know if those independently generated indices match my calculated indices.

    I do not want to waste Gronbog's time if my indices are incorrect.

    Thanks
    Top 6 six deck indices.pdf


  8. #125


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    Quote Originally Posted by bjanalyst View Post
    I wouidl ike to double check the top 6 HL w 7m9c indices that I am using.

    The two counts I am considering in my top 6 are HL + 2*(7m9c) and HL + 3*(7m9c).

    psrc1 = HL + 2*(7m9c) has tag values of 1, 1, 1, 1, 1, 2, 0 , -2, -1, -1 for ranks 2, 3, 4, 5, 6, 7, 8, 9, T, A respectively.
    psrc2 = HL + 3*(7m9c) has tag values of 1, 1, 1, 1, 1, 3, 0 , -3, -1, -1 for ranks 2, 3, 4, 5, 6, 7, 8, 9, T, A respectively.
    It seem like you still don't understand card counting. How many time did we say "counting the 9s as negative will have a harmful effect on insurance"? If I were you I would drop the 9s from the system completely, and make it 0.

    For HL + 2*(7m9c) has tag values of 1, 1, 1, 1, 1, 2, 0 , -2, -1, -1 PE = .469, BC = .85 and IC = .566
    HL + 3*(7m9c) has tag values of 1, 1, 1, 1, 1, 3, 0 , -3, -1, -1 PE = .386, BC = .733 and IC = .454

    Did you bother to do the calculations for the PE, BC and IC before you decide which tag values to use?

  9. #126


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    Quote Originally Posted by seriousplayer View Post
    It seem like you still don't understand card counting. How many time did we say "counting the 9s as negative will have a harmful effect on insurance"? If I were you I would drop the 9s from the system completely, and make it 0.

    For HL + 2*(7m9c) has tag values of 1, 1, 1, 1, 1, 2, 0 , -2, -1, -1 PE = .469, BC = .85 and IC = .566
    HL + 3*(7m9c) has tag values of 1, 1, 1, 1, 1, 3, 0 , -3, -1, -1 PE = .386, BC = .733 and IC = .454

    Did you bother to do the calculations for the PE, BC and IC before you decide which tag values to use?
    You do not understand the system.

    You are using the stand-alone HL 90% of the time so there is no pollution with the negative tag value of the 9 because 90% of the time you are using the HL which counts the 9 as zero.

    You are keeping a side count of 7m9c. And you are using 7m9c for only two purposes.

    1. Betting; instead of using HL for betting you are using brc = HL + (1/2)*(7m9c).

    2. You are using 7m9c with the HL for ONLY SIX strategy changes which are surrender 8,8 v T DAS, hard 14 v 9, T, A, hard 13 v T and standing on hard 14 v T

    3. EVERYTHING ELSES you are using the stand alone HL.

    So you only use 7m9c with the HL when it helps the HL. Otherwise you use HL alone.

    What I was asking was to check the indices that I came up with for the SIX strategy changes where 7m9c is used with the HL. I just want SIX indices checked.

    So if someone has software that generates indices, I would like to check my indices for six strategy changes where the 7m9c is used as per my previous post.

    What is important is the sim results. I want the correct indices for the SIX HL w 7m9c strategy changes to give Gronbog when he does his sims. Anything other than these top 6 plays ONLY THE HL Is used (the 7m9c is NOT used) and of course the HL indices are used.

    If someone can check these six indices I calculated for HL w 7m9c shown in the previous post I would appreciate it.

  10. #127


    1 out of 1 members found this post helpful. Did you find this post helpful? Yes | No
    Quote Originally Posted by bjanalyst View Post
    You do not understand the system.

    You are using the stand-alone HL 90% of the time so there is no pollution with the negative tag value of the 9 because 90% of the time you are using the HL which counts the 9 as zero.

    You are keeping a side count of 7m9c. And you are using 7m9c for only two purposes.

    1. Betting; instead of using HL for betting you are using brc = HL + (1/2)*(7m9c).
    Firstly, you are no longer counting the 7m9c as (1/2). You are doubling both 7s and 9s, in this case (2)*7m9c. In what literature did you read that say side counting the 7m9c would help you improve betting? Side counting the 7s would help with playing strategies more than betting.

    Quote Originally Posted by bjanalyst View Post

    2. You are using 7m9c with the HL for ONLY SIX strategy changes which are surrender 8,8 v T DAS, hard 14 v 9, T, A, hard 13 v T and standing on hard 14 v T
    Side counting the 7s alone would help improve the 14 vs T plays but since you are incorporating the 9s, it might hurt the play. Side counting the 9s alone would improve the hard 14s, 15s and 16s playing decision. Why are you choosing the deviation for 13 vs T and NOT 15 vs 9, T, A? Doubting those 6 plays would increase SCORE significantly.

  11. #128


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    Quote Originally Posted by seriousplayer View Post
    Firstly, you are no longer counting the 7m9c as (1/2). You are doubling both 7s and 9s, in this case (2)*7m9c. In what literature did you read that say side counting the 7m9c would help you improve betting? Side counting the 7s would help with playing strategies more than betting.

    Side counting the 7s alone would help improve the 14 vs T plays but since you are incorporating the 9s, it might hurt the play. Side counting the 9s alone would improve the hard 14s, 15s and 16s playing decision. Why are you choosing the deviation for 13 vs T and NOT 15 vs 9, T, A? Doubting those 6 plays would increase SCORE significantly.
    7m9c does help with betting. And 7m9c helps mainly with the top 6 plays. You are not side counting 7s or 9s, your side count is the difference, 7m9c.

    I think I figured out the corrected indices. I will attach a PDF with the correction and I will give what I believe is the corrected top 6 below. For some reason my Excel file did not seem to calculate some of these indices correctly.

    Stand hard 14 v T if HL + 3*(7m9c) >= 12*dr
    Surrender 8,8 v T DAS if HL + 2*(7m9c) >= 2*dr
    Surrender hard 14 v 9 if HL + 2*(7m9c) >= 8*dr
    Surrender hard 14 v T if HL + 2*(7m9c) >= 3*dr
    Surrender hard 14 v A if HL + 2*(7m9c) >= 6*dr
    Surrender hard 13 v T if HL + 2*(7m9c) >= 9*dr

    Last edited by bjanalyst; 12-14-2019 at 07:18 AM.

  12. #129


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    Quote Originally Posted by bjanalyst View Post
    7m9c does help with betting. And 7m9c helps mainly with the top 6 plays. You are not side counting 7s or 9s, your side count is the difference, 7m9c.
    Citations needed. If you think that it is bad to side count 7s and 9s separately you have to think again. It could improve playing even more if you side count them separately. Don't believe me read "The Theory of Blackjack".

    I think I figured out the corrected indices. I will attach a PDF with the correction and I will give what I believe is the corrected top 6 below. For some reason my Excel file did not seem to calculate some of these indices correctly.

    Quote Originally Posted by bjanalyst View Post
    Stand hard 14 v T if HL + 3*(7m9c) >= 12*dr
    Surrender 8,8 v T DAS if HL + 2*(7m9c) >= 2*dr
    Surrender hard 14 v 9 if HL + 2*(7m9c) >= 8*dr
    Surrender hard 14 v T if HL + 2*(7m9c) >= 3*dr
    Surrender hard 14 v A if HL + 2*(7m9c) >= 6*dr
    Surrender hard 13 v T if HL + 2*(7m9c) >= 9*dr
    Still don't understand why you decided to improve surrendering hard 13 and not hard 15?
    Last edited by seriousplayer; 12-14-2019 at 09:07 AM.

  13. #130


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    Quote Originally Posted by seriousplayer View Post
    Citations needed. If you think that it is bad to side count 7s and 9s separately you have to think again. It could improve playing even more if you side count them separately. Don't believe me read "The Theory of Blackjack".

    I think I figured out the corrected indices. I will attach a PDF with the correction and I will give what I believe is the corrected top 6 below. For some reason my Excel file did not seem to calculate some of these indices correctly.


    Still don't understand why you decided to improve surrendering hard 13 and not hard 15?
    Of course, if you kept a side count of 7s and 9s you get more information But that is keeping two side counts and also these side counts are not a simple plus/minus side count.

    My goal was, for the players who want to keep the HL, to come up with the simplest side count possible to improve the HL. I believe 7m9c is the simplest side count. It is level one plus/minus count and counts only two ranks and also neither of those ranks are in the primacy HL count making it even easier to count and less confusion.

    Unfortunately, the 7m9c does not help with hard 15 surrender decisions. Only hard 14 and 13 surrender decisions.

    This can be seen in the logic in the following example:
    Surrender hard 14 v A if psrc = HL + 2*(7m9c) ? 6*dr
    If 7m9c is positive then more 7s than 9s came out of the shoe and so there is a deficiency of 7s and excess of 9s left in the shoe. So the more positive 7m9c is the more likely dealer has a 9 in the hole giving dealer an A9 for a total of 20 and the less likely for the dealer to have a 7 in the hole giving the dealer an A7 for a total of 18. Also the deficiency of 7s means it is less likely for player to pick up a 7 if the player hits his hard 14 for a perfect 21 and more likely for player to pick up one of the excess 9s and bust his hard 14 if player hits. Thus the larger 7m9c is the more advantageous it is for the player to surrender on his hard 14 v A than hit. This logic agrees with the formula. As 7m9c increases, psrc increases and eventually psrc exceeds 6*dr and player surrenders.

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