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Thread: Zenfighter: EoR's HITTING 17 - 12 Table 1

  1. #21
    Zenfighter
    Guest

    Zenfighter: Re: EoR's Table 5 (missing line added)

    DEALER 8


    HITTING 17 ? 12


     
    17 16 15 14

    A -2.2913 -1.05088 -0.626284 -0.457921
    2 -2.33871 -1.38594 -0.314613 0.0424502
    3 -2.85997 -2.43771 -1.34779 -0.255674
    4 -2.47536 -2.19894 -1.76435 -0.7419
    5 1.37724 -2.36073 -2.04525 -1.60912
    6 1.6552 1.72456 -2.03732 -1.77118
    7 1.83993 1.92535 1.90629 -1.89921
    8 2.18038 2.37604 2.31794 2.28689
    9 1.78107 0.201884 0.325984 0.448319
    T 0.282875 0.801591 0.896347 0.989336

    m -12.3434 5.22865 9.02769 12.8089

    ss 41.2946 34.31359 26.08121 19.5066

    Cks -0.00002 -0.000002 -0.000005 -0.0000018


     
    13 12

    A -0.291204 -0.12559
    2 0.152055 0.261938
    3 0.120518 0.24809
    4 0.282184 0.563732
    5 -0.608089 0.394101
    6 -1.38626 -0.387063
    7 -1.62222 -1.22888
    8 -1.53287 -1.30068
    9 0.567841 -3.09399
    T 1.07951 1.16709

    m 16.5563 20.2719

    ss 12.45866 18.99195

    Cks -0.000005 0.000018





    The fact that hard 17 is the most volatile of the stiff hitting situations is revealed by the 12th column figure of 41.0.
    A player who split three eights and drew (8,9), (8,7,9), and (8,9) would be more than 5% better off to hit the last total of 17 even though the hand was dealt from a full pack!


    P. Griffin

  2. #22
    Zenfighter
    Guest

    Zenfighter: Re: Further practical applications

    Griffin?s examples revisited

    Another use is to find some of the ?composition? dependent departures from the simplified basic strategy defined in Chapter Two.

    Before removing any number of cards from a specific table we need an adjusting factor (actually a multiplier) to reflect exactly the increased effect the removed cards will have upon the obviously smaller number of the remaining ones.

    Adjusting factor = 51/ (52 ? nr) where nr = number of removed cards

    1) Should you hit or stand with (4, 4, 4, 4) v 8?

    From table 5 (the corrected one!) we have:

    ((4 * -2.19894) + 2.37604) * 51/47 = -6.966079

    Adjusting m we have then:

    m = 5.22865 ? 6.966079 = -1. 737429 that?s

    You are better off standing, something that makes perfect sense with the pack ripped off from 4s.

    2) Just for drill the reader might confirm the 2.3% advantage hitting (6, 4, 6) v T mentioned in Chapter One

    From table 3 we have:

    ((2 * 1.64458) + (-1.72785) + 1.11513)) * 51/48 = 2.843718

    Adjusting m again we have:

    m = -0.445861 + 2.843718 = 2.397857 that?s

    You should hit the hand. A clearly demonstration that 3-card composition dependent hands totalling 16 vs a dealer?s T should be hit if one or more sixes are included in your hand. Statements coming out from a pocket calculator!

    Stay tuned.

    Sincerely

    Z

  3. #23
    Zenfighter
    Guest

    Zenfighter: Re: Cac, did you check The Waterkooler? *NM*


  4. #24
    Cacarulo
    Guest

    Cacarulo: Re: Cac, did you check The Waterkooler?

    E-mail sent! Sorry, I've forgotten about the existence of those pages. Will have to drop there more often.

    Sincerely,
    Cac

  5. #25
    Zenfighter
    Guest

    Zenfighter: Re: EV's inferences

    Approximating EV?s with a pocket calculator.

    As Griffin taught us, these methods with the aid of EoR?s tables are only approximate. You won?t be able to match perfectly exact expectations derived with the straightforward computations of powerful BJ?s algorithms. Let?s work an example with the aid of Cacarulo?s EV tables from bjmath.com.

    		standing	hitting 

    8,7 vs T -.51402 -.47479



    From the above figures we learn that the player is better by a 3.923% when hitting.

    See if we can approach this exact figure with the aid of Table 3 (hitting 15) and a pocket calculator.

    Remove the 3 cards:

    (0.0852692 + (-0.536984) + 1.19918) * 51/49 = 0.777974

    Adjusting m:

    m = 3.11027 + 0.777974 = 3.888244

    That is, our prediction is a roughly 3.9% advantage for hitting over standing, for this particular hand.

    Extracting algebraic indexes is another feature of these tables. I?ll post an example next time.

    Sincerely

    Z

  6. #26
    Zenfighter
    Guest

    Zenfighter: Re: Algebraic indexes

    Extracting EoR?s derived algebraic indexes is another important feature of the above tables.
    Following Snyder?s methodology outlined in his technical paper (Algebraic Approximation of Optimum Blackjack Strategy) and with the aid of our newly revised hit-stand tables, I?ve got the following generic indexes rounded to the nearest decimal.


    SD, s17

     
    2 3 4 5 6 7 8 9 T A

    16 4.1 -0.1
    15 3.6

    13 -0.0 -1.4
    12 4.4 2.6 0.6 -1.0 -0.1*

    * -2.5 (hit soft 17)



    Sincerely

    Z

  7. #27
    bjmagic
    Guest

    bjmagic: Re: EoR's Table 3

    > DEALER TEN
    > HITTING 17 ? 12
    > 13 12
    > A 0.00847634 0.09782
    > 2 0.456437 0.452561
    > 3 0.404035 0.404137
    > 4 0.205549 0.465538
    > 5 -0.26448 0.236017
    > 6 -0.433355 0.035243
    > 7 -3.21515 -2.05502
    > 8 -3.47997 -2.5215
    > 9 0.88191 -2.85689
    > T 1.35957 1.43552
    > m 10.1258 13.5765
    > ss 31.28749 27.6371
    > Cks 0.00001334 -0.000014

    Unless I have a math error. I don't think that the EOR for hard 13 v T adds up to .00001334.

    My addition says .0017323.

    Am I confused or is this a typo.

    P.S. What's the possibility of getting a copy of these tables posted in excel.

  8. #28
    Zenfighter
    Guest

    Zenfighter: Re: Nothing to worry

    Surprised by your Cks result, I?ve redone the whole table again with exactly the same results as printed. All the entries are fine. I couldn?t believe my eyes, given that I double checked all ss and Cks. Despite the fact that any given EoR?s table is fair enough if the checksum stays within [+/- 0.01], for the tables printed a benchmark of 0.0000 accuracy was established. For handling these types of data, computer algorithms and/or powerful statistical calculators are better than standard pocket calculators, obviously.

    Maybe you?ll be able to perform a couple of calculations with Excel, but I?m afraid you have quite a bit of work in front of you. You?re alone on this.

    Enjoy the tables.

    Sincerely

    Z


  9. #29
    bjmagic
    Guest

    bjmagic: Re: EoR's Table 11

    > DEALER 3
    > HITTING 17 ? 12
    > 17 16
    > 15 14
    > A -1.90624 -1.45334 -1.01251 -0.857938
    > 2 -1.86041 -1.3045 -0.697699 -0.337793
    > 3 -2.3697 -2.06704 -1.45909 -0.81705
    > 4 -3.64045 -3.98711 -3.2493 -2.49714
    > 5 -1.06665 -4.46385 -3.71528 -2.95299
    > 6 -0.674933 -0.298143 -3.73405 -3.01373
    > 7 -0.229311 0.234025 -0.461686 -3.01093
    > 8 0.310966 0.683309 0.877153 1.07256
    > 9 2.04728 2.26886 2.26782 2.2675
    > T 2.34736 2.59695 2.56532 2.53688
    > m -41.4418 -21.3389
    > -15.549 -9.73056
    > ss 53.9375 76.6445
    > 74.3943 66.6568
    > Cks -0.000008 0.000011
    > 0.00001 0.000009

    In the above table the sings are incorrect on entry 7 v 15 This is just a typo but I thought I'd point it out.

    The correct version should have 7v15 positive .461686

  10. #30
    bjmagic
    Guest

    bjmagic: Re: Nothing to worry

    Just so you know what I was using it for. I was creating a spreadsheet in excel using your EOR numbers to calculate the gain for playing perfectly. Below is a representation of it. I can key in at the top my tag values for the system I am using and it will calculate the gain for me.

    I am interested in what the top 20 or so plays are for single deck games when you flat bet.

    Dealer T

    Total Cards 52
    Penetration 75% 13 32.5

    A 2 3 4 5 6 7 8 9 T J Q K
    Count Values 0 0 1 1 1 1 0 0 0 -1 -1 -1 -1 0

    Effects of Removal Prob m SS Corr EOR Check
    Hard 16 (0.50) (0.29) (0.80) (1.73) (2.57) 1.64 (0.71) (0.06) 0.55 1.12 1.12 1.12 1.12 3464 (0.45) 19.05 64% (0.0000201)

    Gain (Thousandth of a Percent) 55.48

    Hard 15 (0.17) 0.19 (0.32) (0.73) (1.75) (2.23) (0.54) 0.09 0.66 1.20 1.20 1.20 1.20 3599 3.11 15.22 89% 0.0000082

    Gain (Thousandth of a Percent) 42.29

    Hard 14 (0.08) 0.44 0.17 (0.26) (0.77) (1.41) (4.21) 0.22 0.77 1.28 1.28 1.28 1.28 3291 6.64 27.80 50% (0.0000018)

    Gain (Thousandth of a Percent) 8.36

    Hard 13 0.01 0.46 0.40 0.21 (0.26) (0.43) (3.22) (3.48) 0.88 1.36 1.36 1.36 1.36 3390 10.13 31.29 35% 0.0017323

    Gain (Thousandth of a Percent) 1.09

    Hard 12 0.10 0.45 0.40 0.47 0.24 0.04 (2.06) (2.52) (2.86) 1.44 1.44 1.44 1.44 3059 13.58 27.64 31% (0.0000140)

    Gain (Thousandth of a Percent) 0.07

    Hard 11 1.61 0.76 0.77 0.79 1.11 0.84 1.53 0.74 (0.61) (1.89) (1.89) (1.89) (1.89) 1416 5.70 23.81 80% 0.0000010

    Gain (Thousandth of a Percent) 12.19

    Hard 10 (1.89) 0.59 0.65 0.80 1.14 0.76 1.72 0.86 (0.11) (1.13) (1.13) (1.13) (1.13) 1064 (2.77) 15.69 70% 0.0000050

    Gain (Thousandth of a Percent) 9.32

    > Surprised by your Cks result, I?ve redone
    > the whole table again with exactly the same
    > results as printed. All the entries are
    > fine. I couldn?t believe my eyes, given that
    > I double checked all ss and Cks. Despite the
    > fact that any given EoR?s table is fair
    > enough if the checksum stays within [+/-
    > 0.01], for the tables printed a benchmark of
    > 0.0000 accuracy was established. For
    > handling these types of data, computer
    > algorithms and/or powerful statistical
    > calculators are better than standard pocket
    > calculators, obviously.

    > Maybe you?ll be able to perform a couple of
    > calculations with Excel, but I?m afraid you
    > have quite a bit of work in front of you.
    > You?re alone on this.

    > Enjoy the tables.

    > Sincerely

    > Z

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