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Thread: Maxim: EORs under ENHC vs 10/Ace

  1. #1
    Maxim
    Guest

    Maxim: EORs under ENHC vs 10/Ace

    Dear Zenfighter and Cacarulo:

    I am here to ask your assistance in extending BJA3 Appendix D, to include EOR under ENHC rules. Since this affects only when dealer upcard is 10 or Ace, I will be very gratufull if you post tables for these conditions. Also, I found your messages with EORs for ES against 10, but are there EORs for ES against Ace? Thanks for your help.

    Sincerely,
    Maxim.

  2. #2
    Zenfighter
    Guest

    Zenfighter: Re: EORs under ENHC vs 10/Ace

    but are there EORs for ES against Ace?

    From a practical point a few, you have all the EoR?s that are really important when the Surrender rule is allowed against an Ace (6dks and ENHC), inside the archived article ?Full ES under ENHC. Vodka & Caviar.? (Best of the Masters)

    When holding 12 through 17, the m (6) is so high that I didn?t bother to print them. If you?re curious I?ll have no problem to extract them also.

    Wait for hitting/standing vs. T and A. We?ll try to do it ASAP.

    Sincerely

    Zenfighter

  3. #3
    Maxim
    Guest

    Maxim: Re: EORs under ENHC vs 10/Ace

    Hi Zenfighter,

    I would like to thank you for assistance.

    Maxim.

  4. #4
    Maxim
    Guest

    Maxim: Re: EORs under ENHC vs 10/Ace

    Hi Zen,

    I hope you have deleted message not because you changed your mind to post indexes here? I was just going to copy it and send you my appreciation of your work, but it just dissapeared.

    Sincerely,
    Maxim.

  5. #5
    Zenfighter
    Guest

    Zenfighter: Re: EORs under ENHC vs 10/Ace

    That?s not the reason why. Actually, I?m not satisfied with the degree of accuracy of a couple of tables. Have patience. The stuff, due to the ENHC rule, looks a little bit more complicated than I thought. You?ll have practical and exact tables, or you won?t have any. We?ll work this out correctly, I guess.

    Sincerely

    Zenfighter

  6. #6
    Zenfighter
    Guest

    Zenfighter: Re:ENHC Hard Hitting vs. T

    6 decks, S17 and ENHC rules



    Dealer?s Upcard T



    Hard Hitting

     

    A 2 3 4 5 6 7 8 9 T m6 ss

    17 -1.0690 -0.6017 -1.5649 -2.3344 1.1260 1.4300 1.0054 -0.4746 0.0828 0.6000-15.2770 15.3988
    16 -0.4411 -0.2864 -0.7507 -1.6270 -2.3455 1.5841 -0.6015 -0.0283 0.5041 0.9981 -0.0215 16.0995
    15 -0.0838 0.1544 -0.3054 -0.7294 -1.5959 -1.9257 -0.4589 0.0874 0.5948 1.0656 3.2454 12.0256
    14 0.0581 0.3816 0.1402 -0.2836 -0.6968 -1.2091 -3.8098 0.2028 0.6852 1.1328 6.5085 22.3554
    13 0.1998 0.3946 0.3683 0.1623 -0.2415 -0.3436 -2.9380 -3.1754 0.7752 1.1996 9.7644 25.6058
    12 0.3413 0.4046 0.3820 0.3979 0.2134 0.0735 -1.9171 -2.3307 -2.6285 1.2659 13.0140 23.0614




    Expected values

     

    Hand Hitting * Standing Difference

    T7vT -0.612682 -0.463626 -0.149056
    T6vT -0.570817 -0.576608 0.005791
    T5vT -0.542439 -0.575779 0.033340
    T4vT -0.507490 -0.575883 0.068393
    T3vT -0.473679 -0.575955 0.102276
    T2vT -0.440984 -0.576039 0.135055


    * Hitting one, and only one card.




    Accuracy test.

    T,5 v T . |Hitting ? Standing| = 3. 3340%

    1) Remove t,5,t

    (1.0656 * 2) + (-1.5959) = 0.5353

    2) Adjust the removals

    0.5353 * ( 51/309) = 0.0884

    3) Finally adjust the full-deck favorability m(6)

    3.2454 + 0.0884 = 3.3338

    Error = |Exact dif| - | Computed dif|

    Error = 3.3340 ? 3.3338 = 0.0002%

    Thus our table is accurate. See Don?s explanations in BJA3, Appendix D.

    Hilo algebraic derived indices

     
    T,6 v T 0.643179 0.6
    9,7 v T 0.017786 0.0
    8,8 v T 0.027440 0.0

    T,5 v T 3.74246 3.7
    9,6 v T 3.75459 3.8
    8,7 v T 3.75484 3.8



    More tables are coming.

    Enjoy!

    Zenfighter

  7. #7
    Maxim
    Guest

    Maxim: Thanks !

    Hi Zenfighter,

    Thanks for tables, they are what I was looking for. Regarding splits vs 10/Ace: I assume that splits yeild worse expectation comparing to other plays, except may be splitting Aces vs 10?

    Sincerely,
    Maxim.

  8. #8
    Zenfighter
    Guest

    Zenfighter: Re:ENHC Hard Hitting vs. Ace

    Dealer?s Upcard Ace (S17)





    Hard Hitting

     
    A 2 3 4 5 6 7 8 9 T m6 ss

    17 -0.2971 -0.9892 -1.6396 -2.0959 0.3890 0.5428 -0.8400 -0.1816 0.4374 1.1685 -5.5970 14.9854
    16 -0.0787 -0.6999 -1.2736 -1.8288 -2.2056 -0.9686 -0.3204 0.2914 0.8656 1.5547 10.2358 21.8708
    15 0.1822 -0.1801 -0.7454 -1.2950 -1.8102 -3.4043 -0.2263 0.3548 0.8982 1.5565 12.0250 27.8393
    14 0.1930 0.0886 -0.2215 -0.7610 -1.2603 -2.9237 -2.6931 0.4173 0.9300 1.5577 13.8037 28.8080
    13 0.2035 0.1031 0.0514 -0.2225 -0.7111 -2.2944 -2.2439 -2.0813 0.9613 1.5585 15.5735 25.8802
    12 0.2109 0.1179 0.0779 0.0640 -0.1625 -1.6659 -1.6461 -1.6633-1.5681 1.5588 17.3357 20.5248



    Expectations
     
    Hitting * Standing Difference

    T7 v A -0.693232 -0.637314 -0.055918
    T6 v A -0.664664 -0.767872 0.103208
    T5 v A -0.649419 -0.769553 0.120134
    T4 v A -0.630064 -0.769750 0.139686
    T3 v A -0.611180 -0.769948 0.158768
    T2 v A -0.593596 -0.770111 0.176515

    * Hitting one, and only one card.




    As it can be deduced from the above EoR?s table, the full deck favorability for hitting is huge. This fact, combined with a moderate
    volatility (ss), leaves the opportunities for basic strategic departures scarce, and if any (16 v A), not worth struggling with it. The European Ace offers very few options for the player.

    Again, you can use the difference in expectations to check the quality of the EoR?s tables, with the same procedure already outlined.

    Sincerely

    Zenfighter

  9. #9
    Zenfighter
    Guest

    Zenfighter: Re:ENHC Soft Hitting tables

    Dealer?s Upcard T


    Soft Hitting

     
    A 2 3 4 5 6 7 8 9 T m6 ss

    18 -0.1874 -0.8662 -1.7552 0.4833 0.3741 0.2298 1.3651 0.6642 -0.3013 -0.0016 3.1934 6.6878




     
    Hitting Standing Difference

    A7 v T -0.2067199 -0.2406308 0.0339109




    A careful study of columns m6 and ss doesn?t leave any room for a realistic departure here. Thus A7 v T => Always hit.


    Dealer?s Upcard Ace


    Soft Hitting

     
    A 2 3 4 5 6 7 8 9 T m6 ss

    18 -0.2774 -0.8334 -1.4597 0.0047 -0.1526 0.8180 0.0276 -0.5922 0.1356 0.5823 0.4259 5.3210




     
    Hitting Standing Difference

    A7 v A -0.3764025 -0.3798034 0.0034009




    Not the case against the Ace. Here the meager m6 points to an early departure.
     
    A7 v A = Stand if TC => 0.579146 0.6




    Sincerely

    Zenfighter

  10. #10
    Maxim
    Guest

    Maxim: Exellent work, thanks.

    Zenfighter,

    I would like to thank you for assistance with the tables. Can you, please, explain briefly how you generate them. Did you write special program for this?

    Also, regarding double 11 vs 10 and split Aces vs 10: do you think EORs can be usefull for this under ENHC?

    Sincerely,
    Maxim.

  11. #11
    Zenfighter
    Guest

    Zenfighter: Re: You're welcome.

    Also, regarding double 11 vs. 10 and split Aces vs. 10: do you think EORs can be useful for this under ENHC?

    Yes, the first one can be used to assess properly the EV maximizing index (Hilo TC = 3). Amazingly this index doesn?t behave like a typical American rules one, when more money at risk hits the felt (e.g. doubling). Here the risk averse index skyrockets due to the ENHC rule in effect (lose all vs. a dealer?s BJ). The final result is that the RA index is so high (TC = 8), that for a player who employs these ones, he/she is doing fairly well, ignoring this option completely.
    Splitting Aces vs. T yields a positive expectation, while hitting AA vs. T an horrendous EV = -.132808. So as you can see this is basic strategy move.

    Given that I?m not satisfied with the degree of exactitude for the EoR?s that I got for these two tables (the player losing all bets make the calculations awkward), I didn?t post them. My bet is that Cacarulo, probably will be able to extract both with exactitude. I?ll ask him.

    Can you, please, explain briefly how you generate them.

    The employment of a CA is a sine qua non condition to extract them.
    Basically what you need, is to select first two strategic options to be tested. E.g. first action H15 vs. T (hit one card) and second option stand on 15 vs. T. The next step is to determine the favorabilities for both logical alternatives so:
    Gain 1 ? Gain 2 is your marginal gain/loss from taking the first action over the second.
    Now and Ace is removed from the specific subset (one pack or 6 decks), and the calculation is repeated:
    Gain 1(ace removed) ? Gain 2 (ace removed) and so on with every denomination. A little bit tedious and long. The entries in the tables are differences in expectations for both selected options (See TOB and Appendix D from BJA3).

    Thanks to your interest, these short tables are a novelty. Sometimes it pays to be curious! :-)

    Sincerely

    Zenfighter


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