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Thread: ENHC surrender 88 vs 10 or A

  1. #66


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    Quote Originally Posted by Gronbog View Post
    The basic strategy for hitting vs stand vs surrender does not change between ENHC and PEEK games because, in the ENHC game, at the precise moment any of those decisions is made, the EV of the player's bet for any of those actions is subject to the identical "penalty" for the case where the dealer has a natural as compared to that exact moment on a hole card game where it is already known that there is no natural. As Cac says, since only one bet is in play, the change is identical and relative for all of those actions. This is also the reason why any indices between these decisions do not change. And, of course, the very reason we don't double or split (except A,A vs T) is because adding the extra unit to our bet increases the "penalty" for the case of a dealer natural for those decisions.

    And the EV that does not change between peek and no peek for stand, hit, and LS is ..... the unconditional EV.
    uncond double EV changes for ENHC by -(prob dealer BJ). In peek game 1 unit is at risk to dealer BJ; in ENHC 2 units.
    uncond split EV also changes but no description here.

    Suppose you're playing ENHC. You have 2-card hand versus T. You have option of late surrender. You take that option. Dealer puts some kind of lammer on your hand to indicate late surrender. Dealer does not check hole card and deals from full 6 card deck absent your 2 cards and his up card. At end of deal 285 out of 309 hands dealer will take half your bet. 24 out of 309 hands dealer will take your full bet. You can complain and say surrender means I lose half my bet because surrender is always -50% because I always display it that way in my data. Dealer says, "tough luck, those are the rules."

    Unconditional EV doesn't care when dealer checks for blackjack.

    Probably more than I should say.

    k_c
    Last edited by k_c; 03-18-2023 at 02:07 PM.

  2. #67
    Random number herder Norm's Avatar
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    But, you didn't surrender. You just indicated a desire to, indicated by a lammer. And, you would have lost a full bet anyhow. The math is the same as US no peek; which is why I get the correct indices using -.5 EV.

    Basically, I think we get the same end result -- it's just that you are putting the numbers in different slots. But, had the surrender actually taken place, the EV would have been -.5 as a matter of definition.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

  3. #68


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    Quote Originally Posted by Norm View Post
    But, you didn't surrender. You just indicated a desire to, indicated by a lammer. And, you would have lost a full bet anyhow. The math is the same as US no peek; which is why I get the correct indices using -.5 EV.

    Basically, I think we get the same end result -- it's just that you are putting the numbers in different slots. But, had the surrender actually taken place, the EV would have been -.5 as a matter of definition.
    For a sim, EV for every individual decision to surrender is -.5, which would be included in the aggregate, yes. What's done with aggregate is up to simmer.

    Needed is apples to apples rather than apples to oranges comparisons.
    Either uncond EV to uncond EV or cond EV to cond EV; no mixing even if you have state of art blender.

    k_c

  4. #69
    Senior Member Gramazeka's Avatar
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    Quote Originally Posted by Cacarulo View Post
    My approximate indices for Hi-Lo are now:

    ES 77vT >= -1.4

    Sincerely,
    Cac
    Ok , composite ?. 14 vs T what you have ? ES. I have -0.7
    Last edited by Gramazeka; 03-18-2023 at 03:08 PM.
    "Don't Cast Your Pearls Before Swine" (Jesus)

  5. #70


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    Quote Originally Posted by Gramazeka View Post
    Ok , composite ?. 14 vs T what you have ? ES. I have -0.7
    Hi Grama!

    For 6D, ENHC and ES I get -0.6 and for LS +3.1.

    Sincerely,
    Cac

  6. #71


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    Smile

    Quote Originally Posted by Gramazeka View Post
    Ok , composite ?. 14 vs T what you have ? ES. I have -0.7
    Hand Algebraic Index
    T,4 v T -0.5920 -0.6
    9,5 v T -0.5156 -0.5
    8,6 v T -0.6973 -0.7
    7,7 v T -1.4720 -1.5

    Or: Early Surrender 14 v T if TC equals or greater than -1 (simulated)

    Not too bad, considering that all this was computed by yours truly 19 years ago.

    C´mon guys. Admit it!

    Zenfighter

  7. #72
    Senior Member Gramazeka's Avatar
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    Quote Originally Posted by Zenfighter View Post
    Hand Algebraic Index
    T,4 v T -0.5920 -0.6
    9,5 v T -0.5156 -0.5
    8,6 v T -0.6973 -0.7
    7,7 v T -1.4720 -1.5

    Or: Early Surrender 14 v T if TC equals or greater than -1 (simulated)

    Not too bad, considering that all this was computed by yours truly 19 years ago.

    C´mon guys. Admit it!

    Zenfighter
    I understand that now you have to average the index according to the probabilities of the hands to get an index of 14 vs 10 ?
    "Don't Cast Your Pearls Before Swine" (Jesus)

  8. #73


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    Quote Originally Posted by Gramazeka View Post
    I understand that now you have to average the index according to the probabilities of the hands to get an index of 14 vs 10 ?
    Yes, if you would like a single, generic index for 14 vs. T, without regard to the composition of the hand.

    Don

  9. #74


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    Quote Originally Posted by Gramazeka View Post
    I understand that now you have to average the index according to the probabilities of the hands to get an index of 14 vs 10 ?
    Or, if you don't want to get too complicated, you could calculate a generic index for 14vT. For this, instead of calculating the index of each particular hand and then averaging,
    you can simply remove a T from the pack and calculate the index of a generic 14 (this takes into account all possible 14s).

    Sincerely,
    Cac

  10. #75


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    Quote Originally Posted by Cacarulo View Post
    This is what I get now for ENHC:

    Code:
    Standing  =  -56.65807149255014% |  -56.65807149255014%
    Hitting   =  -22.12141526286563% |  -22.12141526286563%
    Doubling  =  -58.83294803078072% |  -58.83294803078072%
    Surrender =  -50.00000000000000% |  -53.06122448979592%
    
    Note that the conditional values can be used for ES and the unconditional values for LS.
    Do we agree now?

    Sincerely,
    Cac

    Conditional late surrender EV is always -.5. Conditional or unconditional early surrender EV is always -.5.
    Conditional EVs can be used to determine strategy (if not no peek) but at some point the fact that dealer may have BJ must be taken into consideration so in that sense they are not permanent. Unconditional EVs can be used to compute strategy as well and are the actual value of the hand. Below computes unconditional EV given conditional EV is known, which is the way traditionally done.

    let cev = conditional EV assuming dealer does not have BJ
    let ucev = unconditional EV where player non-BJ loses to dealer BJ
    let PDBJ = probability of dealer BJ

    Code:
                     peek                             no peek
    
    stand            ucev = cev - pDBJ*(1 + cev)      ucev = cev - pDBJ*(1 + cev)
    hit              ucev = cev - pDBJ*(1 + cev)      ucev = cev - pDBJ*(1 + cev)
    double           ucev = cev - pDBJ*(1 + cev)      ucev = cev - pDBJ*(2 + cev)
    split            ucev = cev - pDBJ*(1 + cev)      ucev = cev - pDBJ*(num expected hands + cev)
    late surrender   ucev = cev - pDBJ*(1 + cev)      ucev = cev - pDBJ*(1 + cev)
    early surrender  ucev = -.5                       ucev = -.5
    
    LS cev = -.5 for both peek & no peek
    ES cev = ucev = -.5 for both peek & no peek

    In order to compute num expected hands for splits recursive function could be used.

    Code:
    pCards = number of pair cards which is always initially 2
    remSp = number of remaining splits = number of allowed splits - 1
    p = number of pair cards present after initial pair and up card have been dealt
    np = number of non-pair cards present after initial pair and up card have been dealt
    
    double getSplitHands(const int &pCards, const int &remSp, const int &p, const int &np)
    {
        if (p == 0 || remSp == 0)
            return double(pCards);
    
        double hands;
        double pP = double(p) / (p + np);
    
        if (pCards >= 2) {
            hands = pP * getSplitHands(pCards + 1, remSp - 1, p - 1, np);
            hands += (1 - pP) * (getSplitHands(pCards - 1, remSp, p, np - 1) + 1);
        }
        else { // if (pCards == 1)
            hands = pP * getSplitHands(2, remSp - 1, p - 1, np);
            hands += (1 - pP);
        }
    
        return hands;
    }
    
    Example 8-8 versus T single deck:
    p=2, np=47
    allowed splits = 1, remSp=0; hands = getSplitHands(2,0,2,47) = 2     
    allowed splits = 2, remSp=1; hands = getSplitHands(2,1,2,47) = 2.0807823129
    allowed splits = 3, remSp=2; hands = getSplitHands(2,2,2,47) = 2.0850340136
    What I do is to initially compute unconditional EVs. All strategies can be determined from this. It is unnecessary to use conditional EVs but I can compute then from the unconditional EVs and that's what I do to relate.

    k_c
    Last edited by k_c; 03-22-2023 at 05:02 PM. Reason: no peek strat needs uncond EV

  11. #76


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    Quote Originally Posted by DSchles View Post
    The new book is now available on Kindle!

    Don
    May I know the content/chapter/topic of your new book ?

  12. #77

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