ENHC surrender 88 vs 10 or A

[Cacarulo]

OK. I agree completely with your USA rules values.

For ENHC I do not compute conditional values at all, only unconditional values. In doing that when overall EV is computed I can use the EV for that hand directly (depending upon what the strategy is) as that hand's contribution.

If strategy for A-4 versus T is late surrender I say that hand's contribution is -.5306, not -.50.
If strategy for A-4 versus T is early surrender I say that hand's contribution is -.50.
(I agree with your ENHC stand, hit, double values as matching unconditional values.)

Unconditional values can always be used that way and that's why I prefer them.
Hope that is clear.

k_c

This is what I get now for ENHC:

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

[k_c]

This is what I get now for ENHC:

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

If your left column is ES and right column is LS we completely agree.
I take your word that conditional values can be used for ES but I only use unconditional.

Note to Don:

The -53.06% value for LS represents the value of the hand before dealer checks for blackjack. Whenever dealer has determined he does not have blackjack this extra information changes the (LS) EV to -50%. I think that in general check happens at end of hand, not beginning like in full peek so it's not out of line to say EV for LS is -53.06% because that's what it is at the time decision to surrender is made.

k_c

[DSchles]

This is what's so funny about both your note to me and Cac's chart above it: You both act as if, in the second column, the person who hits or stands actually DID that, even if the dealer later has a natural. In the latter case, the person did NOT hit and he did NOT stand; it just looks as if he did, because he goes through the motions. To calculate the EVs, you do nothing different from the standard American game. If the dealer has a natural, you IGNORE what the player did with his hand.

Note to k_c: Your words are clear, but the notion simply doesn't describe anything relating to blackjack! The TIMING as to when the dealer reveals his hole card cannot possibly change ANY expectations, and certainly not that of LS. Yet again, SPEAKING the word "Surrender" is NOT surrendering. You don't get to surrender until the dealer has seen his hole card. And thinking that it changes the surrender EV depending on whether the dealer sees his hole card at 7:30:25 or 7:30:26 is just plain silly.

Game 1: Don heads-up against the dealer in Las Vegas. I get 16 vs. T and, while the dealer is sliding his ten into the little camera to read the hole card, I yell out "Surrender." The dealer ignores me, sees an Ace underneath, and says, "No can do," and he takes my full bet.

Game 2: K_c heads up against the dealer in the good ol' A.C. days: You get 16 vs. T and yell out "Surrender." The dealer ignores you, slides a card out of the shoe, flips the Ace, and says: "No can do," and he takes your full bet.

If you somehow see ANY MATHEMATICAL DIFFERENCE WHATSOEVER in these two scenarios, then you simply have spent too much time analyzing blackjack and not enough time playing it.

Don

[k_c]

This is what's so funny about both your note to me and Cac's chart above it: You both act as if, in the second column, the person who hits or stands actually DID that, even if the dealer later has a natural. In the latter case, the person did NOT hit and he did NOT stand; it just looks as if he did, because he goes through the motions. To calculate the EVs, you do nothing different from the standard American game. If the dealer has a natural, you IGNORE what the player did with his hand.

Note to k_c: Your words are clear, but the notion simply doesn't describe anything relating to blackjack! The TIMING as to when the dealer reveals his hole card cannot possibly change ANY expectations, and certainly not that of LS. Yet again, SPEAKING the word "Surrender" is NOT surrendering. You don't get to surrender until the dealer has seen his hole card. And thinking that it changes the surrender EV depending on whether the dealer sees his hole card at 7:30:25 or 7:30:26 is just plain silly.

Game 1: Don heads-up against the dealer in Las Vegas. I get 16 vs. T and, while the dealer is sliding his ten into the little camera to read the hole card, I yell out "Surrender." The dealer ignores me, sees an Ace underneath, and says, "No can do," and he takes my full bet.

Game 2: K_c heads up against the dealer in the good ol' A.C. days: You get 16 vs. T and yell out "Surrender." The dealer ignores you, slides a card out of the shoe, flips the Ace, and says: "No can do," and he takes your full bet.

If you somehow see ANY MATHEMATICAL DIFFERENCE WHATSOEVER in these two scenarios, then you simply have spent too much time analyzing blackjack and not enough time playing it.

Don

I give up. No big deal.

k_c

[k_c]

This is what I get now for ENHC:

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

                 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.

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