Quote Originally Posted by Gronbog View Post
I didn't forget about this experiment. It just took some time for me to get to it.

Under the conditions suggested above, for doubling over hitting A,A vs 3 I now get +8 as the index S17 (was +9). This matches Cac's simulation result. However, I'm still getting +8 for H17 where Cac's simulation result is +7.

Some suggestions regarding the H17 difference:

  1. Encountering this hand with at least three aces and a 3 removed at +7 and +8 is a rare event occurring only 122,878 and 98,232 times respectively over the course of 100 billion rounds I simulated. As such, the EVs that were computed are separated by only 0.5 standard deviations (the standard deviation of the difference in the EVs) giving a probability of about 30.85% that doubling might be correct at +7.
  2. My software never computes indices in isolation. It always includes the effects of other related index plays. It does this automatically and I've never found a practical reason to prevent it. In the case of A,A vs 3 at +8, the only relevant index play which can also be triggered downstream would be 12 vs 3 (stand) at +2 (there are others but their indices are too negative for them to be relevant in this situation). I would be interested to see what index Cac and others get for this situation (A,A vs 3, at least 3 aces removed, H17) when 12 vs 3 is also enabled. This would tend to increase the value of hitting and therefore tend to make the index for doubling higher.

This is how I might handle additional removals.
Code:
//    add additional specific removals here to change pRank[]
//    pHand[0] += 1;

    subsetList *l = NULL;
    long elems;
    if (cd)
        l = new subsetList (inputCount, decks, pen, rc, pHand);
    else { // (if ! cd)
        short specificRem[10] = {0};
        l = new subsetList (inputCount, decks, pen, rc, specificRem);
    }

    l->getProbRC(rc, probRC, pRank);
    elems = l->elems;
    delete l;
    l = NULL;

//    delete additional specific removals here
//    pHand[0] -= 1;

    if (elems == 0) {
        cout << "\nAbove (player hand pen/running count/side count) input is not possible.";
        cout << "\nPress any key to continue";
        ch = getch();
        return;
    }
I guess for a sim you would remove the extra ace following reshuffle of a full shoe, then replace it before reshuffle.

For 6 decks HiLo these are my approximations for around mid-shoe (155 cards.) I just use best strategy.:

S17
AA v 3 (dbl v hit no ace removed)
RC=23 dbl: 13.514%, hit: 13.238% diff: .276%
RC=22 hit: 12.910%, dbl: 13.054% diff: -.144%
interpolate: RC=22.34, TC=7.5

AA v 3 (dbl v hit 1 ace removed)
RC=22 dbl: 13.572%, hit: 13.241% diff: .331%
RC=21 dbl: 12.972%, hit: 13.059% diff: -.087%
interpolate: RC=21.21, TC=7.1

H17
A-A v 3 (dbl v hit no ace removed)
RC=22 dbl: 13.304%, hit: 13.186% diff: .118%
RC=21 dbl: 12.699%, hit: 13.001% diff: -.302%
interpolate: RC=21.72. TC=7.3

A-A v 3 (dbl v hit 1 ace removed)
RC=21 dbl: 13.347%, hit: 13.185% diff: .162%
RC=20 dbl: 12.747%. hit: 13.003% diff: -.256%
interpolate: RC=20.61, TC=6.9

k_c