Originally Posted by

**Gronbog**
What I'm wondering about is the CA methods used by Cac, Zen and Gramazeka (and you? and others?) for computing indices. Cac speaks about removing specific cards and Zen references exact EOR numbers, but these only represent the situation off the top of the shoe. However, each true count is represented by a vast number of possible remaining deck compositions multiplied by a variety of penetrations. Cac then goes on to reference an assumed level of penetration (4.5/6 in this case).

I can only speak for myself. I can try to illustrate approximately A-A versus 6, h17. This does not remove an additional ace which would be the case if A-A resulted from splitting aces.

Basically,

1. Compute rank probabilities based upon the running count of a given counting system and number of cards remaining, allowing for cards known to be specifically removed. This can immediately be used to find RC/cards remaining where insurance is +EV. However, for other indexes only player cards are specifically removed but not up card in order to adapt to the way my CA works.

Code:

Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
Player hand composition: 2, 0, 0, 0, 0, 0, 0, 0, 0, 0: Soft 12, 2 cards
Decks: 6 (possible input for cards remaining: 1 to 312)
Cards remaining before up card (current = 156, no input = no change):
Initial running count (full shoe): 0
Running count (before up card is dealt, no input defaults to 0): -4
No subgroup (removals) are defined
Number of subsets for above conditions: 37
Prob of running count -4 with above removals from 6 decks: 4.78680e-002
p[1] 0.069183 p[2] 0.079342 p[3] 0.079342 p[4] 0.079342 p[5] 0.079342
p[6] 0.079342 p[7] 0.077406 p[8] 0.077406 p[9] 0.077406 p[10] 0.30189
Press any key to continue:

2. Create a shoe for the rank probs/cards remaining and teach my CA to compute using this shoe to get reasonable estimates of EVs for the input counting system. (Here RC = -4 before up card)

Code:

Number of decks: 6 Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
Player hand composition: 2, 0, 0, 0, 0, 0, 0, 0, 0, 0: Soft 12, 2 cards
After player hand is dealt - Cards remaining: 156, Running count: -4
Subgroup removals: No subgroups are defined
Shoe comp (A-5): {10.7925, 12.3774, 12.3774, 12.3774, 12.3774}
Shoe comp (6-10): {12.3774, 12.0753, 12.0753, 12.0753, 47.0946}
After up card is dealt - Cards remaining: 155
Running count (up card 1 to 10): {-5,-3,-3,-3,-3,-3,-4,-4,-4,-5}
Up card Stand Hit Double Split 1 Split 2 Split 3 Surr Strat
1 -72.406 -34.583 -71.762 -23.633 split
2 -29.435 8.442 -7.219 46.241 split
3 -25.528 10.667 -0.754 50.887 split
4 -21.226 12.863 5.990 55.808 split
5 -17.099 15.612 12.667 60.977 split
6 -12.900 18.219 18.509 65.142 split
7 -47.170 16.954 -17.892 45.021 split
8 -50.909 10.044 -31.606 33.259 split
9 -53.371 0.711 -44.945 21.492 split
10 -56.674 -11.666 -52.851 7.861 split
Overall hand EV vs all upcards: 30.6019
Press c or C for EV conditioned on no dealer blackjack, any other key to exit

3. Go through the range of all possible running counts and record RC indexes. I can only do this for one cards remaining value at a time.

Code:

____________________________________ h17 ___________________________________
Count tags {1,-1,-1,-1,-1,-1,0,0,0,1}
Composition dependent indices for hand, rules, number of decks, and pen
Player hand composition: 2, 0, 0, 0, 0, 0, 0, 0, 0, 0: Soft 12, 2 cards
Decks: 6 (possible input for cards remaining: 1 to 312)
Cards remaining before up card = 156
No subgroups are defined
2 3 4 5 6 7 8 9 T A
Stand h h h h h h h h h h
Double >=38 >=22 >=11 >=3 >=-3 - - - - -
Pair p>=-36 p>=-37 p>=-39 p>=-41 p>=-45 p>=-30 p>=-26 p>=-24 p>=-25 p>=-16
LS - - - - - - - - - -
ES - - - - - - - - - -
Press any key to continue

4. Interpolate. Compute a more accurate true count that applies to the input cards remaining if desired,

Code:

Let up card = 6 and display hit and dbl EV
RC = -3, hit EV = .18219, dbl EV = .18509, diff = .00290
RC = -4, hit EV = .18017, dbl EV = .17833, diff = -.00184
interpolate: -3.611814 (appox RC where hit EV = dbl EV)
TC = 52 * (-3.611614) / 155 (156 - 1 to allow for upcard because this is relative to how my CA computes)
TC = -1.2 for 155 cards remaining, RC = -3 after up card of 6

I would guess that Cac has multiple methods and Zen uses algebraic approximation using eors. Not sure of what Gramazeka does.

Hope this is helpful.

k_c

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