Edit: I think what I posted is relative to a starting shoe composition of {0,0,0,0,0,13,0,5,0,0} rather than {0,0,0,0,0,11,0,5,0,0} but the principle remains the same.
This is how it could possibly be done. The EV values are from my gui CA, the purpose of which is to show a lot of rounded off values rather than a few very accurate ones. I manipulate the input so the desired condition is output and I hope there are no errors.
Split 6-6 from shoe comp {0,0,0,0,0,11,0,5,0,0} (rank 1-10), 3 allowed splits
Draw 2 sixes so there are 4 split hands with zero splits remaining with (shoe comp {0,0,0,0,0,9,0,5,0,0} (rank 1-10))
** prob p = 9/14, prob n = 5/14 **
** prob of first card 6 = 1 **
** if a p is drawn:
EVPair_ppp - Stand: -.6970, Double: -.01515, Hit: -.007576 (best strat = hit)
** if an n is drawn:
Code:
*** Preliminary data needed to compute EVn_pp given a forced strategy ***
Hand Prob Stand EV Double EV Hit EV Best EV
6-6 v 6 9/14*8/13 -.6970 -.01515 -.007576 -.007576
6-6 v 8 9/14*5/13 .1515 .6424 .3212 .6424
6-8 v 6 5/14*9/13 -.8182 -.01212 -.006061 -.006061
6-8 v 8 5/14*4/13 -.09091 .2364 .1182 .2364
EVx_pp(strat) 1 -.45057 .17582 .08791 .1803
*** EVn_pp(strat) = (EVx_pp(strat) - 9/14*EVPair_ppp(strat)) / (1 - 9/14) ***
EVn_pp(stand) = (-.45057 - 9/14*(-.6970)) / (1 - 9/14) = -.006996
EVn_pp(double) = (.17582 - 9/14*(-.01515)) / (1 - 9/14) = 0.519566
EVn_pp(hit) = (.08791 - 9/14*(-.007576)) / (1 - 9/14) = 0.2597848
EVn_pp(best strat) = (.1803 - 9/14*(-.007576)) / (1 - 9/14) = 0.5184768
Code:
Hand 1 EV strategy
6-6 -.007576 hit
6-8 0.519566 double
** Hands 2,3,4
Hand 2 possible additional removals: pp, pn*2, nn
Hand 3 possible additional removals: ppp, ppn*3, pnn*3, nnn
Hand 4 possible additional removals: pppp, pppn*4, ppnn*6, pnnn*4, nnnn
I have shown how hand 1 may be computed. Hands 2, 3, and 4 might be computed using similar logic.
When a single n is removed EV can be computed in terms of p cards removed right away. When more than one n card is removed I think it is possible to eventually express EV in terms of EVx_pRemoved and EVPair_pRemoved through a series of calculations. MGP has methods of dealing with multiple n cards removed. The split algorithm I developed continuously eliminates EVn_pRemoved by updating multipliers for EVx_pRemoved and EVPair_pRemoved for varying numbers of pRemoved for varying number of splits allowed so that no more than one n is ever considered at a time. However, here there are zero splits allowed so the algorithm is not immediately applicable. I think that your split algorithm somehow computes n hands to eliminate the possibility of any "wayward" n hands so that any EVn_pRemoved is equal to any other EVn with the same pRemoved. A "wayward" n hand occurs when an n is removed and the effect of this is immediately computed outside of any other context.
That's about the best analysis I have to offer. Hopefully I'm at least not way out of line.
k_c
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