Quote Originally Posted by k_c View Post
I made another attempt at this because I didn't vary some of the data by up card as it should have been. I also tried to address a starting shoe comp of {0,0,0,0,0,11,0,5,0,0} where 4 hands of split 6s are ready to be played as I originally intended. I hope this is an improvement.

** prob 6 = 7/12, prob 8 = 5/12 **
** prob of first card of 6 = 1 **

Code:
** hand 1 **
EVPair_ppp versus 6: Stand EV = -.5556, Double EV = .1667, Hit EV = .0833
EVPair_ppp versus 8: Stand EV = .3333, Double EV = 1.000, Hit EV = .500

Compute EVx_pp(strat)
----------------------------------Up card = 6--------------------------------
Hand     Prob          Stand          Double         Hit            Best
6-6      7/12*6/11     -.5556         .1667          .08333         .1667
6-8      5/12*7/11     -.7333         -.2667         -.1333         -.1333
EVx_pp                 -.6364         -.0303         -.015155       .0303

----------------------------------Up card = 8--------------------------------
Hand     Prob          Stand          Double         Hit            Best
6-6      7/12*5/11     .3333          1.000          .5000          1.000
6-8      5/12*4/11     .0667          .2167          .1083          .2167
EVx_pp                 .23634         .7152          .35756         .7152


Compute EVn_pp(strat) = (EVx_pp(strat) - 7/12*EVPair_ppp(strat)) / (1 - 7/12)
----------------------------------Up card = 6--------------------------------
EVn_pp(stand) = (-.6364 - 7/12*(-.5556)) / (1 - 7/12) = -.74952
EVn_pp(double) = (-.0303 - 7/12*(.1667)) / (1 - 7/12) = -.3061
EVn_pp(hit) = (-.015155 - 7/12*(.0833)) / (1 - 7/12) = -.151992 (best)

----------------------------------Up card = 8--------------------------------
EVn_pp(stand) = (.23634 - 7/12*(.3333)) / (1 - 7/12) = .100596
EVn_pp(double) = (.7152 - 7/12*(1.000)) / (1 - 7/12) = .31648 (best)
EVn_pp(hit) = (.35756 - 7/12*(.5000) / (1 - 7/12) = .158144

Hand 1    Up Card     EV         Strategy
6-6       6           .1667      Double
          8           1.000      Double

6-8       6           -.151992   Hit
          8           .31648     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
k_c
I'm having trouble interpreting this. Before digging deeper, it's still unclear to me what the intended answer to my original question is? That is, having split and resplit 6s (specifically vs. dealer 8) from the given shoe, to four now-all-incomplete hands, and subsequently drawing an 8 to the first split hand (so that seven 6s and three 8s remain face-down in the shoe), how do we read the table of information above to determine what we should do at that point (stand or double down)? Which is it?

And what should the strategy be for the subsequent second, third, and fourth split hands as well, to complete the round? Once we know that, we can compute the overall EV for the original 6-6 vs. 8 split (since presumably we aren't trying to change the split-otherwise-double strategy for the other split situations) ... where the objective is to specify such a strategy that realizes the overall EV for the original 6-6 vs. 8 split of 1548/715=2.165, that CDP strategy suggests is achievable.

Of course, if the intent of the above response is to describe how to compute a strategy that eventually realizes a different overall EV for the split, i.e. any value other than 1548/715=2.165, then, well, okay... but then I'm not sure what the point is. We can describe any number of other strategies-- split-and-resplit-then-mimic-the-dealer has a particular EV that we could easily compute; truly optimal perfect play a la ICountNTrack has a particular EV that we (or rather ICountNTrack) could also compute, etc. But the whole point here is to demonstrate that the *particular* strategies, namely those referred to by CDP and CDPN, require making strategy-varying decisions that depend on information that the player doesn't have when he needs it.

E