Quote Originally Posted by k_c View Post
CDZ+ means making each post split decision considering all removals at the time of the decision.

For SPL1 there are 2 hands, each with its own EV. hand1EV is simply the optimal EV of drawing to the first pair card allowing for one pair
card removed. This is what is done to compute CDP1. For CDP1, EVx = optimal EV of first split hand and EV(CDP1) for SPL1 = 2*EVx where
strategy for hand2 is the same as strategy for hand1. For CDZ+, hand2EV and strategy for one allowed split is variable depending upon what
has been drawn to hand1 as well as what is currently drawn to hand2.

*Here are some things I do to compute hand2:
1. In the course of computing hand1 I use busted as well as unbusted hands. Busted hand1 hands have no effect on hand1EV and strategy but do
effect hand2.
2. For each hand1 composition I compute a parameter I call h2EVX. h2EVx is the optimal hand2EV
for that particular hand1 comp. To compute h2EVx only unbusted hands need to be considered because for SPL1
no more split hands follow. I do not save this set of hand2 hands, only the h2EVx parameter for this hand1 comp.
3. I have parameters I call h2EVx_stand, h2EVx_double, and h2EVx_hit which depend on hand1 strategy. h2EVx_stand = h2EVx because no cards are
drawn for the hand1 comp being referenced. hand2EV is computed while going through all hand1 hands using above values. If by some quirk of
fate strategy of all hand1 hands is stand then hand2EV would equal hand1EV.

I'm sure there's room for improvement.

- This is what I get for the sample shoe comp -

Shoe composition: {0,0,0,0,0,11,0,5,0,0}
Split EV for 6-6 (SPL1), S17, DAS:

** versus 6 **
hand1EV = -0.0069930069930069488
hand2EV = 0.028749028749028734
hand1EV + hand2EV = 0.0217560217560217852 = CDZ+(single split)

** versus 8 **
hand1EV = 0.51748251748251750
hand2EV = 0.52307692307692299
hand1EV + hand2EV = 1.04055944055944049 = CDZ+(single split)

k_c
Isn't this optimal in the sense of maximizing EV among *all* possible strategies? That is, the "Z" in CDZ+ is out of place; "zero memory" is pretty consistently agreed to mean a strategy that depends only on the cards in the current hand (vs. any additional cards or "state" of the round). Maybe ICountNTrack can confirm/weigh in on this small shoe example for comparison (since I know he has implemented optimal EV-maximization).

I'm also not sure what EVPN(CDZ-) means; CDZ- refers to a well-defined strategy (maximize CD strategy temporarily prohibiting splits, then apply that strategy in evaluating candidate splits), in which case it has a definite expected value, no matter how we choose to implement an algorithm to compute it. Maybe you meant something like E(CDPN), or E(something-like-CDPN-that-we-haven't-named-yet-but-is-demonstrably-executable-at-the-table-unlike-CDP-or-CDPN)?

In that case, yes, there is certainly opportunity to define and evaluate playing strategies that depend on more information about the round than just the cards in the current hand (but constrained to information actually available at the time of each necessary playing decision). CDP1 is such a strategy. And one could certainly do better, with some yet-to-be-named-strategy S, so that E(CDZ-)<=E(CDP1)<=E(S)<=E(OPT, i.e. what you're calling CDZ+).

E