The earliest discussions of notation that I am familiar with were back in the bjmath.com days, where although the "Z" was consistently established to indicate "zero memory," meaning that strategy is only a function of the current hand, I never saw us settle on notation to refer to perfect EV-maximizing play. (There was discussion back in 2003 with Steve Jacobs proposing "CDB," where the "B" indicated knowledge of cards in all past "branches" of a round, which would effectively mean perfect play in the sense of maximizing EV for the round... but I neither observed nor used this notation myself at any time after that discussion. I've used "OPT" to refer to this in the past in my own internal scribblings; I suppose we haven't really settled on anything because nobody was able to actually compute it, other than ICountNTrack.)
You are correct that CDP is unplayable at the table with realistic rules. However, if we hypothesize a dealer that fleshes out all split hands to two cards before accepting stand/hit/double decisions on any of them, then the expected return produced by the CDP calculation (in this example, 1548/715) *is* able to be realized/accounted for... it just takes an interestingly complicated playing strategy to realize it. I described this strategy in
this earlier comment. (I don't want to give the impression that the strategy described there should be a priori intuitive or at all obvious-- it certainly wasn't to me, and it took quite a bit of experimentation with various strategies to yield an EV that agreed with that produced by CDP.)
At any rate, you're right that "as long as the strategy is fixed we know there are no problems for any number of splits." That is, SPL1 *doesn't* have this same problem, essentially because CDP is the same as CDP1 in that case, and CDP1 does *not* have this problem in general (for SPL3 or SPL1). That is, when we try to describe CDP1 strategy to a player that wants to use it, our laminated card only needs to indicate *whether* the current hand is a result of splitting a particular pair card P. It doesn't need to indicate the additional dependent information like *numbers* of observed pair (or non-pair) cards that are not generally available to the player. (Note also that the fact that CDP1 is "problem-free" has nothing to do with the fact that it is *optimal* in any particular sense; it's problem-free simply because of the limited information on which the strategy depends. For example, it would make sense to define a strategy that plays CDZ- pre-split, but plays mimic-the-dealer post-split. Such a strategy is both computable *and* playable.)
E
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