I didn't know whether to hijack Tarzan's thread or to create a new one. So, without risking injury on my part, (nor to sabotage the Ape Man's thread itself), I shall ask here.
While there seems to be some recent discussion about this idea of "Perfect Play", it got me wondering what the hell is PP? How would one go about curating a system for Combo PP? What will this allow for us a players at the table?
So, perfect play would allow me to double T, 7 vs 8, with a surplus of 3's and 4's in this case?
What would EV look like to the CPP player? Assuming flat betting?
And...how would one go about simming this PP concept? I take it Farmer, Schlesinger, Gron, et al. have the answer to that?
-1__This_became_the_BEST_current_thread_on_the_subje ct_of_PP.Originally Posted by DSchles
It_became_such_when_the_redoubtable_ERIC_FARMER_jo ined_us!
His_post_actually_taught_me_something_and_I_am_tru ly_grateful.
Sorry,_but_my_shift_key_just_decided_to_betray_me!
Actually, it's a good question. Although the answers given are "correct" as they fit the definition; "perfect play" isn't really quite perfect. For example, perfect play does not take into account a situation where not splitting with a close call will get you an additional round with a favorable shoe.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
I agree that it's a good question. In my recent posts of analysis results, although I have tried to be precise in at least the up-front description of strategy assumptions, I have also admittedly used the more vague and hand-wavy terms "optimal" and "perfect" in casual discussion, particularly where the details of the strategy were not the main point of discussion. Norm has pointed this out more than once, and I haven't done a good job of listening.
I won't try to define either of those terms here. But it's maybe worth at least describing in more detail what a current best "computer player" looks like (i.e., the assumptions behind all of my analysis results), and pointing out some of the many ways that I am wrong when I describe that computer player as representing "optimal play."
Norm's example is a good start: when determining the strategy for a particular round in the middle of a depleted shoe, the "horizon" stops at the end of that round. Not the end of the shoe, the end of the trip, etc. That is, for the purpose of evaluating any single round, the sole objective is maximizing the result of that round, as if the computer player planned to sit down, play that round, then get up and walk away. There is no consideration of, for example, making a "local" strategy decision that *hurts* expected return for that round, in exchange for improved "global" long-term performance of the shoe/trip/etc.
(However, although *playing* strategy is "local," we can still evaluate and optimize *betting* strategy with a "global" perspective, as discussed in posts of recent analysis results.)
Furthermore, that single-round playing strategy is not risk-averse. That is, by "maximizing the result of that round," I mean that the computer player's sole objective is to maximize the expected value of the overall outcome of the round, without consideration of variance.
(Again, however, although single-round *playing* strategy is not risk-averse, the *betting* strategy does account for variance/distribution of round outcomes to limit risk, also as discussed in recent analysis.)
Actually, I just said that the computer player's objective is to maximize expected return for a single round; this isn't quite true. Splitting pairs is complicated: if you split 2s vs. dealer 6, and draw a 10 to the first half of the split, it may be optimal to stand... but subsequently drawing another 10 to the second half, it may *now* be optimal to hit. This is the "Z" in "CDZ-" (composition-dependent zero-memory) strategy; we confine our possible *specification* of playing strategy to depend only on the dealer up card and the cards in the player's *current* (possibly post-split) hand. Sticking to zero-memory allows significant speedup in calculation of expected returns/variances, without sacrificing accuracy (i.e., it's still exact).
But it's even worse. Even constrained to zero-memory playing strategy, the computer player still doesn't necessarily realize the *best* such strategy: that is, the computed strategy may yield an overall expected return that is slightly less than the best possible expected return among all possible zero-memory (and composition-dependent) strategies. This is the minus sign in "CDZ-": CDZ represents truly EV-maximizing composition-dependent zero-memory strategy, but we can only efficiently compute CDZ-.
For an explicit example of the issue, consider single deck S17 DAS, and you're dealt 2-6 vs. dealer 5. EV-maximizing strategy is to hit... unless you are encountering this hand after having split 2s, in which case you should double down. If we are constrained to zero-memory strategy, so that we must decide to *always* hit or *always* double down in this situation, which yields a better overall EV?
CDZ- strategy always hits. That is, we compute "pre-split" strategy for all possible hands, then apply that same strategy to all *post-split* hands as well whenever we encounter them.
(The good news is that this suboptimality CDZ-<CDZ is very rare, and when it happens, the resulting difference in EV is pretty small. I can track down examples if there is interest. Also, I should point out that we can actually compute and evaluate better strategies than CDZ-. My CA also allows some refinements, referred to as CDP1 and CDP, that allow separate pre- and post-split strategy. But if we want more than just EV, but also variance for betting analysis, currently only CDZ- is supported.)
PE was originally defined with the constraints that 70 variations associated with hard totals 10-16 and insurance were used in a single deck game with 20 cards left. Keep in mind that the IBM 704 was slower than playing tag on the moon.
"I don't think outside the box; I think of what I can do with the box." - Henri Matisse
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