At this link https://www.qfit.com/card-counting.htm
,it says its:
"PE indicates how well a counting system handles changes in playing strategy. Playing efficiency is particularly important in hand-held games (one or two decks.)"
What in gawd's green earth does that mean exactly? And how important is it vis a vis betting correlation, which seems pretty straightforward and very important?
Thanks!
Playing efficiency is calculated by how a count performs for a static set of playing decisions. That is about as much as I have been able to find out when I was curious.
Generally the wider you spread the more importance BC becomes compared to PE. With fewer decks used or left to be played PE becomes more valuable. So with spreads being confined by heat concerns of pitch games and the fewer cards used PE becomes at least as important as BC if not more important. But in shoe games, especially with poor cuts, where large spreads are generally tolerated BC becomes much more important than PE. That all said what really matters is how playing interacts with your ramp not the BC and PE stats. A sim can tell you all you need to know.
P.E. is a measure of how close the count's tags mirror the E.O.R.'s
of the ten ranks; but more importantly, it is a measure of how well
the count's index adjustments improve the play of the full range of
possible hands, adjusted, via weighted averages, for their frequency,
and at varying True Counts, also weighted.
Note that simple counts make it simple for the casino to see what you
are up to. If you bet accurately, with an aggressive bet spread, in a
game with good rules and deep penetration, P.E. means rather little,
but that aggression will have you 86'd sooner, rather than later.
A Double Deck game needs a spread of just 4-1 to 6-1 (depending on
table conditions) to perform admirably. With one or two decks, P.E. is
always of paramount importance.
Last edited by ZenMaster_Flash; 12-04-2017 at 06:09 PM.
From Eric Farmer; go here: https://possiblywrong.wordpress.com/2013/09/15/efficiency-of-card-counting-in-blackjack-part-3Originally Posted by Joe Mama
The figure above essentially shows the “distance” between a basic strategy player and a perfect player. The performance of any actual card counting system, no matter how simple or complex, will lie somewhere in between these two extremes. If we define the playing efficiency of basic strategy to be zero, and the playing efficiency of perfect play to be one, then the efficiencyof any other strategy is calculated using its per-round expected return
according to
Don
Last edited by DSchles; 12-05-2017 at 08:28 AM.
Thanks, that's helpful. I'll let that roll around in my head for a while.
All the discussions concerning "best" systems can create fog in my head. After reading and reading and thinking and thinking, some things start to become clearer. For me, the fog is starting to lift a bit on this subject. A recent revelation for me is, in general, counts that include aces are better for BC and counts that don't include aces are better for PE. If you want the best of both, find a count that's comfortable and side count aces and adjust. In counts that include aces adjust playing deviation count downwards for excess aces. In counts that don't includes aces adjust betting count upwards for excess aces.
Now this observation may be because my count uses like 500 bins that can be moved for fine tuning betting, but I found that getting that last point, 1.0 being a point, in maximizes SCORE required spending a lot of EV (20%+ of EV) while getting that second to last point didn't cost much at all (1%- of EV). I like to say the difference between the way other systems construct a ramp and how my system does it like this. You are trying to make a wooden sculpture and the other systems use a dull rock to shape the wood while my system uses an Exacto knife set. Meaning the kind of fine adjustments that allow my system to see this type of diminishing returns may not exist the way other systems do things so take that comment on diminishing returns with a shaker of salt. Experiment with your system to see how it does when maximizing that last bit of SCORE. I expect it won't see the diminishing returns that I see with the extensive number of bins I can use to fine tune SCORE. But you never know.
https://possiblywrong.wordpress.com/...ackjack-part-3
Interesting research-
" Finally, we can compute the corresponding playing efficiencies:
Hi-Lo Illustrious 18 has playing efficiency PE = 0.309.
Hi-Lo with full indices has PE = 0.470.
Hi-Opt II with full indices has PE = 0.639.
I think this analysis raises as many questions as it answers. For example, these more accurate calculations of playing efficiency are lower than the approximations given by Griffin (see Chapter 4 in the reference below). There are several possible reasons for the difference: is the approximation inherently biased, or is it simply due to different assumed number of decks, penetration, etc.? "
Don, what you think ?
"Don't Cast Your Pearls Before Swine" (Jesus)
This is a good point, although I suspect it's actually the former (more on this shortly); in fact, note the "disclaimer" in the same linked/quoted write-up of my past analysis:
"(A word of caution: before anyone runs off quoting this as “the” formula for playing efficiency, note that these particular constants depend on all of the rule variations, number of decks, and penetration assumed at the outset of this discussion.)"
In other words, the provided "definition" of PE(v) = (v+0.004239)/0.001906 is only valid for 6D with 75% pen, S17, DOA, DAS, SPL3, NS... and even then, we still need to compute v, the actual expected return from using whatever playing strategy is under consideration, ranging from fixed basic strategy at one end to optimal (CDZ-) at the other end.
If you want to evaluate this proposed PE metric for, say, 2D with different rules, or 4D with yet another set of rules, or whatever, then three steps are needed:
1. Compute the expected return v_min for fixed basic strategy (the "lower bound" on reasonable achievable EV). Even this requires substantial computing resources, at least for a fixed burn card position (vs. fixed number of hands), to account for the cut-card effect, etc.
2. Compute the expected return v_max for optimal strategy (the "upper bound" on achievable EV). This is hard to do efficiently, and was/has been the primary goal of my CA over the last 20 years or so.
3. Compute the expected return v for the playing strategy being evaluated (e.g., Hi-Lo I18 indices, or Hi-Opt II full indices, etc.). The ability to compute this *exactly* for any sampled depleted shoe is a more recent addition to my CA.
Given these values, the proposed measure of playing efficiency is (v-v_min)/(v_max-v_min). In other words, how far does the evaluated strategy get you towards optimal (100% PE), with fixed basic strategy as the starting point (0% PE)?
If this sounds like a lot of work, it is. But this proposed definition, I think, more closely reflects our intuition, what we really *want* to measure, whether it's computationally hard to do so or not; Griffin's approach of using effects of removal is a good approximation... but it's an approximation based on limitations of algorithms and computing resources both of which have improved significantly in the intervening years. We can do better now. (We had almost exactly this same discussion some years back in one of the private forums, in that case focusing on betting correlation (BC), whose approximate formula suffers from the same problem. Amusingly, a forum search for posts by ericfarmer with keyword "drunk" will get you there.)
So to answer Three's question: why are my reported numbers in the referenced write-up different from those reported elsewhere, even for the same setup (number of decks, penetration, rules, etc.)? The short answer is because they are computed differently. Most reported figures use the calculation described by Griffin, based on single-card removals, effectively "linearizing" behavior which is decidedly non-linear. My figures use what I argue is a more useful/intuitive-- but much more computationally expensive-- method of calculation.
Eric
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