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Thread: What is "Playing Efficiency"?

  1. #14


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    Quote Originally Posted by Gramazeka View Post
    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 ?
    I think the latter. People just throw out PEs without ever giving the rules and conditions. Obviously, they matter.

    Don

  2. #15


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    Quote Originally Posted by DSchles View Post
    I think the latter. People just throw out PEs without ever giving the rules and conditions. Obviously, they matter.

    Don
    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

  3. #16
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    Thanks Eric. You are always thorough and usually easy to understand as you were in this case. No follow up questions or pointing out of ways to get more useful answers from me this time as I think you nailed this on both approach and explanation.

  4. #17
    Senior Member Gramazeka's Avatar
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    Quote Originally Posted by Gramazeka View Post
    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 ?
    Eric, why do not we see this difference in numbers when the game is simulated?
    "Don't Cast Your Pearls Before Swine" (Jesus)

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    Quote Originally Posted by moses View Post
    PE. Something most everyone worries about but few can define.
    Don did it. So everyone can do it now.

  6. #19


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    Quote Originally Posted by moses View Post
    As Don also pointed out. It all comes down to SCORE. It's possible to have a 100 point differential in PE and and better SCORE with the lower figure. IC is actually where your significant dollars are won and lost.
    The very best discussion in print about the interaction of BC, PE, and IC can be found in Bryce Carlson's Blackjack for Blood, Chapter 5, pages 59-67. It is crystal clear, very well written, and perfectly accurate.

    And no, Moses, of the three, insurance is surely the least important consideration, simply because it doesn't occur frequently enough. Dealer has an ace up 1/13 of the time (slightly higher in high positive counts), and TC >= +3 only about 9% of the time. Together, we insure only about 1 hand out of 145, and when the TC is right at +3, the edge is obviously minimal. By +4 or +5, it's greater, but then, clearly, the frequency is even smaller still.

    Don

    P.S. I know your insurance threshold is lower, for SD, but you're the only person on the planet who plays SD, so I'm writing for a wider audience.

  7. #20
    Senior Member Gramazeka's Avatar
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    Quote Originally Posted by Gramazeka View Post
    Hi-Lo Illustrious 18 has playing efficiency PE = 0.309.
    Hi-Lo with full indices has PE = 0.470.
    Moses, I specifically mean these figures.
    "Don't Cast Your Pearls Before Swine" (Jesus)

  8. #21


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    "Suppose you have a max bet out of $1600. Perfect Insurance picks up two bets that regular insurance would've missed. That is a savings of $3,200. But you'd have to guess correctly on 32 minimum bets to achieve the same value."

    You have a strange way of reasoning, as if "perfect insurance" means that you win every insurance bet you make!! The vast majority of the time, insuring with 100% efficiency or with 75% efficiency is going to lead to identical results. Naturally, knowing more is better than knowing less, but the gain from perfect insurance over counts that have, say, 75% IC can't be very much.

    Don

  9. #22


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    "Also, know one is going to get in your business ..."

    This one is bad, even by your standards!

    Don

  10. #23
    Senior Member Joe Mama's Avatar
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    Quote Originally Posted by moses View Post
    Suppose you have a max bet out of $1600. Perfect Insurance picks up two bets that regular insurance would've missed. That is a savings of $3,200. But you'd have to guess correctly on 32 minimum bets to achieve the same value.
    This dollar amount is true only if all ten value cards are left in the deck, I think any "regular" insurance index would pick that situation up. Perfect insurance's value is its incremental difference from "regular" insurance.

  11. #24
    Senior Member Joe Mama's Avatar
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    Quote Originally Posted by moses View Post
    Not necessarily Joe. Even in a straight up game Ive had rare instances where two hand of 20 pushed the threshold below the line.

    But the more players at the table the more tens could come out in a high TC correct?
    I guess part of what I am saying is "perfect" insurance can lose up to two third's of the time, but still be the correct bet to make. "Regular" insurance index could make a bet you collect on that "perfect" would tell you not to bet on and vice/versa. Your statement implies (I infer) there is no overlap between "perfect" and "regular" indices, where in fact the overlap is substantial, 95+% in many cases.

  12. #25
    Senior Member Joe Mama's Avatar
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    Quote Originally Posted by moses View Post
    You lost me a little Joe. Don can probably explain this better than me. The threshold for insurance is 33% 10s remaining. The ideal for this is Perfect Insurance. No it does not win every decision but it always provides the threshold. Now you can make the perfect decision based on having an exact threshold.

    Imagine taking unsurance when the threshold is 28% with two hands of two 10s each. Imagine not taking insurance on two crappy hands when the threshold jumps to 50%.

    Yes. It's that 5% difference that it does make a difference that matter...because of the amount bet.
    I overstated the overlap, 75-85% is more like it. I don't believe a "regular" index would fail to pick up 50% tens remaining in the deck very often. The point is, "regular" insurance indices do have value relative to "perfect".

  13. #26


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    Quote Originally Posted by Gramazeka View Post
    Eric, why do not we see this difference in numbers when the game is simulated?
    I'm not sure I understand the question. These *are* numbers generated via simulation (actually a combination of simulation and CA). Can you describe what simulation environment and results you're referring to?

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