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Thread: The “why” of the floating advantage

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    The “why” of the floating advantage

    In another thread, a question was asked about why the floating advantage happens and what the “mechanics” are behind it. The thread quickly devolved, without, I think, really helping the OP much. I’ve re-read the relevant sections of BJA3 and Griffin multiple times, and put a lot of thought into it, and I think I finally understand it myself, but I had to talk myself through it in a different, more explicit way than BJA3 or Griffin describe it. My explanation to myself may help others understand it as well.

    Here goes:

    First, I propose we define the Floating Advantage Theorem: “As the pack is depleted, the true count count indicating a given advantage decreases in the most common true counts.”

    As to why this happens, here’s my best understanding:


    1. Average advantage is the same at all points in the pack; there is no inherent advantage change as the pack is depleted (some may want to read that again).
    2. True count is a tool to indicate and estimate advantage; it is not advantage unto itself.
    3. At very high and very low true counts, advantage *per true count* is lower than at moderate true counts (due to more pushes in very high true counts and poor double-down prospects in very low true counts)
    4. As the pack is depleted, very high and very low true counts become more common and the mean absolute value of the true count increases.
    5. As the pack depletes, very high and very low true counts become a larger fraction of all true counts. To maintain the same average advantage throughout the pack (refer to point #1 again), advantage per true count at more common true counts must rise to offset the lower advantage per true count at the now-more-common very high and very low true counts.
    6. Therefore, as the pack depletes, the true count *indicating* a given advantage must decrease at moderate true counts. These “moderate” true counts are approximately high-low -4 to +4 (by God!) as indicated in BJA3.


    Throw out your corrections / improvements to what I’ve said, or, if it’s perfect as is, go ahead and inflate my ego. If I'm way off, enlighten me.

  2. #2


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    Point 4 is very important, as deck volatility increases substantially. Be prepared for the big jump as deck depletes.

    Point 5 - I would still calculate the same true count, simply assigning a bonus to your normal bet, as you progress deeper into the shoe. This bonus would be minor at the 4.5 deck mark, progressing to a higher bonus at the 5.0 deck mark, maxing out at the 5.5 deck mark.

    Point 6 looks to be incorrect. Why woulD a positive true count ever decrease its strength in a positive true count?

    Point 1 is incorrect, point 2 is correct,

  3. #3


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    At the risk of "devolving" again i cant help but notice nothing about HE at a neutral count. Is it not true that at a neutral count HE on average would be much lower or non existant with 1 deck to remain than... oh say at the start of the 6 deck shoe?

  4. #4
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    What is the Floating Advantage effect?

    “...the advantage of a true count increases as we travel more deeply into the shoe.”

    https://www.blackjackincolor.com/blackjackeffects2.htm

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    Quote Originally Posted by angle_sh00ter View Post
    At the risk of "devolving" again i cant help but notice nothing about HE at a neutral count. Is it not true that at a neutral count HE on average would be much lower or non existant with 1 deck to remain than... oh say at the start of the 6 deck shoe?
    One deck remaining from a six-deck shoe is not the same as a single-deck game.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

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    Ive said that myself... Im not sure how many times

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    Quote Originally Posted by Freightman View Post
    Point 6 looks to be incorrect. Why woulD a positive true count ever decrease its strength in a positive true count?
    He worded things ambiguously. He said advantage when he means HE. It was more clear when he was talking about a BS player. But when he switched to talking about TC, implying counter it was less clear. I think he gets it.

  8. #8


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    Quote Originally Posted by Three View Post
    He worded things ambiguously. He said advantage when he means HE. It was more clear when he was talking about a BS player. But when he switched to talking about TC, implying counter it was less clear. I think he gets it.
    I put some time into wording my post, and chose my terms carefully.

    To me, "advantage" is opposite of HE. If HE for the upcoming round is 1%, "advantage" is -1%. Is that not how others use those terms? Or is "HE" the overall edge of a given game vs. BS?

    When I say "advantage", I mean the player advantage (or disadvantage) in the round about to be dealt. This advantage is the same for all players. The only difference between counters and BS players is that counters are aware of their advantage and in a position to exploit it.

  9. #9


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    The FA is traditionally framed as having a higher advantage at a given TC toward the end of the pack. While that statement is true, framing it that way has confused some here, including me, by implying that having fewer remaining cards is inherently advantageous, which is false. Then people start throwing in the fact that playing with fewer decks in the pack is advantageous (true, but totally irrelevant to the FA) and you have, well, that other thread.

    So I've attempted here to re-frame the FA in a way that doesn't confuse me or imply that fewer cards remaining is itself advantageous. My framing says that you need to look at the TC differently as the pack depletes. To accurately determine your advantage, you need to know both the TC and the depth in the pack.

    An analogy: How cold you get when you go outside in winter is a function of both the temperature and the wind speed. Their combination is how the "wind chill factor" is calculated.

    True count : temperature
    Pack depth : wind speed
    Advantage : wind chill factor

  10. #10


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    Quote Originally Posted by Optimus Prime View Post

    An analogy: How cold you get when you go outside in winter is a function of both the temperature and the wind speed. Their combination is how the "wind chill factor" is calculated.

    True count : temperature
    Pack depth : wind speed
    Advantage : wind chill factor
    The FBM ASC is versatile in its calculation of many things, including the fine tuning of wind chill during periods of adverse cold weather conditions.

    Shrinkage is measurable and, utilized with a table of declining winter temperatures, one can more accurately predict the impact of wind chill to adverse temperature.

    Midwest Player, you would be well advised to incorporate the FBM ASC into your winter schedule. It would assist you in the proper timing of roof snow removal.

  11. #11


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    Quote Originally Posted by Freightman View Post
    The FBM ASC is versatile in its calculation of many things, including the fine tuning of wind chill during periods of adverse cold weather conditions.

    Shrinkage is measurable and, utilized with a table of declining winter temperatures, one can more accurately predict the impact of wind chill to adverse temperature.

    Midwest Player, you would be well advised to incorporate the FBM ASC into your winter schedule. It would assist you in the proper timing of roof snow removal.
    Of course, utilization of a fur lined jock strap negates the effectiveness of FBM ASC for calculation of wind chill factors. Ball to ball carpeting has long been known as a negative factor in this regard.

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    Quote Originally Posted by Optimus Prime View Post
    I put some time into wording my post, and chose my terms carefully.

    To me, "advantage" is opposite of HE. If HE for the upcoming round is 1%, "advantage" is -1%. Is that not how others use those terms? Or is "HE" the overall edge of a given game vs. BS?

    When I say "advantage", I mean the player advantage (or disadvantage) in the round about to be dealt. This advantage is the same for all players. The only difference between counters and BS players is that counters are aware of their advantage and in a position to exploit it.
    In that case I agree with Freightman rather than think you are both right but there is a communication issue.
    Last edited by Three; 11-25-2018 at 09:23 AM.

  13. #13


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    Quote Originally Posted by Optimus Prime View Post
    In another thread, a question was asked about why the floating advantage happens and what the “mechanics” are behind it. The thread quickly devolved, without, I think, really helping the OP much. I’ve re-read the relevant sections of BJA3 and Griffin multiple times, and put a lot of thought into it, and I think I finally understand it myself, but I had to talk myself through it in a different, more explicit way than BJA3 or Griffin describe it. My explanation to myself may help others understand it as well.

    Here goes:

    First, I propose we define the Floating Advantage Theorem: “As the pack is depleted, the true count count indicating a given advantage decreases in the most common true counts.”

    As to why this happens, here’s my best understanding:


    1. Average advantage is the same at all points in the pack; there is no inherent advantage change as the pack is depleted (some may want to read that again).
    2. True count is a tool to indicate and estimate advantage; it is not advantage unto itself.
    3. At very high and very low true counts, advantage *per true count* is lower than at moderate true counts (due to more pushes in very high true counts and poor double-down prospects in very low true counts)
    4. As the pack is depleted, very high and very low true counts become more common and the mean absolute value of the true count increases.
    5. As the pack depletes, very high and very low true counts become a larger fraction of all true counts. To maintain the same average advantage throughout the pack (refer to point #1 again), advantage per true count at more common true counts must rise to offset the lower advantage per true count at the now-more-common very high and very low true counts.
    6. Therefore, as the pack depletes, the true count *indicating* a given advantage must decrease at moderate true counts. These “moderate” true counts are approximately high-low -4 to +4 (by God!) as indicated in BJA3.


    Throw out your corrections / improvements to what I’ve said, or, if it’s perfect as is, go ahead and inflate my ego. If I'm way off, enlighten me.
    I'm pretty late to the thread. There are a lot of interesting things to discuss here, and always so little time. Just focusing on item 1 (and item 4 at the end) to start: you're right that it seems like there has been some confusion on this point, in part because I think it's important to clarify under exactly what conditions it's actually true.

    For example, playing strategy matters; expected return is invariant with respect to shoe depth only if the playing strategy does not depend on shoe composition. The following figure compares the expected return for a round played with fixed, basic, total-dependent strategy (in red), and for a round played with Hi-Opt II with full indices (in blue), as a function of number of decks remaining in a 6-deck shoe. (Six decks are not ideal for a discussion of floating advantage, but it's the setup for which I have data readily available.)

    etct.png

    To interpret this plot: start with a fully-shuffled 6-deck shoe, observe, for example, 5 decks' worth of playing, then sit down and play a heads-up round from the remainder. Do this millions of times (i.e., shuffle the shoe, watch 5 decks go by, then play a round), and average the resulting outcomes. For the player utilizing basic *playing* strategy (whether he is counting for the purpose of *betting* or not), the expected return of about -0.48% is no different than it would be from the top of the shoe. For the Hi-Opt II player, expected return does improve (in this case, to about +0.15%), even "on average" over all encountered true counts, as the shoe is depleted.

    The point here is that advantage is only independent of shoe depletion if the playing strategy doesn't depend on the composition of the depleted shoe. For example, even for an otherwise fixed, "basic," total-dependent strategy player, if he is using a count *only* to take insurance, then this independence no longer holds, albeit with a smaller extent of change in EV.

    Also, particularly in discussion of FA where *extremely* depleted shoes are important (unfortunately I only have readily available data to 5/6 pen), we must be precise about exactly "how depleted" the shoe can get and still preserve constant EV for the fixed-strategy player. We can't run out of cards, or we risk the cut-card effect: suppose that instead of watching 5 decks get burned before playing a round, we instead watch, say, 48 heads-up *rounds* get played before we sit down to play, then watch another 48 rounds from another full shoe before playing, rinse and repeat, and average the results. The following figure shows the result.

    cce.png

    The problem is that our "experiment" may fail during some repetitions: for a burn card at 5/6 penetration, some shoes may not even make it past 43-ish rounds. That effective conditioning on a 49th round even *existing* skews the uniformity of the distribution of possible arrangements of cards in the shoe.

    Have to stop for now, but one last comment on item 4: I may misunderstand what's being said here, but I'm not sure I agree with this. The *exact* invariance of fixed-strategy EV should also apply to any linear combination of shoe rank probabilities, of which a true count is an example. A proof of this is here, including mathematically-gory details about what "fixed" strategy means, and what "not running out of cards risking the cut-card effect" means.

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