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  1. #118


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    Post #207! Actually #208 if you include this one. I knew we could get there!

  2. #119
    Random number herder Norm's Avatar
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    Moses, I fail to see the profundity. But, if you want such, try reading the documentation. Or, just move the mouse over any spot in the results on that page and the balloon says: "The Initial advantage for each player for each first two cards vs. the dealer up card is shown." You don't even have to click.

    Read more and post less.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

  3. #120
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    Quote Originally Posted by DSchles View Post
    You're all talking at cross-purposes. First of all, SD or 6D? It matters. Second of all, the difference between the lower percentages and the higher ones is that the lower ones are for an initial two-card holding, while the higher ones are for any totals of 14, 15, or 16.

    Don
    Thank Don.
    I was thinking MGP's Blackjack Combinatorial Analyser was for initial two cards.
    BTW, can we overall trust it ? I don't see many reference about that software.

  4. #121


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    "BTW, can we overall trust it ? I don't see many reference about that software."

    The best there is. :-)

    Don

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    Great.
    I bet that with such a letter of recommendation I will see more references.

  6. #123
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    Quote Originally Posted by moses View Post
    Confusion. T3 quotes BC is slop.
    It is nice to get the quote right when you quote someone. You keep misquoting me and Don which indicates you didn't understand our individual points to begin with. First of all BC is a relative term that doesn't show any quantifiable difference between counts. BC simply says how well the count's tags correlate to the full deck betting EoR's for each rank. The slop in betting comes from how much error is produced by the betting counts assumptions. A level 1 count assumes all low cards have the same EoR and weights each one the same. The slop comes in when the expected failure of this assumption results in the count's inaccuracy in the optimal bet compared to the actual deck composition's optimal bet. If there is the same number of each rank removed the assumption doesn't produce inaccuracy. If more higher or lower magnitude EoR cards are removed you start to see slop. Every count assumes even distribution of ranks removed within a group. The cost of the failure if the assumption (slop) varies by how the cards are counted.

    You can't avoid the slop because ranks won't be removed proportionally. You can affect the cost (range and frequency of actual deck composition optimal bet being different from the count's optimal bet) of the slop by your choice of how to count the cards removed. Level 2 counts help reduce the slop in betting. Column counts can help reduce the slop in betting if the info gathered is used properly. This said you can't avoid the slop altogether unless you use a combinatorial analyzer and counting every rank which nobody can do.

    I will let Don address your misquoting of what he said. I will say betting and playing decisions interact to produce optimal bets and determine SCORE. You can't effectively look at them individually to get a sense of how they affect your overall results. That is what SCORE, n0, and CE are for.

  7. #124


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    Woah... how is this post still going? I thought this one died?

  8. #125
    Senior Member Gramazeka's Avatar
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    https://www.blackjackinfo.com/bb/sho...kb-post-159948

    Post by Brett Harris-

    There is a short answer and a rather long answer.

    The short answer is for any advantage player, at a given time, will be betting with a given spread, say $B_min to $B_max, with intermediate amounts for counts in between. There are also the given rules, and it depends on whether they leave at certain negative counts - these will all affect the result.

    But lets break things up: [assume they true count Hi-Lo in a 6-deck game]

    1/ Divide everything by $B_min - so that a $20 to $240 spread (assuming play-all), starting to rise at TC=+2 (say $40) up to $240 at TC=+8 [a bad spread] becomes:

    Bet 1 unit at +1 or less
    Bet 2 units at +2
    .
    take your pick < +8
    Bet 12 units at +8 or greater. [ok so far...right]

    This is known as a 1-12 unit spread (or 1-12u for short).

    2/ Say the EV per 100 rounds is about $25 (I said is a bad spread), and the SD per 100 rounds is about $750.

    Firstly convert this to per round, remembering that the EV is divided by 100, but the SD is divided by 10 (ie VAR is divided by 100).

    So EV/r = $0.25 and SD/r = $75.00.

    Then doing the division gives: 'ev' = 0.0125u ; 'sd' = 3.75u .

    The quantities 'ev' and 'sd' are the unit EV and unit SD per round. If you think the 'ev' looks small you are right, but since the bets range between 1-12u (mostly at the low end) the 'sd' is reasonable.

    In general if B_min is just called $B ($20 in this case), and keeping things per round (the 100 round thing is just confusing) then we simply have:

    EV = $B * ev
    SD = $B * sd
    VAR = $B * $B * (sd)^2

    3/ Probability theory for large N, says that you have about one 33% chance of being 1 standard deviation below expectation after SQRT(N)*SD. Now this works for either EV(ev) or SD(sd) as the $B cancels out, so an unlucky player(33%) could be zero (or less!) after N hands if

    0 = N * EV - SQRT(N)*SD or N*N*EV*EV = N*SD*SD .

    Canceling the N and rearranging gives N = (SD/EV)^2 = VAR/(EV)^2 where we get the (famous?) value

    N0 = (sd/ev)^2 = (SD/EV)^2

    which is called the long run index.

    4/ You will have to take my word on this, but Kelly Theory says that for a game using unit 1-M spread, with a given 'ev' and 'sd' has what is called an Equivalent Kelly Bankroll (ekb) given by

    'ekb' = sd^2/ev = var/ev.

    It is no coincidence that if we put back the $B, we get the dollar EKB

    EKB = (SD^2/EV) providing the EV is per round, not 100.

    So for the example above we get

    N0 = [(3.75)/(0.0125)]^2 = 90000 rounds (lousy)
    ekb = (3.75*3.75)/(0.0125) = 1125

    and EKB = $20 * 1125 = $22500
    (which means if this is your bankroll you have a risk of ruin of 13%. Not a good return on investment. Also notice (it drops out from the math) that

    EKB/N0 = $0.25 = EV - not a coincidence!

    Therefore your win rate per hand is simply your Equivalent Kelly Bankroll divided by your long run index.

    Optimal Betting Theory says that simply by reducing your high bet down to TC=+4, you can halve N0, lower your EKB and increase your win rate at the same time.

    But there is another trick - for a given 'ekb', you can choose your unit bet $B so that you can match your Kelly Bankroll. Now what happens if you optimise your betting spread (minimise N0), and adjust your $B such that your EKB is $10000???

    You guessed it - your win rate EV/r = $10000/N0 !

    Then if you wanted to have a win rate per 100 rounds you get

    EV(100) = ($10000/N0)*100 which just happens to be the SCORE!!

    I originally came up with N0 with my work on Optimal Spread Theory. Any N0 more than around 20000 is probably unplayable, unless you Wong which really can lower it, and good single deck games should be less than 10000.

    Don felt that players relate better to win rate rather than long run chances of being ahead, so he invented SCORE - which is really just (1/N0) multiplied by $1,000,000. The main difficulty I have with it is just that players may just consider it a win rate, which can be calculated for any non-Optimal spread (that is to really 'KNOW' a game, you you need to know the ev and sd (or equivalently NO and ekb, not just N0 which you get from SCORE).

    In other words, you should know the $B Don has used to convert the unit 'ekb' to $10000. He may well do this in his book, you need to check.

    I believe QFIT has programs like CVCX to compute Optimal Betting Spreads - doing a Google is a good idea.

    If all this has been a bit messy, you can always go to:

    http://www.blackjackforumonline.com/...#Bettingsystem

    and find my two articles under 'Blackjack Betting for Card Counters'. The first 'How-To' article explains the stuff I said above, the second one is really only for the mathematically inclined who may have access to simulator data.

    Cheers,
    Dr. Brett Harris.
    Last edited by Gramazeka; 10-12-2016 at 10:17 AM.
    "Don't Cast Your Pearls Before Swine" (Jesus)

  9. #126
    Senior Member Bodarc's Avatar
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    The link isn't working for me Gramazeka
    Play within your bankroll, pick your games with care and learn everything you can about the game. The winning will come. It has to. It's in the cards. -- Bryce Carlson

  10. #127
    Senior Member Gramazeka's Avatar
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    Yesterday this link worked. I don't know, why Ken Smith has closed this discussion yesterday . Can to him there isn't enough money now?

    Last edited by Gramazeka; 10-13-2016 at 03:10 AM.
    "Don't Cast Your Pearls Before Swine" (Jesus)

  11. #128


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    Quote Originally Posted by Gramazeka View Post
    I don't know, why Ken Smith has closed this discussion yesterday
    Ken posted on blackjacktournaments.com that he is no longer involved with moderating the forums there nor at blackjackinfo.com.

  12. #129
    Senior Member Gramazeka's Avatar
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    Now link works. This is the best discussion on a subject cSCORE in any forum-

    https://www.blackjackinfo.com/bb/sho...kb-post-159948
    "Don't Cast Your Pearls Before Swine" (Jesus)

  13. #130
    Random number herder Norm's Avatar
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    If you are betting optimally, they are all the same thing.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

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