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Thread: What is the fastest way to get to the long run in Blackjack?

  1. #14
    Senior Member brh's Avatar
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    Quote Originally Posted by brh View Post
    It doesn't work that way. The value of N0 depends solely on the game, your count, your unit (ie 1-M) spread and your Wong point.
    What fraction of your ekb (equivalent Kelly Bankroll) you are using to determine your betting unit makes no difference to N0.
    That's just how things work.
    Brett.
    BA,

    Sorry to sound a bit harsh, but I am getting a little tired of having to explain over and over again - its not your fault.

    Again to quote this paper http://www.blackjackforumonline.com/...eads-howto.pdf :

    I suggest you look at Equation 11:

    Your Kelly bankroll doubling time is given by t = (0.693)/( k - k*k/2) * N0 rounds, which is minimised for k = 1,
    where t = 1.39 x N0.

    For k=>Sqrt(2)=1.41, your Kelly doubling time is infinite - effectively meaning you are overbetting
    and you are guaranteed to lose your bankroll, period. If k=0 you are betting nothing and again your
    doubling time is infinite.

    If you are able to plot quadratic functions, look at y = k - k*k/2 and you will see what I mean.

    As I said earlier N0 is determined ONLY by your count, your unit (ie 1-M) spread and your Wong point.

    Your Kelly doubling rate depends on your Kelly fraction k and N0.

    The only way you can decrease your Kelly time for a fixed fraction k = BANKROLL/EKB is to DECREASE N0.

    N0 does NOT depend on either your Bankroll or EKB. N0 only depends on your UNIT 1-M spread and your Wong point.

    Fiddling with your unit bet $B = k * BANKROLL/ekb, where ekb is your UNIT Equivalent Kelly Bankroll
    ( again only dependent on your UNIT 1-M spread and your Wong point ) cannot change N0.

    So reducing your bet size will decrease your Kelly fraction k and reduce your Kelly growth.
    Mucking around with your unit spread will only increase N0 and reduce your Kelly growth.

    End of story.

    Brett.

  2. #15
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    I don't particularly like discussions about N0. Frankly when you get into discussions that involve these kind of formula's that Mr Harris is discussing, I am lost. It's just way over my head. To me N0 is one of those things that works in the world of simulations, with a single game, single set of rules, same penetration, same bet spread and ramp, but I don't think it translates into the real world of blackjack today. Earlier in my career, based out of AC, I played mostly a very similar game, although some were 8 decks and some were 6 decks. Rules varied slightly as Borgata let you split to more hands and of course penetration varied, but still was in a similar range. Now, I play double deck and 6 deck games, the rules vary a lot more, penetration varies much more and my bet spread is all over the place as I tailor my spread and ramp for each location based on what I feel the casino will tolerate. So attempting to figure any sort of N0 is fruitless, unless you are going to break it down for each individual game played. I just concentrate on racking up as much combined EV as I can. By the time I get to year's end and that combined EV grows towards 100k, my results seem to come in line with EV, regardless of how far they fluctuated earlier in the year. So I figure that is about the long run for me. I am sure I am being naive and over simplifying things. Maybe a year isn't my long-term. Maybe some year I will have a year where EV and results don't come close. Maybe I will have a losing year.

  3. #16
    Senior Member brh's Avatar
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    Quote Originally Posted by brh View Post

    Your Kelly bankroll doubling time is given by t = (0.693)/( k - k*k/2) * N0 rounds, which is minimised for k = 1,
    where t = 1.39 x N0.

    As I said earlier N0 is determined ONLY by your count, your unit (ie 1-M) spread and your Wong point.

    Your Kelly doubling rate depends on your Kelly fraction k and N0.

    The only way you can decrease your Kelly time for a fixed fraction k = BANKROLL/EKB is to DECREASE N0.

    N0 does NOT depend on either your Bankroll or EKB. N0 only depends on your UNIT 1-M spread and your Wong point.

    Fiddling with your unit bet $B = k * BANKROLL/ekb, where ekb is your UNIT Equivalent Kelly Bankroll
    ( again only dependent on your UNIT 1-M spread and your Wong point ) cannot change N0.

    Brett.
    Tthree,

    Couldn't have put it better myself.

    Just to complete the picture:

    ROR = e ^(-2k) = e^(-2 *BANKROLL/EKB)

    Where to quote the above:

    "N0 does NOT depend on either your Bankroll or EKB."

    There "k" or "ROR" does NOT depend on "NO".

    As Tthree said, change your ROR to your heart's content, it will only change your unit bet $B,
    which when converted to a $B * ( 1 - M ) betting scheme will only change N0 by a small amount
    after rounding the resulting betting values.

    Brett.

  4. #17


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    Brh

    Help me here
    Is N0 a measure of the long run?

    Does N0 refer to a 13.53% fixed ror?
    Or
    Does it refer to Kelly resizing?

    Doesn't N0 or the long run go up about 4 times
    Fixed betting vs Kelly resizing?

    The more frequently one resizes the longer their time horizon, so doesn't that mean a small fraction of Kelly has a shorter time horizon?

    Thanks for your time
    Last edited by blackjack avenger; 10-25-2012 at 09:18 AM.

  5. #18
    Senior Member brh's Avatar
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    Quote Originally Posted by KJ View Post
    I don't particularly like discussions about N0. Frankly when you get into discussions that involve these kind of formula's that Mr Harris is discussing, I am lost. It's just way over my head. To me N0 is one of those things that works in the world of simulations, with a single game, single set of rules, same penetration, same bet spread and ramp, but I don't think it translates into the real world of blackjack today. Earlier in my career, based out of AC, I played mostly a very similar game, although some were 8 decks and some were 6 decks. Rules varied slightly as Borgata let you split to more hands and of course penetration varied, but still was in a similar range. Now, I play double deck and 6 deck games, the rules vary a lot more, penetration varies much more and my bet spread is all over the place as I tailor my spread and ramp for each location based on what I feel the casino will tolerate. So attempting to figure any sort of N0 is fruitless, unless you are going to break it down for each individual game played. I just concentrate on racking up as much combined EV as I can. By the time I get to year's end and that combined EV grows towards 100k, my results seem to come in line with EV, regardless of how far they fluctuated earlier in the year. So I figure that is about the long run for me. I am sure I am being naive and over simplifying things. Maybe a year isn't my long-term. Maybe some year I will have a year where EV and results don't come close. Maybe I will have a losing year.
    KJ,

    For today's player you are probably correct.

    I guess my over reliance on NO comes from living in a town where there is only one casino
    called "Crown Casino" - you might have seen another thread by "Koz". It's a place whey actually kill
    you if you get up their nose and the closest casino is 1000km away.

    However, all you need is a laptop with Norm's CVCX with you in your hotel room and you can analyse
    The games you intend to play each day. Not the perfect solution if you are mixing things up
    but it's a start.

    Brett.

  6. #19
    Senior Member brh's Avatar
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    Quote Originally Posted by blackjack avenger View Post
    Brh

    Help me here
    Is N0 a measure of the long run?

    Does N0 refer to a 13.53% fixed ror?
    Or
    Does it refer to Kelly resizing?

    Doesn't N0 or the long run go up about 4 times
    Fixed betting vs Kelly resizing?

    Thanks for your time
    BA,

    Yes NO is a measure of the long run, but (see my response above) it technically refers to an individual game,
    with a particular count, a fixed (1 - M) UNIT spread (that is for example 1, 2, 3, 4, 5 per count value for a 1-5
    spread - it's usually more complicated than that for an Optimal spread such as 3.34 etc by stay with me),
    and a Wonging strategy such as "leave at all counts less than -1". NO is minimised when the exact
    1-M spread is found for these conditions is found. As I alluded to above, the intermediate bets will
    be fractional, such as 3.34 etc. the minimum bet will still be 1, the maximum bet will still be 5 in the above
    example, it will tell you when you should bet the maxim, such as TC=+6, and when you are Wonging
    your bet is 0.

    At this stage, there is no money involved.

    The same game as described above generates another parameter called "ekb" or Equivalent Kelly Bankroll.

    Together (N0,ekb) characterise the optimal spread for this "game".

    N0 has no effect on the ROR, what it does tell you is how many rounds it will tel you to have an ev = ekb.

    It is ekb which is critical for ROR - it tells you how to calculate you monetary unit bet $B, which will be
    your minimum bet in the real world should be in the real world for a given ROR.

    Just say for some six deck game, we have a 1-10 spread, leave at Hilo TC=-1.
    Typically for a game like this, N0 will be 40000 rounds and ekb will be 500 units.

    Say you have a $10000 bankroll:

    If we divide $10000 by N0 and multiply by 100 we get SCORE = 10000/40000 x 100 = $25.

    If divide $10000 by ekb we get $B = $10000/500 = $20.

    That is your betting scheme will be $20 - $200.

    Now let's go in reverse and multiply ekb by $B: $B x ekb = $20 x 500 = $10000. This is called the EKB - your
    actual Equivalent Kelly Bankroll.

    If your actual bankroll was $10000, and you spread $20 -$200 your ROR would be 13.53%,
    That's why we call $10000 the EKB. Notice that the ROR does not depend on N0.

    Once you know the EKB you can calculate your Kelly fraction.

    In this case, for a real bankroll of $20000 your Kelly fraction would be k = EKB/$20000 = 0.5 and your ROR = 5%.

    I can understand this is quite difficult and you really need a simulator to work it all out.

    Luckily we have the "veritable" Norm, so with a laptop and CVCX it will do it all for you.

    As Tthree says, you can play with the CVCX tool on this site.

    Cheers,
    Brett.

  7. #20
    Senior Member Anton Chigurh's Avatar
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    Quote Originally Posted by blackjack avenger View Post
    The more frequently one resizes the longer their time horizon, so doesn't that mean a small fraction of Kelly has a shorter time horizon?
    N0 is the number of hands at which your EV for that number of hands equals one standard deviation for that number of hands.

    For any number of hands, both EV and standard deviation are directly proportional to bet level, assuming all bets in your ramp are multiplied by the same constant. So if you spread 10-200 on odd-numbered days and spread 25-500 on even-numbered days, except for the 29th of each month, when you spread 100-2000, your N0 will not change, even though your EV and standard deviation will, and your chances of achieving negative bankroll will be higher or lower accordingly.

    Multiplying all bets by 1/2 cuts EV by 1/2 and standard deviation by 1/2, and hence has no effect on N0.

  8. #21


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    I haven't looked at this area of BJ in a while si I might not give the most intelligent answer . But in mind, N0 is the number of rounds after which the accumulated expectation is equal to the accumulated standard deviation. I personally prefer N0 because in order to calculate it all you need is the expectation value and standard deviation (in fact i was so fascinated with standard deviation, that I wrote a CA that calculates both the expectation value and standard deviation). N0 is the measure of overall intrinsic advantage of the game you are playing, which includes number of decks, casino rules, penetration, playing strategy, betting strategy. Kelly fraction, ROR etc... has nothing to do with the "juiciness" of the game you are playing. The only relationship is that the juicier is the game (i.e the lower the N0) you will make more money for the same risk.
    Chance favors the prepared mind

  9. #22
    Random number herder Norm's Avatar
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    Quote Originally Posted by brh View Post
    Norm - could these two posts be put somewhere here so I don't keep referring to them
    If you are the author, they can be placed in the Blog section. If not, I'd need permission from the author.
    "I don't think outside the box; I think of what I can do with the box." - Henri Matisse

  10. #23
    Senior Member brh's Avatar
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    Quote Originally Posted by Norm View Post

    If you are the author, they can be placed in the Blog section. If not, I'd need permission from the author.
    Yes I most certainly am the Author - they are excerpts from by Brh Systems Book -go for your life.

    Much appreciated.

    Brett.

  11. #24


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    Quote Originally Posted by blackjack avenger View Post
    Why doesn't n0s measure long run? Isn't that what it does?
    N0 as a measure of overcoming 1 standard deviation with EV is still gambling. A much safer (not foolproof) measure would be to look at 4XN0 or overcoming 2 standard deviations as a more reasonable view of the long term. Reducing N0 through wonging is also reducing variance, both good things to do.
    Luck is nothing more than probability taken personally!

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