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Thread: Mike H: Kelly Betting fractions and SCORE

  1. #1
    Mike H
    Guest

    Mike H: Kelly Betting fractions and SCORE

    To bet a fraction of Kelly do you just bet that fraction of what the full Kelly bet would be (for half Kelly just divide the full Kelly bet by 2)? I assume full Kelly would optimize WinRate? In general is there a ballpark fraction of Kelly to bet that will optimize SCORE?

  2. #2
    Don Schlesinger
    Guest

    Don Schlesinger: Re: Kelly Betting fractions and SCORE

    > To bet a fraction of Kelly do you just bet that
    > fraction of what the full Kelly bet would be (for half
    > Kelly just divide the full Kelly bet by 2)?

    Yes.

    > I assume full Kelly would optimize WinRate?

    Full Kelly optimizes the logarithmic growth of your bankroll.

    > In general is there
    > a ballpark fraction of Kelly to bet that will optimize
    > SCORE?

    SCORE is determined by betting optimally and then not resizing your bets as bankroll fluctuates. As such, risk of ruin is about 13.5%. SCORE requires that you bet both full Kelly and optimally, in the beginning, but that you don't change that initial approach, as bank varies.

    As you may know, in an optimal world, ROR from pure Kelly betting is zero, but, from a practical, real-world point of view, betting pure Kelly ( no matter what the fraction) is quite impossible.

    Don

  3. #3
    Mike H
    Guest

    Mike H: Re: Kelly Betting fractions and SCORE

    I guess I should have phrased the question as, "What fraction of Kelly will optimize cScore or DI?"

    Can you explain the differing goals of a counter whom tries to maximize WinRate, one whom tries to maximize EV or Initial Bet Advantage, and another whom tries to maximize DI or cScore.

  4. #4
    Don Schlesinger
    Guest

    Don Schlesinger: Re: Kelly Betting fractions and SCORE

    > I guess I should have phrased the question as,
    > "What fraction of Kelly will optimize cScore or
    > DI?"

    Phrasing it that way won't/can't help. It shows a lack of understanding of what you're asking. It would help somewhat if you would read the book or simply read more about Kelly.

    SCORE doesn't use Kelly betting, because, well, it's impossible to bet that way. As to what fraction of Kelly maximizes logarithmic growth of bankroll, that answer is, obviously, 100%.

    > Can you explain the differing goals of a counter who
    > tries to maximize WinRate, one whom tries to maximize
    > EV or Initial Bet Advantage, and another who tries to
    > maximize DI or cScore.

    A counter who tries to maximize how much money he wins (win/100) without regard to risk could be said to be attempting to maximize hourly win. Clearly, the way to do that is to bet as much as you possibly can. Now, it may be that 99 out of 100 people who bet that way will go broke, but the one who doesn't will win all the money in the world and will make up for all the others who go broke. Unfortunately, you can't ordain ahead of time that you will be that one, so it's obviously not a very intelligent way to play.

    Maximizes your IBA is, in essence, an attempt to play the best games, where your edge, expressed as a percentage of initial bets placed, is as high as possible. This, of course, is a noble goal, but the game with the highest IBA doesn't always have the highest SCORE, because SCORE also introduces the notion of risk.

    Maximizing SCORE assures a tradeoff between risk and reward. It maximizes the Sharpe ratio, and they gave the Nobel prize in economics to William Sharpe who first enunciated the notion that this was a rather intelligent thing to want to do.

    Don


  5. #5
    Mike H
    Guest

    Mike H: Re: Kelly Betting fractions and SCORE

    Thanks for your patience with me on this topic. There's really no way to maximize SCORE because to get SCORE you must follow all the preconditions. The only way to change SCORE for a specific game is to change count systems. If you change to some fraction of Kelly you no longer have SCORE, but you still have c-SCORE or fractional-Kelly-SCORE. If a fractional-Kelly-SCORE is higher than the real SCORE, would that betting strategy be more attractive? If so is there a fraction of Kelly that generally outperforms the others? I think I'm beginning to understand but it's late and my brain is fried.

  6. #6
    Don Schlesinger
    Guest

    Don Schlesinger: Re: Kelly Betting fractions and SCORE

    > Thanks for your patience with me on this topic.
    > There's really no way to maximize SCORE because to get
    > SCORE you must follow all the preconditions.

    Given a particular set of rules, pen, etc., a game can have only one SCORE. So, yes, in that sense, there is nothing to maximize.

    > The only
    > way to change SCORE for a specific game is to change
    > count systems.

    Right.

    > If you change to some fraction of Kelly
    > you no longer have SCORE, but you still have c-SCORE
    > or fractional-Kelly-SCORE.

    Right.

    > If a fractional-Kelly-SCORE
    > is higher than the real SCORE,

    Impossible. Except for rounding to reasonable real-world bet sizes, changing the Kelly fraction does nothing to the SCORE. You bet half as much, you win half as much, the variance is half as much, and SCORE doesn't change.

    > would that betting
    > strategy be more attractive?

    See above.

    > If so is there a fraction
    > of Kelly that generally outperforms the others?

    You keep asking the wrong question.

    > I think I'm beginning to understand but it's late and my
    > brain is fried.

    I'm beginning to notice! :-)

    Don

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