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Thread: MJ: CVCX Question: Optimal betting

  1. #1
    MJ
    Guest

    MJ: CVCX Question: Optimal betting


    Suppose I set the kelly-factor to 0.5, and then adjust minimum chip size to $25. The ROR now jumps up to 20.3%, even though the k-f is set at 0.5. Does this mean that the k-f is affectively 1.25? Would this still be considered as "optimal" betting?

    Also, why does CE become -$24? I thought CE is 50% of EV.

    See link below.

    Thanks,
    MJ



  2. #2
    Norm Wattenberger
    Guest

    Norm Wattenberger: Re: CVCX Question: Optimal betting

    If you input settings that are contradictory, the program must decide which to follow. When you set a min bet and ramp such that it is impossible to create a ramp that conforms to the requested KF, CVCX will create a ramp that gets as close as possible. With absurd settings, it obviously can't get close. Is this 'optimal?' Well, within the requested constraints, yes. But, it is hardly optimal from a practical view.


    Serious Blackjack Software

  3. #3
    David Spence
    Guest

    David Spence: Re: CVCX Question: Optimal betting

    > Also, why does CE become -$24? I thought CE is 50% of
    > EV.

    CE depends not only on EV, but also on variance, your desired level of risk (as measured by your Kelly fraction), and your bankroll. If your variance is too high in comparison to the other factors, you can easily have a negative CE. The approximate formula for CE is

    CE = EV - variance/(2*your Kelly fraction*bankroll)

    Greater EV, lower variance, greater risk tolerance (as measured by your Kelly fraction), and greater bankroll all increase CE.

    David

  4. #4
    MJ
    Guest

    MJ: Re: CVCX Question: Optimal betting

    > CE depends not only on EV, but also on variance, your
    > desired level of risk (as measured by your Kelly
    > fraction), and your bankroll. If your variance is too
    > high in comparison to the other factors, you can
    > easily have a negative CE.

    The variance in this case is reasonable, being that SD is about 16 times the size of EV.

    The approximate formula for
    > CE is

    > CE = EV - variance/(2*your Kelly fraction*bankroll)

    Using your formula the CE works out to be $47.50638. This is about 50% of the EV, which is $94.59.

    However, the software reports a negative CE. What formula/operation does the software perform to arrive at a negative CE?

    > Greater EV, lower variance, greater risk tolerance (as
    > measured by your Kelly fraction), and greater bankroll
    > all increase CE.

    Given your formula, that all makes sense. But I don't like the idea of increasing the kelly-factor to enhance CE.

    MJ

  5. #5
    MJ
    Guest

    MJ: Re: Specific question


    > Is this
    > 'optimal?' Well, within the requested constraints,
    > yes. But, it is hardly optimal from a practical view.

    The reason I ask is because I am curious what the kelly-factor would be given the constraints I am using. Clearly, the kelly-factor is NOT 0.5. What then, if any, is the kelly-factor for the bet schedule?

    The simple ROR calculator gives 20.3% ROR. Would solving the equation below for 'x' yield the k-f?

    Let x = kelly-factor

    0.1353^(1/x) = 20.3%

    Don wrote in another thread below,

    "If you're betting optimally, originally, without resizing, then, yes, your formula is correct".

    Given Don's criteria, is this formula applicable in this situation?

    Thanks,
    MJ



  6. #6
    David Spence
    Guest

    David Spence: Re: CVCX Question: Optimal betting

    > Using your formula the CE works out to be $47.50638.
    > This is about 50% of the EV, which is $94.59.

    Here's what I get, using the hourly data in the image attached to your previous post:

    CE = EV - variance/(2*kelly*bankroll)

    CE = 94.59 - 2,375,976/(2*.5*20,000) = -$24.21

    > However, the software reports a negative CE. What
    > formula/operation does the software perform to arrive
    > at a negative CE?

    The CE in CVCX agrees with the above calculation. Did you remember to SQUARE the s.d. to compute variance?

    > Given your formula, that all makes sense. But I don't
    > like the idea of increasing the kelly-factor to
    > enhance CE.

    The use of the Kelly fraction in the CE formula is not meant to encourage overbetting. It's better thought of as a measure of your desired risk. If your risk tolerance is best described by a Kelly number of .2, then that's the number you should use in the formula. Don't increase your Kelly fraction just to get a higher CE. CE needs a variable to quantify your risk tolerance, and that's exactly the function of the Kelly fraction in the formula.

    David

  7. #7
    MJ
    Guest

    MJ: Re: CVCX Question: Optimal betting

    > Here's what I get, using the hourly data in the image
    > attached to your previous post:

    > CE = EV - variance/(2*kelly*bankroll)

    > CE = 94.59 - 2,375,976/(2*.5*20,000) = -$24.21

    Ok, the reason our answers differ is because I used a kelly-factor of 1.25 in my equation.

    CE = 94.59 - 2,375,976/(2*1.25*20,000) = $47

    Why use a kelly-factor of 0.5 when the ROR is 20%? A kelly-factor of 0.5 has an ROR of 1.8% assuming no resizing of unit.

    Clearly, CVCX did not use a k-f of 0.5 when designing the bet schedule, so why use it in your equation to determine CE?

    In case you are wondering where I came up with k-f of 1.25, I used the following equation:

    Let x = kelly-factor

    0.1353^(1/x) = 20.3%

    1/x ln 0.1353 = ln 20.3%

    1/x = ln 20.3% / ln 0.1353

    x = 1.254

    Perhaps my logic is flawed, but does that make sense?

    > The use of the Kelly fraction in the CE formula is not
    > meant to encourage overbetting. It's better thought of
    > as a measure of your desired risk. If your risk
    > tolerance is best described by a Kelly number of .2,
    > then that's the number you should use in the formula.
    > Don't increase your Kelly fraction just to get a
    > higher CE. CE needs a variable to quantify your risk
    > tolerance, and that's exactly the function of the
    > Kelly fraction in the formula.

    Thanks for the clarification.

    MJ

  8. #8
    Norm Wattenberger
    Guest

    Norm Wattenberger: Re: Specific question

    Well yes. But setting contradictory inputs isn't really a great way to do that. Setting the chip size to 1 and changing the k-f until the bets are what you want would work better.

  9. #9
    David Spence
    Guest

    David Spence: Re: CVCX Question: Optimal betting

    > Ok, the reason our answers differ is because I used a
    > kelly-factor of 1.25 in my equation.

    > CE = 94.59 - 2,375,976/(2*1.25*20,000) = $47

    > Why use a kelly-factor of 0.5 when the ROR is 20%? A
    > kelly-factor of 0.5 has an ROR of 1.8% assuming no
    > resizing of unit.

    The Kelly factor in the image you included in your original post, on which the CVCX and my calculations are based, shows is .5.

    > Clearly, CVCX did not use a k-f of 0.5 when designing
    > the bet schedule, so why use it in your equation to
    > determine CE?

    See above.

  10. #10
    MJ
    Guest

    MJ: Re: CVCX Question: Optimal betting

    > The Kelly factor in the image you included in your
    > original post, on which the CVCX and my calculations
    > are based, shows is .5.

    I understand the k-f in the image is 0.5. I concede that the software used a k-f of 0.5 in the CE calculation. However, when the software determined the optimal bets given the constraints which were entered, it did NOT use k-f of 0.5. Rather, a k-f of around 1.25 was used in bet calculation.

    So, I am asking, why should CVCX use a k-f of 0.5 for determination of CE but a k-f of 1.25 in determination of the bet schedule? All I am saying is that the software should be consistent. Use the SAME k-f for the bet schedule as well as the CE calculation.

    Having said that, I am probably complicating things by entering GIGO like constraints. I will have to stop doing that. :-)

    MJ

  11. #11
    MJ
    Guest

    MJ: Re: Specific question

    > Well yes. But setting contradictory inputs isn't
    > really a great way to do that. Setting the chip size
    > to 1 and changing the k-f until the bets are what you
    > want would work better.

    Thanks! That is a good idea, I'll just do that from now on.

    MJ

  12. #12
    Norm Wattenberger
    Guest

    Norm Wattenberger: Re: CVCX Question: Optimal betting

    Actually it did use .5 k-f. But, it failed to find an answer given the constraints as there was no answer. So it did the best it could and provided the RoR.

    > I understand the k-f in the image is 0.5. I concede
    > that the software used a k-f of 0.5 in the CE
    > calculation. However, when the software determined the
    > optimal bets given the constraints which were entered,
    > it did NOT use k-f of 0.5. Rather, a k-f of around
    > 1.25 was used in bet calculation.

    > So, I am asking, why should CVCX use a k-f of 0.5 for
    > determination of CE but a k-f of 1.25 in determination
    > of the bet schedule? All I am saying is that the
    > software should be consistent. Use the SAME k-f for
    > the bet schedule as well as the CE calculation.

    > Having said that, I am probably complicating things by
    > entering GIGO like constraints. I will have to stop
    > doing that. :-)

    > MJ

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