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Thread: Alexxx: optimal bet

  1. #1
    Alexxx
    Guest

    Alexxx: optimal bet


    according to wikipedia,

    Kelly bet is: f* =(bp-q)/b
    where

    f* is the fraction of the current bankroll to wager;

    b is the net odds received on the wager (i.e. if the odds are 2-to-1 ("even money") then the value of b is 1) ;

    p is the probability of winning;

    q is the probability of losing, which is 1 − p.

    but, some people say,
    optimal bet = bankroll x EV/Var

    which is correct?



  2. #2
    Don Schlesinger
    Guest

    Don Schlesinger: Re: optimal bet

    > according to wikipedia,

    > Kelly bet is: f* =(bp-q)/b
    > where

    > f* is the fraction of the current bankroll to wager;

    > b is the net odds received on the wager (i.e. if the
    > odds are 2-to-1 ("even money") then the
    > value of b is 1) ;

    You don't mean 2-to-1 for an even-money bet; you mean 1-to-1, which is the very definition of even money.

    > p is the probability of winning;

    > q is the probability of losing, which is 1 − p.

    > but, some people say,
    > optimal bet = bankroll x EV/Var

    > which is correct?

    Both! :-) If you have a game where the payoff for a winning wager is some multiple of the wager, and that is always the case (fixed payout), then the wikipedia formula is fine. Note that when b = 1, for the even-money game, the numerator is simply p - q, which is your edge or e.v., and the variance is 1. But, the general expression of bp - q expresses the edge no matter what multiple of odds you receive.

    Now, for a game like blackjack, there are all sorts of payoffs, not just one. After placing a wager, you might win one unit, 1.5, 2, 3, 4, etc. So, to replace the b in the above formula, we calculate instead the average squared result of a hand of blackjack (see Griffin, p. 167) and use that in the Kelly formula. It turns out that this is, for all practical purposes, the same thing as the variance of a hand of blackjack (again, see the same page in Griffin, below the calculation), whence the e.v./var. formula for blackjack.

    Don

  3. #3
    Alexxx
    Guest

    Alexxx: Re: optimal bet

    Thanks,

    If I have a game where the payoff for a winning wager is some multiple of the wager, and that is always the case (fixed payout), for example special side bet bonus promo,

    (bp-q)/b always equals Ev/Var ?

  4. #4
    Don Schlesinger
    Guest

    Don Schlesinger: Re: optimal bet

    > Thanks,

    > If I have a game where the payoff for a winning wager
    > is some multiple of the wager, and that is always the
    > case (fixed payout), for example special side bet
    > bonus promo,

    > (bp-q)/b always equals Ev/Var ?

    No, I didn't say that! I said that there are two formulas, for two different cases, and that the formula for the case that you mention above is (bp-q)/b. E.v./var. is the formula for blackjack. They're not necessarily the same thing. You apply one formula in one circumstance and the other in the other.

    Don

  5. #5
    Alexxx
    Guest

    Alexxx: I see. Thanks for your explanation. *NM*


  6. #6
    Prince Dragon
    Guest

    Prince Dragon: For example

    optimal bet = bankroll x EV/Var
    Var=SD^2
    If:
    BR=10000
    EV=0.91%
    SD=1.158
    Then:
    Optimal bet=67.86

    But in CVCX,the OB is 7.62
    Did i get this right?

    P.D.

  7. #7
    Don Schlesinger
    Guest

    Don Schlesinger: Re: For example

    > optimal bet = bankroll x EV/Var
    > Var=SD^2
    > If:
    > BR=10000
    > EV=0.91%
    > SD=1.158
    > Then:
    > Optimal bet=67.86

    > But in CVCX,the OB is 7.62
    > Did i get this right?

    OB in CVCX is probably being expressed in units, not dollars.

    Don

  8. #8
    Prince Dragon
    Guest

    Prince Dragon: Re: For example

    > OB in CVCX is probably being expressed in units, not
    > dollars.

    > Don

    Yes,it was expressed in Units,so the OB in CVCX is $76.20(I was using $10U)
    Then is was off by 1U according to my manual calc.

    Don...What did i miss here?

    P.D.

  9. #9
    Don Schlesinger
    Guest

    Don Schlesinger: Re: For example

    > Yes,it was expressed in Units, so the OB in CVCX is
    > $76.20(I was using $10U)
    > Then is was off by 1U according to my manual calc.

    > Don...What did i miss here?

    If it was an optimal bet, I doubt that the units were exactly $10. You may be "mixing and matching" here. Would have to see the screen.

    Don

  10. #10
    Aruuba
    Guest

    Aruuba: Re: For example

    > optimal bet = bankroll x EV/Var
    > Var=SD^2
    > If:
    > BR=10000
    > EV=0.91%
    > SD=1.158
    > Then:
    > Optimal bet=67.86

    > But in CVCX,the OB is 7.62
    > Did i get this right?

    I don't fully understand "optimal bets", that's for sure, but I was wondering if this may have to do with the EV of 0.91% being maybe an avg adv and CVCX using fixed Kelly-betting rather than "true" Kelly betting?

    I mean $67.86 seems right from a pure Kelly point of view if at some point in time you have that adv with that roll
    but, on the other hand, let's face it, if CVCX says so, believe it.

  11. #11
    Prince Dragon
    Guest

    Prince Dragon: Re: For example

    > If it was an optimal bet, I doubt that the units were
    > exactly $10. You may be "mixing and
    > matching" here. Would have to see the screen.

    > Don

    Hmm...I don't see any feature in this forum that i can upload a screen shot.
    And i don't know how to provide a URL link :-(

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