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Thread: Relating Kelly fraction to ROR quickly

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    Relating Kelly fraction to ROR quickly

    Is there a quick way to convert the Kelly fraction you're using for your betting into ROR without having to sim out the specifics? For example, if I'm betting 1/2 Kelly, to me that means my bet is .5 * advantage * bankroll. If I stick to that, with no betting maximum, what is my ROR? Or am I oversimplifying?

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    That is 7/10th Kelly.

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    Not sure if it's a linear correlation, but keep in mind that in reality it's not really possible to actually bet Kelly, or some fractional Kelly amount. It assumes you're always betting that percent of your bankroll related to your advantage, but in reality over half your bets are typically into a disadvantage situation, along with other concerns, so the 13.5% ror associated with betting Kelly with likely be higher if you try to bet full Kelly in real play. Also Kelly betting guarantees never going broke, but doesn't mean, say, that you won't dwindle 10000 down to 500 before making it back, in which case the table min will be higher than you can even afford to bet and you're basically broke. Not ideal if you want to make sure you reach profit in your lifetime. So I don't think relating your bet size to what Kelly fraction you're betting is thbest way to gauge of ROR

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    Quote Originally Posted by Meistro123 View Post
    That is 7/10th Kelly.
    That was another question I had - what constitutes "full Kelly?" Is it 0.7 x Advantage x Bankroll, meaning that "half Kelly" is 0.35 x Advantage x Bankroll?

    And if full Kelly means 13.5% ROR, what ROR is associated with 1/2 Kelly?

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    Quote Originally Posted by Optimus Prime View Post
    That was another question I had - what constitutes "full Kelly?" Is it 0.7 x Advantage x Bankroll, meaning that "half Kelly" is 0.35 x Advantage x Bankroll?

    And if full Kelly means 13.5% ROR, what ROR is associated with 1/2 Kelly?
    Lots of confusion here. I assume you haven't read the ROR chapter in BJA3, which not only spells all of this out, but much, much more.

    First, ROR for betting pure Kelly is zero. The 13.5% ROR represents beginning with full Kelly bets and NEVER resizing them until either you go broke or win all the money in the world.

    The formula you're looking for is simple: if you don't resize, to calculate ROR for fractional Kelly, raise 0.135 to the power of the reciprocal of the Kelly fraction. So, for example, if half Kelly, then raise 0.135 to the second power (reciprocal of 1/2), and get ROR = 0.135^2 = 0.0182 = 1.82%.

    Clear?

    Don

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    Quote Originally Posted by DSchles View Post
    Lots of confusion here. I assume you haven't read the ROR chapter in BJA3, which not only spells all of this out, but much, much more.
    Just finally got my hands on a copy - I'm on my way.

    Quote Originally Posted by DSchles View Post
    First, ROR for betting pure Kelly is zero. The 13.5% ROR represents beginning with full Kelly bets and NEVER resizing them until either you go broke or win all the money in the world.
    Right - that part I knew.

    Quote Originally Posted by DSchles View Post
    The formula you're looking for is simple: if you don't resize, to calculate ROR for fractional Kelly, raise 0.135 to the power of the reciprocal of the Kelly fraction. So, for example, if half Kelly, then raise 0.135 to the second power (reciprocal of 1/2), and get ROR = 0.135^2 = 0.0182 = 1.82%.
    Clear?
    Thank you, Don. It's nearly clear - my only remaining question is this: when we refer to the "Kelly fraction" in this context, is that fraction our bet (as % of bankroll) divided by our advantage or do we take that number and multiply by 0.7?
    Last edited by Optimus Prime; 11-01-2018 at 08:59 PM.

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    Quote Originally Posted by Optimus Prime View Post
    That was another question I had - what constitutes "full Kelly?" Is it 0.7 x Advantage x Bankroll, meaning that "half Kelly" is 0.35 x Advantage x Bankroll?
    Yes

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    Quote Originally Posted by Optimus Prime View Post
    ...if I'm betting 1/2 Kelly, to me that means my bet is .5 * advantage * bankroll.
    Don't forget about the variance! (Or average squared result, as some prefer)

    0.5 * advantage / variance * bankroll

    -Sonny-

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    Quote Originally Posted by Sonny View Post
    Don't forget about the variance! (Or average squared result, as some prefer)

    0.5 * advantage / variance * bankroll

    -Sonny-
    You're misunderstanding. He accounted for the variance for full Kelly by multiplying by 0.7.

    Don

  10. #10


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    Quote Originally Posted by DSchles View Post
    You're misunderstanding. He accounted for the variance for full Kelly by multiplying by 0.7.

    Don
    Originally he said 0.5 * advantage * BR for 1/2 kelly. Someone corrected him and said full kelly would be 0.7 * advantage * BR, or 0.35 * advantage * BR for half kelly.

    Maybe you're misunderstanding!

    As I'm sure he's reading in the BJA now that you also have to include variance into the calculation, but it makes more sense (from a learning perspective) to say you have to include variance and not just say it's 0.7 or 0.35 times BR times advantage.



    Quote Originally Posted by Optimus Prime View Post
    Thank you, Don. It's nearly clear - my only remaining question is this: when we refer to the "Kelly fraction" in this context, is that fraction our bet (as % of bankroll) divided by our advantage or do we take that number and multiply by 0.7?
    Kelly fraction refers to what fraction of kelly you're betting.

    Alice might play full kelly, so she'd say "full kelly".

    Bob might play half (or 1/2) kelly, so he'd say "half kelly" or "1/2 kelly".

    Eve might play quarter (1/4) kelly, so she'd say "quarter kelly" or "1/4 kelly".

    It has nothing to do with what fraction of your bankroll you're betting at a time, because you'll bet different amounts based on the advantage. If you have a 0.5% advantage or a 2% advantage, you're going to be betting different amounts. Or perhaps you're playing a different game altogether where the variance and/or edge is much different. If you're playing half kelly, you might bet $1,000 with a $200k BR with an advantage a bit over 1%....but a 1% advantage on video poker (where the variance is considerably higher), you may be betting $25. Or if you're hole-carding (let's say 5% edge and similar variance to BJ), then your optimal bet may be $5,000. All of those would be "half kelly", but the amounts wagered are considerably different.
    "Everyone wants to be rich, but nobody wants to work for it." -Ryan Howard [The Office]

  11. #11


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    Quote Originally Posted by Optimus Prime View Post
    Is there a quick way to convert the Kelly fraction you're using for your betting into ROR without having to sim out the specifics? For example, if I'm betting 1/2 Kelly, to me that means my bet is .5 * advantage * bankroll. If I stick to that, with no betting maximum, what is my ROR? Or am I oversimplifying?

    ROR(%) = 100 * e^(-2/k), where e= 2.71828, k = kelly ratio.

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    Lots of good info here. I think I’ve got it. Thanks!

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