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Originally Posted by
DSchles
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.
Originally Posted by
Optimus Prime
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]
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