#11




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What if I'm in a game where the Kelly Fraction is hard to define, but I know my risk of ruin based on my bets (and win rate and standard deviation)? Is there a formula that can derive the kelly fraction from that information? 
#12




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"Kelly Factor is an alternate method of specifying risk for those familiar with Kelly theory. A Kelly Factor of 1.0 equates to a risk of 13.5%. A factor of 0.5 means that you will be betting with double the bankroll required for a risk of 13.5%. In a perfect world, this would mean that yours bets would be half as much. But, this is not quite true because of bet simplification and the inability to bet fractions of a dollar. Some professionals play .33, .25 or even lower Kelly factors. These represent substantially less risk; and obviously less income."
__________________
"Chance favors the prepared mind." – Louis Pasteur 
#13




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log(bankroll+CE) = <log(bankroll+outcomestake)> where outcome is a random variable with certain probability and odds, and <...> is the average over this random variable. Is that correct ? 
#14




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#15




Thanks man. I didn't know the FAQ yet. But then I would rather name it "utility equivalent certainty" to make the origin more clearly.

#16




I Hate Risk
The probability of not losing 20% of bank with constant resizing kelly fractions:
kelly 20.0% 1/2 kelly 48.8% 1/3 kelly 67.2% 1/4 kelly 79.0% 1/5 kelly 86.6% 1/6 kelly 91.4% 1/8 kelly 96.4% One can come close to eliminating ror or risk of drawdown at which point CE=WR almost, we can't eliminate all variance. happy variance 
#17




Confusion over CE
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It is said that the ratio of CE to WR should be 0.5, when betting optimally. OTOH, if CE nearly equals WR, wouldn't that mean that the counter should only forgo the opportunity if somebody offers them their EV (or close to it) upfront? This would seem to suggest that CE approaching WR means that the opportunity is quite favorable, thus the counter requires more $$$ to passup the opportunity whereas if CE = 0.5 x EV he would require less money to pass up the opportunity. So to reiterate, is CE approaching EV a good thing or a bad thing? It would seem that one can make a case for either side. Many thanks to anybody that can clarify this point of confusion. MJ 
#18




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Say you are betting a very small Kelly Fraction, such that your RoR is miniscule. Therefore your CE is close to your Win Rate. This means that you are pretty much guaranteed that level of income (CE). Now, as your Kelly Fraction rises, your Win Rate increases but so does your RoR. And your CE is diminished due to the variance involved and the probability of losing a significant portion of the bankroll. So the question becomes, how much Certainty do you want in that income stream. Higher CE/WR ratio maximizes the certainty that you will make that money. Maximizing the WR by increasing the Kelly Fraction decreases the CE/WR ratio. I've always heard to maximize the CE as much as possible. You may not want it higher than .75 or .8, otherwise you may only be making peanuts. 
#19




wow
Well said paddywhack
I would add: Most pros & teams probably play from 1/4 to 1/8 Kelly. With small fractions of Kelly one does not have to resize bets on losses dramatically. Their long run is a lot shorter. Probably at/beyond 1/8 Kelly one resizes so little that the long run is basically that of a fixed bettor, but with 0% ror. It's hard to be conservative with small banks. Most APs fail due to variance, so eliminate it!
__________________
Keys to Counting Success: Mental toughness and discipline Mastery of your count Play quality games aggressively Play 1,000 hours Bet conservatively to last 1,000 hours May your A get painted 
#20




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CE = EV  [Var / (2 * Br * KF)] Quote:
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MJ 
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