vpFREE2 Forums

Kelly strategy simplified

#1

At each option point, under the Kelly strategy one would chose the option with highest CE, with approximate CE being EV-VAR/2Bankroll. This assumes you will be betting the optimal bet amount, which is approximately Bankroll x EV / VAR. Of course in the real world, that’s probably not a valid bet size, so you take the betsize that is lower, never higher. Now, if it turns out your betsize is substantially below the optimal, then that formula for approximate CE is probably no longer valid and instead you rank by maxEV or closer to maxEV than maxCE. I don’t know at what point that happens, 10% of Kelly optimal?, 1% of Kelly optimal? The safe bet of course is to stick with CE, it may be suboptimal but it won’t go over the line (average bankroll shrinkage) which maxEV might.

How this plays out for slots is first you determine the Kelly strategy for the game, ranking decisions by CE. This then gives you a net EV and VAR for the game using your Kelly strategy. Now you can approximate the Kelly optimal bet size, and you can play if that or a lower bet size is an option. Repeat this for each decision point. That’s GTO if your goal is to minimize the number of plays it takes to double your bankroll.

#2

There is NO such thing as “X% of Kelly”. People are always afraid of full Kelly. The whole point of Kelly is that ALSO optimizes the growth of the bankroll.

Otherwise, you’re just using Kelly for ROR and there’s plenty of good formulas for that already.

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On Thu, Sep 18, 2014 at 2:04 PM, nightoftheiguana2…@…com [vpFREE] <vpF…@…com> wrote:

At each option point, under the Kelly strategy one would chose the option with highest CE, with approximate CE being EV-VAR/2Bankroll. This assumes you will be betting the optimal bet amount, which is approximately Bankroll x EV / VAR. Of course in the real world, that’s probably not a valid bet size, so you take the betsize that is lower, never higher. Now, if it turns out your betsize is substantially below the optimal, then that formula for approximate CE is probably no longer valid and instead you rank by maxEV or closer to maxEV than maxCE. I don’t know at what point that happens, 10% of Kelly optimal?, 1% of Kelly optimal? The safe bet of course is to stick with CE, it may be suboptimal but it won’t go over the line (average bankroll shrinkage) which maxEV might.

How this plays out for slots is first you determine the Kelly strategy for the game, ranking decisions by CE. This then gives you a net EV and VAR for the game using your Kelly strategy. Now you can approximate the Kelly optimal bet size, and you can play if that or a lower bet size is an option. Repeat this for each decision point. That’s GTO if your goal is to minimize the number of plays it takes to double your bankroll.

#3

In my mind the greatest difference between the Kelly system and the ROR calculation is that the Kelly system tells you when to stop and drop down in denomination or find a lower risk gamble (approximately when your current bankroll x edge / variance is less than your current betsize). The ROR calculation assumes you’ll fire away to the very last cent. That assumption strikes me as gambling out of control. You could set the risk of ruin very low, say 0.1%, but then your bankroll growth is also very low. What’s an acceptable risk? Kelly has that answer, the ROR calculation does not.

#4

Again, that’s missing the forest for the trees. The greatest difference for Kelly is that it’s the optimal number to grow your bankroll. Mentioning ROR is for allegory, choose any other formula you want, it doesn’t matter. But using Kelly to keep you from going broke is like using a Ferrari to go to the grocery store. You could do that, but there’s better ways and a misuse of the Ferrari . . .

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On Sep 19, 2014, at 12:36 PM, nightoftheiguana2…@…com [vpFREE] <vpF…@…com> wrote:

In my mind the greatest difference between the Kelly system and the ROR calculation is that the Kelly system tells you when to stop and drop down in denomination or find a lower risk gamble (approximately when your current bankroll x edge / variance is less than your current betsize). The ROR calculation assumes you’ll fire away to the very last cent. That assumption strikes me as gambling out of control. You could set the risk of ruin very low, say 0.1%, but then your bankroll growth is also very low. What’s an acceptable risk? Kelly has that answer, the ROR calculation does not.

#5

funny.young.guy wrote: “Again, that’s missing the forest for the trees. The greatest difference for Kelly is that it’s the optimal number to grow your bankroll. Mentioning ROR is for allegory, choose any other formula you want, it doesn’t matter. But using Kelly to keep you from going broke is like using a Ferrari to go to the grocery store. You could do that, but there’s better ways and a misuse of the Ferrari . . .”

Seems like
a lot of misinformation here. ROR is a centerpiece of Kelly, not an “allegory”. And there is only one formula for ROR, not multiple formulas
as you imply. And a feature of Kelly is that there is zero chance of going broke. Seems like the only way to go to the grocery store, assuming you don’t want to take any chance of going broke and you want to minimize the number of hands it takes to double your bankroll. If you want to minimize risk, there is minROR strategy. But you still need Kelly to tell you when to stop, before you go broke. Far from being a Ferrari, Kelly is like the brake, sure you might make it to the grocery store without needing to brake, but that’s hardly the low risk way to travel. Kelly tells you the mathematical point to brake. The ROR formula asks you what risk you are willing to take that you needed to brake, assuming you will go ahead anyway, to your death if that’s what the fates allow.