Kelly questions

**BenzBentley** · 03-04-2023, 06:01 AM

1…Where can I find the math analysis which led to the Kelly Criterion?
2…Resizing bets…what are the collateral effects at 10%, 20%, 30% resizing, other than increasing time spent to reach a given goal…and of course the ROR will be zero ??

**DSchles** · 03-04-2023, 09:48 AM

https://www.eecs.harvard.edu/cs286r/...terion2007.pdf

Don

P.S. If you Google "Kelly Criterion explained for blackjack," you will find dozens of articles.

**BenzBentley** · 03-09-2023, 05:15 AM

Thank you very much, Don S. Will my question re. resizing also be covered by those references you mention ?

**DSchles** · 03-09-2023, 07:47 AM

Not having read all of the papers all the way through, I'm afraid you'll have to do some research into that. But pp. 114-15 in BJA3 would be a good place to start. There's also a general formula for ROR, not just for doubling before halving, but for any fraction. That formula, along with my methodology in BJA3, ought to be able to answer your second question.

BTW, for that second question, you have to make sure you really understand what you're asking. For example, suppose you say you're going to wait till you lose 30% of your bank before resizing. Then what? What's the plan after that? Will there be future resizings, always after losing 30% of the current bank? Or, will you change the percentage? Or will you not ever resize again after the first resizing at 30% loss? Have you already answered these questions in your mind?

Don

**BenzBentley** · 03-09-2023, 10:01 AM

To clarify my methodology re. resizing...

I resize whenever the bankroll fluctuates.
My bet size will always be calculated on the basis of the resized bankroll...ad infinitum

Thanks, Don, for your help. I will try to use your referenced pages in BJA3 to ensure that I am optimizing the percent fluctuation at which I resize my betting.

**DSchles** · 03-09-2023, 05:12 PM

Originally Posted by BenzBentley

I resize whenever the bankroll fluctuates.

It isn't possible to play that way. You can't make the fractional bets with any kind of practical scheme that would be playable in a casino.

Originally Posted by BenzBentley

My bet size will always be calculated on the basis of the resized bankroll...ad infinitum

The point being??

Don

**BenzBentley** · 03-10-2023, 09:29 AM

Yes, of course I round off the bets.

The point being, I don't ever want to lose the entire bankroll. I am content to keep playing with my current bankroll.

**G Man** · 03-10-2023, 12:53 PM

But you understand than the goal is to take money from your bankroll at some point.... When ?

**2Bornot2B** · 03-10-2023, 03:39 PM

Yes. I follow a plan similar to your own plan about creaming off...quote...

"Here's what I'm doing.I start playing with a bankroll that has 0.25% RoR or if you like 1/3 Kelly.I play till I have a 25% bankroll growth then I take the cream off and restart.Since I use a "stop point" with no time constraint, using the double barrier formula brings my effective RoR down to 0.21%That also means my chance of succes is 99.79%To cover my entire bankroll, I need to reach that goal 4 times. The rate of succes is then 99.16% making the RoR 0.84%Playing instead to the "usual" double the starting bankroll would have a RoR of 0.28% and a rate of succes of 99.72%The difference between 0.84% and 0.28% is 0.56%, which is the cost in RoR to "cream" my bankroll. The smaller your starting RoR and the easier it is to take the cream at different points. With a large bankroll and a very small RoR (say 1/5 or 1/10 Kelly) taking cream every 10% increase cost almost nothing."

**Trixar** · 03-10-2023, 05:42 PM

Originally Posted by 2Bornot2B

Yes. I follow a plan similar to your own plan about creaming off...quote...

"Here's what I'm doing.I start playing with a bankroll that has 0.25% RoR or if you like 1/3 Kelly.I play till I have a 25% bankroll growth then I take the cream off and restart.Since I use a "stop point" with no time constraint, using the double barrier formula brings my effective RoR down to 0.21%That also means my chance of succes is 99.79%To cover my entire bankroll, I need to reach that goal 4 times. The rate of succes is then 99.16% making the RoR 0.84%Playing instead to the "usual" double the starting bankroll would have a RoR of 0.28% and a rate of succes of 99.72%The difference between 0.84% and 0.28% is 0.56%, which is the cost in RoR to "cream" my bankroll. The smaller your starting RoR and the easier it is to take the cream at different points. With a large bankroll and a very small RoR (say 1/5 or 1/10 Kelly) taking cream every 10% increase cost almost nothing."

I am not sure how to feel about this post. On one hand, it has educated me, but with the other hand, something feels weird about it.