Kelly betting

[sagefr0g]

Originally Posted by ThodorisK
In the real world it is not necessary to follow any betting system. Even if you greatly overbet kelly and lose your bankroll, you will have another bankroll in the future, and if you overbet again, you will have another bankroll in the future, and so on. Evetually you are bound to make a profit from all these trials, which will be close to the EV=(money wagered)(edge), unless you are the most unlucky person on earth. And if you want to win 1,000,000$ with a starting bankroll of 1,000$ by betting kelly, then you will die before that unless you are the most lucky person on earth.

Kelly does not maximize the growth of the bankroll. Saying this is like saying it maximizes EV. It maximises EV only if you have exactly the average luck. Overbetting kelly has the same EV as betting kelly if the money wagered is the same. EV is always (money wagered)(edge). The only difference is that by overbetting you win too much if you have a rare good luck, and you will not win that much if you do not overbet. This counterbalances (and explains) the negative EV that betting more than 2 times kelly gives when you have the average luck. If this was not the case, one could beat roulette by using a betting system that equals forcing the casino to bet more than 2 times kelly.

See the kelly formula I gave you in my previous posts in this thread, to understand what I mean.

Hm, however, as the number of played hands tends to infinity, the luck you will have will tend to the average luck. And if you have the average luck then there is a negative EV if you bet more than 2 times kelly. This is a paradox. Can roulette be beaten? LOL.

There are formulas and thoughts expanding kelly when considering taking money out of the bankroll over time or adding to the bankroll over time.

Even in the short term, optimal means optimal.:joker::whip: To say Kelly continuous resizing is the best in the long term but not the short term, or several short terms over time is incorrect. Our play is continuous, sessions are artificial breaks in continuous play.

The reason betting over double kelly is negative EV is because the bankroll drop when losing cannot be made up by wins. Go play some practice positive hands of bj where you bet resized 25% of bank on each hand, you will see how you can have a positive edge yet the bankroll spirals down.

I put it to you, what is the style of betting that is superior to Kelly continuous resizing?

Did you agree that given average luck Kelly is superior? Well over time your luck would converge to average and Kelly would prove optimal.

thanks guys these two post's have been enshrined in the voodoo/luck thread!
http://www.blackjackinfo.com/bb/showpost.php?p=100709&postcount=112::joker::whip:

now i gotta go look up that formula, might play some roulette today :joker::whip:

one question does that betting 2 times Kelly mean you gotta have a really bankroll, not an imaginary one.

 

[Sonny]

I suspect you may be intentionally talking in circles now.

It's making me a little dizzy too. :vomit:

-Sonny-

 

[sagefr0g]

Kelly = 0% ror
...

i'd agree with this if that's what infinetesimals mean in calculus.
but i'm not sure what infinetesimal in calculus means. :joker::whip:

 

[sagefr0g]

i'd agree with this if that's what infinetesimals mean in calculus.
but i'm not sure what infinetesimal in calculus means. :joker::whip:

oops i forgot you divide by infinetesimals in calculus so they can't be zero.

 

[ThodorisK]

Well, you cannot really force casinos to overbet more than 2 times kelly their edge at roulette, because there is a maximum and a minimum bet. Also, it would mean that the more you lose, the more you bet, and you do not have an infinite bankroll.

 

[squeeks]

I thought that I understood kelly betting after the first couple of pages. But I finally toke the time to read through the rest of this thread, and I got pretty confused. So, could someone give me an example. Let's say you had a 10k bankroll, then what would be the kelly spread for that?

 

[EasyRhino]

I thought that I understood kelly betting after the first couple of pages. But I finally toke the time to read through the rest of this thread, and I got pretty confused. So, could someone give me an example. Let's say you had a 10k bankroll, then what would be the kelly spread for that?

assume the variance for BJ is 1.2

On hands where you have a 1% advantage, bet $83
On hands where you have a 2% advantage, bet $167
On hands where you have a 0% advantage, bet $0

 

[rukus]

assume the variance for BJ is 1.2

On hands where you have a 1% advantage, bet $83
On hands where you have a 2% advantage, bet $167
On hands where you have a 0% advantage, bet $0

but what about the next hand after you win or lose, what do you do bet then? :devil::grin::joker:

 

[sagefr0g]

but what about the next hand after you win or lose, what do you do bet then? :devil::grin::joker:

wouldn't that be where the vengful one would raise or lower his unit accordingly in a ideal world?

 

[blackjack avenger]

Very Convenient Resizing

assume the variance for BJ is 1.2

On hands where you have a 1% advantage, bet $83
On hands where you have a 2% advantage, bet $167
On hands where you have a 0% advantage, bet $0

Let's build on this:
First let's cut the bets to more convenient numbers, also to account for human error:
tc 1 $75
tc 2 $ 150

Now if you lose your a third of your bankroll you cut your bets:
tc 1 $50
tc 2 $100

If you lose half of your remaining bank you cut your bets again:
tc 1 $25
tc 2 $50

On the positve side you can bet more as you win or build units to lower ror.

This is simple real world resizing. :joker::whip:

Start with a lower fraction of kelly, and you can bet so you never overbet your bankroll.