CE/WR ratio

[blackjack avenger]

Lucky 13.53%

ok thanks bja, and with the above the errhh 'rate' of risk or i dunno maybe level of risk varies some way as well i guess?
i've never done a study of how that goes, but i believe the risk can go down as you whack away at full Kelly which i believe has that 'magic' number of circa 13.5% ror, sorta thing.
easy enough to see how it goes with some sims, i guess.

Don't forget the magic of 13.53% is with continuous or near so resizing. If you don't resize then 13.53% is just a fixed bet ror number like any other with no magic.:joker::whip:

 

[aslan]

Don't forget the magic of 13.53% is with continuous or near so resizing. If you don't resize then 13.53% is just a fixed bet ror number like any other with no magic.:joker::whip:

IOW, the magic's in the process, and the proof is in the pudding.

 

[sagefr0g]

Don't forget the magic of 13.53% is with continuous or near so resizing. If you don't resize then 13.53% is just a fixed bet ror number like any other with no magic.:joker::whip:

what's with that number 13.53% anyway?
i know i've asked about this before, darn it all and if it's been explained well i''ve forgotten how it is that we end up with 13.53% ror for full kelly optimal betting sort of stuff.:whip:
edit: errhh, i guess it has to do with a given sized bankroll, for some given game is gonna have some min bet and spread that is optimal for that bankroll & game & the 13.53% just happens to be a fact of life for kelly betting and optimal stuff???

 

[blackjack avenger]

Cool Kelly at the Casino

what's with that number 13.53% anyway?
i know i've asked about this before, darn it all and if it's been explained well i''ve forgotten how it is that we end up with 13.53% ror for full kelly optimal betting sort of stuff.:whip:
edit: errhh, i guess it has to do with a given sized bankroll, for some given game is gonna have some min bet and spread that is optimal for that bankroll & game & the 13.53% just happens to be a fact of life for kelly betting and optimal stuff???

Cool Kelly is at the casino. He is betting his bank using the Kelly criterion EV/Variance so he is resizing his bets after every round. Suddenly, he is told by the pit boss that he can no longer resize his bets, he must bet the same thing from now on. If Kelly continues to play he will now have a 13.53% chance of losing all.

13.53% fixed ror approx 1 in 7 chance of losing all
10% fixed ror 1 in 10 chance of losing all
20% fixed ror 1 in 5 chance of losing all
With fixed bets you ror is what it is:joker::whip:

Now, if you resize your bank at all it takes on more of the characteristics of a resizing bank vs fixed bank.:joker::whip:

 

[kewljason]

So if you are playing full kelly with a 13.53% RoR, it is really only that high if you don't resize and ride the same size all the way down to zero right? If you are willing to resize several times along the way, your RoR is in actuality much smaller right?

 

[blackjack avenger]

Kelly is as Kelly Does

So if you are playing full kelly with a 13.53% RoR, it is really only that high if you don't resize and ride the same size all the way down to zero right? If you are willing to resize several times along the way, your RoR is in actuality much smaller right?

Yes,
However:joker::whip:
it's probably not good to have any bet over 13.53% ror. As an example, if your bank is 50g Kelly and you lose your first bet you are suppose to lower your bets.
Because:joker::whip:
Betting 1.5Kelly and .5Kelly have the same growth rate with .5Kelly having much lower variance. Of course this is with continuous resizing.

Even this is probably not set in stone, a slight overbet to play a much better game is probably acceptable; but the exception, not the rule.:joker::whip:

So it's probably better to bet a lower fraction of Kelly so you have some resistence to variance before you have to lower bets due to negative variance.:joker::whip: What fraction of Kelly? Different people have different opinions on that. I guess one could ask themselves how much variance can I handle?:joker::whip:

 

[aslan]

Is this the :whip: & :joker: website?

 

[sagefr0g]

Cool Kelly is at the casino. He is betting his bank using the Kelly criterion EV/Variance so he is resizing his bets after every round. Suddenly, he is told by the pit boss that he can no longer resize his bets, he must bet the same thing from now on. If Kelly continues to play he will now have a 13.53% chance of losing all.

13.53% fixed ror approx 1 in 7 chance of losing all
10% fixed ror 1 in 10 chance of losing all
20% fixed ror 1 in 5 chance of losing all
With fixed bets you ror is what it is....

Now, if you resize your bank at all it takes on more of the characteristics of a resizing bank vs fixed bank.:joker::whip:

uhmm, ok, lets say Cool Kelly has ten grand bankroll. he sits down at the table and bets full kelly. he's got that magic 13..53% ror. by some miracle while in the process he pushes every hand (betting full kelly, so he ain't changed nothin ), but during the process the count goes sky high. (erhh i guess that could happen).
so now Cool Kelly say he makes a monster bet and ends up splitting to the max number of hands and doubling those. but of course he loses!:whip:
so but now he ain't got ten grand, he's got much less.
so now to have that magic 13.53% ror and to bet full kelly still, what's he gotta do? does he gotta maybe reduce his betting spread or maybe go about resizing his bets down or run another sim, :devil::whip:? errhh i mean in a perfect world with a perfect player like Cool Kelly.:whip:

 

[kewljason]

Yes,
However:joker::whip:
it's probably not good to have any bet over 13.53% ror. As an example, if your bank is 50g Kelly and you lose your first bet you are suppose to lower your bets.


So it's probably better to bet a lower fraction of Kelly so you have some resistence to variance before you have to lower bets due to negative variance.:joker::whip: What fraction of Kelly? Different people have different opinions on that. I guess one could ask themselves how much variance can I handle?:joker::whip:

Well thats exactly what I do. I am willing to resize if I were to lose a substantial portion of BR, say 25-33%, (which thankfully has yet to happen) but I don't want to resize very often, so I start with about 2% RoR. Since I would resize if need be, I figure this is really playing at practically a zero RoR. I know nothing is zero, but this is very small. I know this is a very conservative way of playing and I am often critized for betting no where near optimal, but with an unreplenishible BR, I just can't get comfortable with anything else.

 

[blackjack avenger]

13.53% Not Kelly

uhmm, ok, lets say Cool Kelly has ten grand bankroll. he sits down at the table and bets full kelly. he's got that magic 13..53% ror. by some miracle while in the process he pushes every hand (betting full kelly, so he ain't changed nothin ), but during the process the count goes sky high. (erhh i guess that could happen).
so now Cool Kelly say he makes a monster bet and ends up splitting to the max number of hands and doubling those. but of course he loses!:whip:
so but now he ain't got ten grand, he's got much less.
so now to have that magic 13.53% ror and to bet full kelly still, what's he gotta do? does he gotta maybe reduce his betting spread or maybe go about resizing his bets down or run another sim, :devil::whip:? errhh i mean in a perfect world with a perfect player like Cool Kelly.

If he is betting with a 13.53% fixed ror and loses that big hand his ror is now higher because he has less money. His bets are fixed so he is willing to go down with the ship.:joker::whip:

If he is betting Kelly resizing and loses that big hand he resizes his bets down to maintain Kelly betting.:joker::whip:

 

[blackjack avenger]

Knowing Ones ror

Well thats exactly what I do. I am willing to resize if I were to lose a substantial portion of BR, say 25-33%, (which thankfully has yet to happen) but I don't want to resize very often, so I start with about 2% RoR. Since I would resize if need be, I figure this is really playing at practically a zero RoR. I know nothing is zero, but this is very small. I know this is a very conservative way of playing and I am often critized for betting no where near optimal, but with an unreplenishible BR, I just can't get comfortable with anything else.

You can know your exact ror.
All you need to know is your ror at each bank resizing interval and then multiply the ror's together.
Example:
If you resize your bank at 4 intervals and losing an interval is a 36% probability then .36^4 = 1.67% ror. The more frequently you resize down on losses the lower your ror. Also, an important point if you don't resize down on losses you are taking a chance of an even larger drawdown.

One can also lower their ror over time by not resizing up aggressively on wins:joker::whip:

 

[kewljason]

You can know your exact ror.
All you need to know is your ror at each bank resizing interval and then multiply the ror's together.
Example:
If you resize your bank at 4 intervals and losing an interval is a 36% probability then .36^4 = 1.67% ror. The more frequently you resize down on losses the lower your ror. Also, an important point if you don't resize down on losses you are taking a chance of an even larger drawdown.

One can also lower their ror over time by not resizing up aggressively on wins:joker::whip:

I don't re-size up at all right now, but its not for reasons of keeping RoR lower. It's more about not wanting to bump my max bet up to a higher amount that will draw additional heat.

 

[KimLee]

CE ~ EV * Bet - [Var * Bet^2/ (2 * k * BR)]

This is a second-order approximation. For small bets, it is proportional to EV. The CE is approximately zero when Bet = 2*k*Bankroll*EV/Var.

For small edges, the optimal bet is approximately proportional to relative risk-aversion, i.e., fractional Kelly. But it is not exact. For example, full-Kelly would bet more than half the bankroll on a really good bet. But double-Kelly would probably not bet the whole bankroll! Sadly, the small edges attainable in the real world keep the approximations accurate.

If you keep the max bet small for cover then use a steep ramp.

 

[muppet]

Well thats exactly what I do. I am willing to resize if I were to lose a substantial portion of BR, say 25-33%, (which thankfully has yet to happen) but I don't want to resize very often, so I start with about 2% RoR. Since I would resize if need be, I figure this is really playing at practically a zero RoR. I know nothing is zero, but this is very small. I know this is a very conservative way of playing and I am often critized for betting no where near optimal, but with an unreplenishible BR, I just can't get comfortable with anything else.

if you resize your bets to adjust for wins/losses a la the kelly criterion, then your ror would be 0% if you could play your bank down to $0. in reality you won't and can't - because you'd probably stop playing before you got down that far, and also because you're limited by table mins + your spread.

so let's say your stopping point is if your bank gets down to 25k, then you should probably calculate full kelly betting based on (your br minus 25k). and that would truly give you 0% ror (unless you get mugged or something )

 

[Jack_Black]

that would truly give you 0% ror (unless you get mugged or something )

LOL!!!!:laugh:

Oh man, that was funny after reading a good thread. But seriously now, this thread is very interesting, yet does anyone actually use full kelly? Is it even practical? I can't calculate kelly after every bet placed. I do use .5 kelly for fixed BR. If anyone uses variable BR kelly, can you tell me how?

 

[SleightOfHand]

My view on Kelly and CE

I haven't read all the posts, but here's my general view on the topic

An old post on SCORE vs CE
http://www.blackjackinfo.com/bb/showthread.php?t=17256

As for kelly betting, as stated above, betting true kelly is impossible due to table limits, the inability to bet $1.2874, the difficulty to calculate your constantly changing bankroll, the fact that kelly does not have a defined spread, etc. CVCX automatically calculates reasonable "optimal" bets for a given spread, bankroll, etc. so I typically will use something very similar to the suggested spread. However, when I start spreading closer to 1:15/20, I disagree with the recommendation, as the max bet according to CVCX is geared towards being placed towards reasonable levels, which is not recommended by kelly.

Although good rules of thumb, I do not follow the 1% of BR max bet rule or the place max bet at 2.5% advantage rule. When placing my max bet when playing with larger spreads (1:30+), I will usually place it on a higher count than usual. It may not be very frequent, but from what I have seen in CVCX, gives a much stronger game. Its not about placing max bets, its about placing optimal ones. However, remember that risk is most important above all (I play with 1% RoR).

Kelly dictates that the betting must be resized on every single bet. Obviously this is not reasonable for real play, but I do my best to resize as often as possible. I bring a laptop when I can to trips lasting longer than 1 day and I will resize (on BR growth or losses) multiple times within the same day if I can. Kelly is about maximizing the logarithmic growth of your bankroll and although impossible to do perfectly, I try to get it as close as possible to make it as close to optimal as possible.

 

[sagefr0g]

.... Kelly is about maximizing the logarithmic growth of your bankroll .......

from: http://www.bjmath.com/bjmath/kelly/kellyfaq.htm (Archive copy)
The Kelly criterion dictates that you should try to maximize the expected logarithm of your total bankroll rather than trying to maximize the expected bankroll itself. In other words, you should try to maximize the exponential rate of bankroll growth.

http://www.knewance.com/latest/linear-v-polynomial-v-exponential-v-logarithmic-growth.html (Archive copy)

sorry magic won, not try to be nit picky here, lol.
errh, just trying to figure here..... like the kelly faq the words above seem to indicate that:
maximizing the expected logarithm of total bankroll is equivalent to maximizing exponential rate of bankroll growth.
no?
i guess what i'm saying is that exponential rate of bankroll growth is different than logarithmic growth of bankroll, no?
or am i just confused and forgetting how these terminologies go?

 

[assume_R]

http://www.knewance.com/latest/linear-v-polynomial-v-exponential-v-logarithmic-growth.html (Archive copy)

sorry magic won, not try to be nit picky here, lol.
errh, just trying to figure here..... like the kelly faq the words above seem to indicate that:
maximizing the expected logarithm of total bankroll is equivalent to maximizing exponential rate of bankroll growth.
no?
i guess what i'm saying is that exponential rate of bankroll growth is different than logarithmic growth of bankroll, no?
or am i just confused and forgetting how these terminologies go?

Take a look at this thread, especially the followups: http://www.bjmath.com/bjmath/loggrow/1225.htm (Archive copy)

as they will explain most of your questions.

Also (Dead link: http://www.bjmath.com/faq/utility/faqmanager.cgi?file=kelly&toc=faq) has a lot of information, including: "The expected time to reach M dollars [for Kelly betting] will be lower than for any other proportional betting strategy for sufficiently large M."

Yes, you maximize the EV of the log of your bankroll. The point is, this leads to the optimal long run growth rate, because it takes into account variance. If you maximized the EV of the exp of your bankroll you'd go broke almost immediately. So to increase your total bankroll, you optimize the EV of the log of your bankroll.

Hope that helps a bit.

 

[sagefr0g]

Take a look at this thread, especially the followups: http://www.bjmath.com/bjmath/loggrow/1225.htm (Archive copy)

as they will explain most of your questions.

Also (Dead link: http://www.bjmath.com/faq/utility/faqmanager.cgi?file=kelly&toc=faq) has a lot of information, including: "The expected time to reach M dollars [for Kelly betting] will be lower than for any other proportional betting strategy for sufficiently large M."

Yes, you maximize the EV of the log of your bankroll. The point is, this leads to the optimal long run growth rate, because it takes into account variance. If you maximized the EV of the exp of your bankroll you'd go broke almost immediately. So to increase your total bankroll, you optimize the EV of the log of your bankroll.

Hope that helps a bit.

great pointers assumer. probably i'll never get the math, lol. but i hope to read over that stuff and i think in there is an original kelly paper by the bell labs guy. i tried to read it once, one of my usual rush job sorta things, lol, but anyway, interesting stuff.
as i recall, sort of these guys were working with the problems of noisy phone lines and trying maybe to get good information across them, sorta thing i think. somehow they come up with this idea of gambling, risk and expectation out of that, is how i sorta remember it.

 

[k_c]

great pointers assumer. probably i'll never get the math, lol. but i hope to read over that stuff and i think in there is an original kelly paper by the bell labs guy. i tried to read it once, one of my usual rush job sorta things, lol, but anyway, interesting stuff.
as i recall, sort of these guys were working with the problems of noisy phone lines and trying maybe to get good information across them, sorta thing i think. somehow they come up with this idea of gambling, risk and expectation out of that, is how i sorta remember it.

This link is to a really informative article about the consequences of betting an advantage according to the magnitude of advantage and current bankroll (i.e Kelly fraction) as opposed to say simply flat betting advantage.

To me, among other things, the article seems to show:
- flat betting an advantage tends to outperform fractional betting in the shorter run but not in the longer run. Probably this is because a flat bettor's average rate of return is initially greater than a fractional bettor's but a fractional bettor's profit is compounded like in the case of compound interest whereas a flat bettor's profit is fixed.

Anyway the article touches upon a lot of points relative to bet sizing and is more understandable than other things I've seen. I've also added a link to the article on my website.