also, while it's definitely interesting to know what's mathematicly optimal, optimal BRM for almost anyone is going to be 'as agressive as you can be without going insane'. for me as a pro that's probably 60-100bi for the highest stake i play depending on my game selection

Thanks a lot jspazz! great thread!

I mean I know I can probably move up given my br but tbh I don't think psychologically I'd be able to play higher without the money/losses to affect me. Plus being on a downswing right now doesn't really help either so... yeah I'm going to have to keep grinding at the 20 level and try to make some decent heater soon... I hope

I have a case where I think this formula doesn't lead to maximal bankroll growth. Say there are only 3 stakes, $100, $200, and $400. Let's assume:

-At the $100, our ROI is 10%
-At the $200, our ROI is 1%
-The $400 is incredibly tough and we lack the talent to ever win there
-Our bankroll is $1 million

Won't this formula tell us that we can play $200 games when in fact we should be playing $100 games for maximal expected bankroll growth?

But surely the kelly criterion is used as a bankroll management system to help players move up to their regular level. that of which would yield them the most profit and they should be playing even with an infinate bankroll.

Once players start to hit their ceiling stakes for their current skill level it should not be so much about bankroll managment as you will quickly become over rolled. Then moving up becomes a product of skill and not bankroll.

This question will probably be meh for alot of people but I do not care.
Do you want to try to explain me, how they come to
E(G) = (1 + (O-1) * X)^p * (1 - X)^(1-p) - 1
in the first paper.
http://www.sbrforum.com/betting+arti...criterion.aspx


I do not fully understand how they come to this formula ...

Variance is the square of the standard deviation which is derived from this formula. fwiw it's easy to point out that the variance of a 2man is 1 buyin (obv you always go 1 BI up or 1 BI down), while it's 4 buyins for 4mans (the math is more complicated but easily doable using the formula). Thus you should use 1 BI as your SD in superturbos (B=1/ROI)

yes, that's true. I dunno how conservative you have to be to profit in MSNL but you should work on your mental game imo, esp. if that highest stake of yours is 4-6 times the stake where you play most of your hands

Assuming you can play X of each game in one hour, your hourly rate for $100s is $10*X while your hourly rate for $200s is $2*X, so altho we're way more than sufficiently rolled for both games, it doesn't change the fact that $100s give us a better hourly. However I'd still mix in $200s and the occasional $400 to work on your game and see if you can beat the learning curve. imo thankfully poker is not football and the degree of "talent" in poker is fairly low, so unless you're mentally ******ed or sth, the reason why you may not be playing $200s right now is something fixable: either you haven't put enough volume, or you haven't worked enough on your game, or you have a mental crutch of some kind etc.

imo your overrolled when you're playing too low stakes while you could play higher stakes and yield a higher profit. As I said to alex23, the most profitable level to play is not necessarily the highest, but considering grinding e.g. $22s in the long term is quite ridic as you will def attain a skill level at some point that allows you to have a higher hourly at $33s at the very least. After a while of not withdrawing too much you'll end up w a huge roll w ability to profitably play any game, but that doesn't mean the mechanics of BRM become wrong, they just can't aim us at a level anymore, so you can focus solely on hourly rate

AFAIK the expected growth is the expectancy of the increase of log(bankroll), which solves the problem of losing your roll (meaning you're banned from playing 4ever) and doubling it up (meaning you just move up a notch in the stakes) having the same absolute value. If you lose your whole roll, log(roll) becomes negative infinity. The formula in the article is a way of adapting EV to work w log(roll) instead of roll itself, so instead of using

EV(roll) = r(x1)*p(x1)+r(x2)*p(x2)+...+r(xn)*p(xn)

where x1...xn are outcomes, r(x) is the roll after outcome x and p(x) is the probability of outcome x; you just raise it up one level

EV(log(roll)) = r(x1)^p(x1)*r(x2)^p(x2)*...*r(xn)^p(xn)

OP - good posts!

however - atm i am sticking to the rule "playing in comfort zone".
this is steering my BI level much more atm than anything else.

i know i am by far overrolled, i also might give away money like this, but if i am uncomfortable to fall e.g. 10BIs at the 50s, even tho i know i am still good with my roll, even tho i am convinced that i can beat that level. i will play worse if i am not comfortable with it. so i play atm at the 22s and even tho i run quite bad i am much more comfortable and i am sure i make more or less my best game.

atm i said - this might change when time comes when i do not care about monetary goals and therefore will be comfortable much higher.

In one month i predict a thread titled "How I went busto, all because of Kelly!"

lol jk, This is a very interesting topic and I'm sure it will encourage people to become more successful players in the long run.

I read this thread a last week before kicking of at husngs again. Without reading this, i would probably be nitting over the $2.25s forever before moving up. I have instead just moved up to the $11.50s aggresively and am certainly not wasting any run good. If i hit a wall and have to move back to the $6.25s, hey at least i will still be ahead of where i would be had i stuck at the $2.25s.

So thankyou spamz for giving me the confidence to attempt an aggresive bankroll managemnet system. All successful husng player interviews and comments i have read have all had a a reoccuring theme, "i wish i moved up threw the micros quicker instead of dosing around for so long".

edit: just to throw in, i am planning to end the kelly brm method at the $11.50s as i am not brave enough to move up to the $22+1s until i have at least 20 buyins as i do feel that the psycological effects of the swings would become an issue for me personally.

I though 4 would be for 1/4 Kelly?

Just want to post this as i think it shows graphically the kelly system in action during a period of low variance (obv i ran really hot, just steady hot, not swingy). Graph displays $2.15 $6.25s and then $11.50s. At this point i would be taking a 1 buyin shot at the $23s with kelly. However i am now switching to a more conservative brm approach.

graphed by buyins.

[IMG] Uploaded with ImageShack.us[/IMG]

graphed by $.

[IMG] Uploaded with ImageShack.us[/IMG]

nice run

at which point can we treat our sample size as a credible variable for roi? i apologize if this was already addressed and i missed it.

http://archives1.twoplustwo.com/show...=2#Post7912125

I'm happy to hear ur success story, nice going quinn. I think starting half Kelly at 20s is good as at some point money will start to bother you and swings regularly taking 1/2 ur roll can drive u insane, esp. heads up

1ptbb=2bb For 1/4 Kelly you should use 8, as SD is expressed in ptbb and big bets are just a problem when u want to determine bankroll size in buyins

Yeah, I missed out on that topic. I don't want to bore you w college-level statistics, so here, this would be a good place to look: http://www.castrovalva.com/~la/win.htm

Put 1 as standard deviation for 2mans and 2 for 4mans, put your ROI in the winrate box (e.g. if it's 12%, write 0.12), and write the number of tourneys played in periods box. The red curves show the 2nd percentile and 98th percentile (i.e. your true ROI is about 95.5% likely to be within these two lines) of the ROI assuming various sample sizes. The black squared dots are the 2nd and 98th percentile of your true ROI at your exact sample size

i dont get it. lets say my roi is 10% =
B=10/1 which means i need 10buyins.

but if my roi is 9%=
B=9/1 i only need 9buyins???

i dont get the formula.what i am missing?

B = the percentage of your bankroll you should risk in each tournament.

thanks. that makes sense. thought B would mean buyin or something.

Great Post on BRM. Nothing new, but an exellent summary. Thanks for taking the time to do that!

shouldn't that be B=ROI/1 or did I miss something?

How many HUSNG are considered to be played at a certain buyin before a true ROI can be determined? I mean, is it necessary to recalculate the Kelly factor after every single tourney? Or is there a minimum number?

1327 tournaments and 2 chops.

Doing some poker writing, and I came up with a nice equation for the pros out there who don't want to risk under-bankrolling themselves. JSpazz mentioned playing professionally briefly, but he didn't write the equation.
-------

Bankrolling as a professional is difficult unless you’ve started paying yourself weekly and working scheduled hours. If you’ve got those two things under control, bankrolling is easy! Here’s the calculation for a quarter-Kelly bankrolling strategy:

r = ROI% (i.e. 12% = .12)
i = $ you pay yourself each week
g = Amount wagered every week (Buyin * # Of Games)
b = Total Bankroll
x = Target buy-in level

b=(4gx)/((gr)-i)

If you play 200 $100s each week with a 6% ROI and you pay yourself $1,000 per week…

b= (4*20000*100)/((20000*.06)-1000)
You need around $40,000 in your bankroll at all times, or you should move down. If your ROI was 12%, you would only need $5,700. If you never cashed out, you would only need $6,700.

sorry for not replying a lot, I had IRL stuff to do so not much ample time besides playing and hanging out here while waiting 4 the games

yes, that's true

For starting out, assume ur ROI is 5-10% and then you can re-evaluate after a couple hundred games. If it's superturbos, start out w 100-200 buyins so that stakes don't matter to you and re-eval after a couple thousand games

that's a good formula, altho imo withdrawing more than 1/2-2/3 of your projected earnings will really stunt your long-term growth and cause you to play unoptimally. E.g. withdrawing a fixed sum of $1000 per month, you can make a swingy living w a $40k roll playing $100s, but you could play $300s withdrawing the same money w less swings, and increasing your bankroll much faster

b=(4*60000*300)/((60000*.06)-1000)~27.6k

and for half a kelly? (being a bit lazy)

tbh when it comes to brm, am I the only one who likes being overrolled because then it makes you more comfortable to play your A game without worrying about the money?