Bankroll Management (Long)

Status
Not open for further replies.
Jagsti

Jagsti

I'm sweet enough!
Silver Level
Joined
Feb 18, 2007
Total posts
5,478
Chips
0
Well to celebrate my 1000th post here on CC I've decided to post my feelings on BRM. I want to give something back to the community and hope that newcomers to CC, and to poker, can take something from this post. It's the 1st time I've done this type of thing, so hopefully you'll find it ok.


Bankroll Management

This is probably the, most important aspect of a poker player’s arsenal.

Seriously, having solid bankroll management (BRM) skills will provide you with a solid foundation to build your poker experience. Why is it so important? Well it allows you to plan your way through the various levels/limits, it provides you with a strategic approach to avoid risk of ruin, and just as importantly, it provides us with the ability to deal with the psychological effects of variance.

To build our BRM strategy you need to have an understanding of:

Variance

Standard Deviation

Kelly Criterion

Risk of Ruin

Where you are in your poker experience is going to have a big affect on your BRM. Are you an experienced player, with an average winrate but poor BRM? Or are you a new guy who’s made several deposits to poker sites, but has yet to develop the skills, knowledge or winrate/roi to make it count. So let’s look at the list above.

Variance and Standard Deviation

It’s very easy, as a new player to poker, to get carried away with your winrate/roi and think that poker is simple. You get AA, shove all your money in as an 80/20 favourite and win the pot, the game or whatever. You win session after session, game after game, and then the unthinkable happens. You go on a huge downswing. Buy in’s are being dropped left, right and centre. You’re out of the money in 15 SNG’s. The result is a decimated bankroll, or more likely Busto, and cries of ‘online poker is rigged’. Seriously, to any new player who reads this, you would not believe how many posts are started by newbs, in this manner. This is simply down to the fact of poor BRM and ignorance of variance.

There are many factors that affect the variance you encounter. Your style of play, i.e. whether you’re an aggressive or passive player, whether you play loose or play tight, the games you play in (NL, Limit, MTT’s, cash etc), your winrate/roi, and your ability to control tilt.

So what is variance? There are many definitions of variance available to us, but the one that I can associate with the best, is from Mike Caro’s site. Simply put variance can be expressed as ‘a measure of the spread of a statistical distribution about its mean or centre’.​
What about standard deviation? Wiki quotes ‘standard deviation remains the most common measure of statistical dispersion, measuring how widely spread the values in a data set are’.

The 2 terms are fairly similar to the un-educated in statistics, i.e. me! But in poker terms, generally speaking, variance is usually used to describe the distribution of your results over a session, and the swings you may encounter in a negative or positive direction. SD can be used as a way of measuring this.

If you’re really into the math behind this, then its way beyond my capabilities, so I suggest you wiki the 2 terms for a thorough understanding.

Kelly Criterion, Risk of Ruin and Psychology

Another useful tool to aid us in BRM decisions is Kelly Criterion. Now I’m not a math specialist so using the formulas in variance, SD and Kelly Criterion can be really off putting, so I’ll try to provide explanations in its simplest form. For more detailed descriptions and the mathematical formulae they relate to, I suggest search on Wiki.

Kelly Criterion

This can be defined as ‘a formula used to maximise the long term growth rate of repeated plays of a given gamble that has positive expected value. The formula specifies the percentage of the current bankroll to be bet at each iteration of the game. The Kelly system maximizes the growth rate in the long run, and therefore also minimizes the risk of ruin, but that risk is not zero. Using the Kelly system cannot result in a bankroll that is identically $0, but the value of the bankroll can approach arbitrarily close to $0, and so a finite probability of ruin does exist.’

Risk of Ruin

The risk of ruin is the chance that SD will destroy your bankroll before you have a chance to win at the levels you expect.

As poker players, our worst case scenario is going broke. Good BRM will make this situation very unlikely. However, this will also be affected by our poker outlook, our long term objectives and our own personalities. For example, if you have a high risk approach to gambling, then very likely you will have very aggressive BRM. You want to get $ as quickly as possible even at the high risk of going broke. This is not something I would advise, but I’m not knocking that approach as it may work for you. However, your RoR is extremely high. For most players, strict adherence to BRM will build up you bankroll at a steady rate. Only you can decide your feelings on RoR.

Psychology

Another aspect of BRM is psychology. How do you cope when things don’t go well for you? Are you a risk taker? Do you have a patient personality? These things can affect your stance on how big of bankroll you need at the level you wish to play at, or indeed what level you should be playing at.

The one thing that causes the greatest concern amongst poker players is dealing with a downswing or prolonged break even stretches. If you’re reading this as a newcomer to poker, you really need to have a grasp of numbers involved with poker. Poker is all about the long run, were luck will even itself out and variance will be negligible. So what is the long run? Well it’s certainly not 1000 cash game hands or 100 SNG’s. This year I have played over 300k hands of poker and I still have fluctuating winrates. You see it’s not uncommon for a cash game player to have 10 or even 20 buy in downswings, or for a SNG player to not cash in 20+ games. I have seen cash game players have 50k hand break even stretches. How do you think you can cope with that? Well let me put it this way, if your bankroll isn’t big enough, or the above puts you on tilt because you fail to look at the bigger picture, then your BRM will suffer as a consequence.

Bankroll Required

Now that we’re a little familiar with the above terms, we’re now better placed to draw some conclusions regarding our bankroll. Now I’ve searched the internet for some simple equations to give us a reasonable calculation of bankroll requirements, so hopefully you’ll find it useful.

Bankroll = -(SD^2/2*winrate)*ln(RoR)

So for example you’re playing 50nl with a winrate of 4PTBB/100 and you have an SD of 33BB/100. Your RoR is 2%.​
So: -(33^2/(2*4))*ln(0.02)​
= -136.125*-3.91​
=532.25

So Bankroll required is 532BB (big bets), which is only like 11 buy ins. I personally think this is a little too risky, but I’m a BRM nit, plus I multi table lots so I have to have a bigger roll to cover the amount of tables I play which is way more than 10. But if you use it in conjunction with the move up/down advice below then it may work for you.

It’s meant to give an indication of the math behind calculating a desired bankroll for a given risk factor. Whether you use it or not is up to you. There are different variants of this available, I personally have some set figures in my head that I adhere to, which have been developed through experience.

Move Up/Down

Moving up or down must be used in conjunction with the above bankroll requirements, for a given level, for the system to be successful. You also have to consider other factors such as confidence levels, knowledge of a given level and whether you’re making a full move to that level or taking shots. So in our example above, we need at least 11 buy ins at 100nl before we can move up.

Likewise if we lose 5 buy ins at 50nl then it’s time to move down to 25nl, so we have the 10-11 full buy in’s available at that particular level. If you can adhere to this religiously, then it should be difficult to go busto, especially if you start with a stricter RoR, say like 1-2% maybe. When moving up make sure you have a relevant sample before doing so and your confidence level is high. Irexes article demonstrates this really nicely so look at the link below.​

Conclusion

The stuff I’ve mentioned above is to actually get you thinking more actively about your BRM. It’s mainly targeted at new players, but I’m sure there’s content there for more experienced players to look. FWIW, because I’ve experienced some vicious downswings, I have a very nitty approach to BRM. I try to keep it fairly simple and I only move up if I have 50 BI’s at that level. I’ll move down if I go below 40BI’s. It works for me and that’s the point of this. When I see people giving advice, and I have done this myself, we usually say oh yes 20-30 BI’s should be enough when we don’t even know anything about them. Everyone’s different, so only you know the real answer to how many BI’s you require. If your unsure, or you think the above formula doesn't give you the desired results, then be a little more cautious in your approach and give yourself more scope. My theory is the more buy ins you have the less impact a downswing has on your emotional state.

I hope you find this post useful. GL all.

 
bob_tiger

bob_tiger

Legend
Silver Level
Joined
Jul 8, 2007
Total posts
2,735
Chips
0
I'm a bit busy in tourneys but as soon as im done i will read, looks like good material tbh
 
c9h13no3

c9h13no3

Is drawing with AK
Silver Level
Joined
Jan 2, 2007
Total posts
8,819
Chips
0
I think most winning regulars are nits with their bankrolls. 20 buy-ins is sorta considered the minimum, but most solid players I know have far more than that for the limit they play at.
 
bob_tiger

bob_tiger

Legend
Silver Level
Joined
Jul 8, 2007
Total posts
2,735
Chips
0
just got done reading while i was waiting for my hu match, yea brm is great for beginners but I'm personally not very strict on mine, I usually like to play with 50% of my profit a lot so lets say i win like 200$ i willl play something little out of my roll because i made profit and try to risk minimum of it possible.
 
zachvac

zachvac

Legend
Silver Level
Joined
Sep 14, 2007
Total posts
7,832
Chips
0
just got done reading while i was waiting for my hu match, yea brm is great for beginners but I'm personally not very strict on mine, I usually like to play with 50% of my profit a lot so lets say i win like 200$ i willl play something little out of my roll because i made profit and try to risk minimum of it possible.

Disagree entirely, it's basically the opposite imo. As a beginner only playing small limits, BRM isn't that important, but only because what's online isn't your true bankroll. If you deposit $5 online, you probably have several more times you could deposit $5 and feel comfortable. Not so when your bankroll gets up to a few thousand dollars.

Also note that taking shots (sort of what you're talking about) and consistently playing a level for long-term winnings are completely different as well. Shots are usually marginally -ev but can result in a big win. In general, the majority of your play should be within BRM and playing for long-term results.
 
bob_tiger

bob_tiger

Legend
Silver Level
Joined
Jul 8, 2007
Total posts
2,735
Chips
0
Disagree entirely, it's basically the opposite imo. As a beginner only playing small limits, BRM isn't that important, but only because what's online isn't your true bankroll. If you deposit $5 online, you probably have several more times you could deposit $5 and feel comfortable. Not so when your bankroll gets up to a few thousand dollars.

Also note that taking shots (sort of what you're talking about) and consistently playing a level for long-term winnings are completely different as well. Shots are usually marginally -ev but can result in a big win. In general, the majority of your play should be within BRM and playing for long-term results.

Ok I think I worded it wrong, what I meant is I follow brm and let's say if I win like 300$ and there is a 75$ omaha h/l tourney that I want to play, I will take a shot and play it. A) because even if I lose the tourney I'm happy with my profit for the day. B) If I do good in the tourney I will have a bigger profit for the day so I'm happy either way. Like you said I take occasional shots at bigger tourneys and I also like to play satelites to the bigger tourneys to save my $.
And I also agree on the long-term results thing, because mainly I'm a mid-stakes player, this is the level I constantly play, I know I'm not a high stakes level player but like mentioned before I take shots to tourneys through sattys.
 
B

bw07507

Legend
Silver Level
Joined
Jan 8, 2007
Total posts
2,219
Chips
0
Nice article Jagsti

I have never really been good at BRM and constantly play outside my roll. With my recent huge downswing, u'd think I might change and I thought I did for awhile, but I just don't have the patience to grind up to 50 BIs at the next level b4 I move up. Im currently 10-12 tabling 25NL with a 500 dollar BR (and i started with 325). I have been playing 25NL for so long that I couldn't stand playing at 10NL and basically just played 4k hands there to get a grip on FR which I haven't played in awhile.

I always think to myself that I should be practicing good BRM, but I never do. I told myself now that I wont move up to 50NL til I have $1500, but I know in the back of my mind I'll be itching to move up as soon as I hit the $1000 mark. I wish I could be as disciplined as some of you :(
 
Jagsti

Jagsti

I'm sweet enough!
Silver Level
Joined
Feb 18, 2007
Total posts
5,478
Chips
0
BW - fwiw I was playing 50nl with $1k BR, I just wasn't playing 20 tables. I was more like 8-10 tabling. Now I'm upto 100nl,, and like you experienced some vicious variance, then for me, and my mind set I like the comfort zone of 40-50 buy ins. Like I say it's a personal thing, I'm just trying to get ppl to think about managing there BR better.
 
Irexes

Irexes

Legend
Silver Level
Joined
Oct 10, 2006
Total posts
7,016
Chips
0
Great, well written stuff Jagsti :)

Bankroll Management


This is probably the, most important aspect of a poker player’s arsenal.






Absolutely agree, without good brm the game turns from one of skill to gambling.

One thing, I'm a bit hazy on how you calculate the Standard deviation in your example?


And thanks for the ref to my post :)
 
c9h13no3

c9h13no3

Is drawing with AK
Silver Level
Joined
Jan 2, 2007
Total posts
8,819
Chips
0
for me, and my mind set I like the comfort zone of 40-50 buy ins.
I'm in this camp. After going on a like 20 buy-in downswing at 2$ NL, I highly approve of having a giant roll for your limit. Especially if you're playing 6-max, or a style of poker that leads to more variance.

I'm currently playing 10$ NL with ~60 buyins.
 
Jagsti

Jagsti

I'm sweet enough!
Silver Level
Joined
Feb 18, 2007
Total posts
5,478
Chips
0

One thing, I'm a bit hazy on how you calculate the Standard deviation in your example?

And thanks for the ref to my post :)

OK, well SD can be calculated manually, but I'd rather scratch my eyes out with a fork. So thankfully, PT2 and HEM does this for us. If your using the above formula, the as long as you use the same units for SD and winrate, then it doesn't matter you can just substitute them in.

So for example if you use your winrate of $/hr for a given level, then as long as you use the SD in $/hr as well, then your result will be expressed in dollars.
 
C

cparker

Enthusiast
Silver Level
Joined
Mar 30, 2008
Total posts
60
Chips
0
does pt3 do this too? i couldn't find where the sd was.
 
Jagsti

Jagsti

I'm sweet enough!
Silver Level
Joined
Feb 18, 2007
Total posts
5,478
Chips
0
CP - I don't think SD has been added yet to PT3, but by all acounts it will be soon.
 
ChuckTs

ChuckTs

Legend
Silver Level
Joined
Feb 2, 2005
Total posts
13,642
Chips
0
sick stuff, can't believe I missed this. Gonna read up on it tonight, brb.
 
zachvac

zachvac

Legend
Silver Level
Joined
Sep 14, 2007
Total posts
7,832
Chips
0
OK, well SD can be calculated manually, but I'd rather scratch my eyes out with a fork. So thankfully, PT2 and HEM does this for us. If your using the above formula, the as long as you use the same units for SD and winrate, then it doesn't matter you can just substitute them in.

So for example if you use your winrate of $/hr for a given level, then as long as you use the SD in $/hr as well, then your result will be expressed in dollars.


In HEM, what units is "std dev bb" in? I would expect something like bb/100 hands or bb/something. It's not standard deviation of bb/entire sample is it? Because if it is something's pretty wrong, one more buy-in up or down would put me out 34% (think that's what it is, +-1 std dev encompasses 68% I believe). And this is after 50k hands. Note that as sample size goes up, standard deviation should also go up, but at a square root relationship, so that standard deviation should double every time # of hands is multiplied by 4.

So yeah, do you know what units "std dev bb" is in?
 
N

nick1usmc

Rock Star
Silver Level
Joined
Jul 28, 2007
Total posts
187
Chips
0
As afairly new player, this article helped me more than most others regarding BRM, as it was put in simpler terms. Thanks!!
 
Jagsti

Jagsti

I'm sweet enough!
Silver Level
Joined
Feb 18, 2007
Total posts
5,478
Chips
0
In HEM, what units is "std dev bb" in? I would expect something like bb/100 hands or bb/something. It's not standard deviation of bb/entire sample is it? Because if it is something's pretty wrong, one more buy-in up or down would put me out 34% (think that's what it is, +-1 std dev encompasses 68% I believe). And this is after 50k hands. Note that as sample size goes up, standard deviation should also go up, but at a square root relationship, so that standard deviation should double every time # of hands is multiplied by 4.

So yeah, do you know what units "std dev bb" is in?

Zach, as far as I'm aware in HEM, SD can be added in the reports section as either bb/100 or BB/100 hands.
 
Boeggs

Boeggs

Rock Star
Silver Level
Joined
Sep 15, 2007
Total posts
174
Chips
0
Great Post. I agree with the 50 buy-ins although once in awhile i will play a bigger buy-in just to test the waters.
 
zachvac

zachvac

Legend
Silver Level
Joined
Sep 14, 2007
Total posts
7,832
Chips
0
Zach, as far as I'm aware in HEM, SD can be added in the reports section as either bb/100 or BB/100 hands.

Here are my options:
 

Attachments

  • std dev.JPG
    std dev.JPG
    16.7 KB · Views: 78
Jagsti

Jagsti

I'm sweet enough!
Silver Level
Joined
Feb 18, 2007
Total posts
5,478
Chips
0
OK, maybe I just imagined this, but I thought it was /100 hands. I have read somewhere that SD can be approximated as 10x your winrate. So when I have done this with mine it seems to be apprx 10x my winrate. I must of come to the conclusion then that if my winrate is /100 then the SD is in the same units, which would seem appropriate for comparing like for like units.
 
D

dumpy620_84

Rock Star
Silver Level
Joined
Sep 1, 2007
Total posts
168
Chips
0
I swear, one of the main reasons why I play better in tournaments than in cash games, is because in cash game my mind see chips as "dollars", and in tourneys my mind sees them as "betting units".

I play way too straight forward & tight in cash games, and if I get sucked out on, I freak.

In tourneys, big moves or suckouts don't bother me at all - I just sign up for the next SNG.

For some reason, I'm just mortified to drop another $100 level in my bankroll because I am so proud of having worked it up over the past 4 months from where it was. (I sit at $1400 from a $50 buy in in October after the 3rd - $50 buy-in try).

If I drop below, $1,300, it really bothers me. I like the steady progress upwards & hate swings. If I drop below $1,300, I find myself dropping to really small games I know I can win, to get up over that $1,300, then go back to my standard games (SNG & MTT). And I only play cash games if I am happy with my bankroll. +ROI is so important to me. I think its all in my head.

Any advice?
 
aliengenius

aliengenius

Cardschat Elite
Silver Level
Joined
Jul 7, 2006
Total posts
4,596
Chips
0
Not sure where you got your formula (maybe a 'limit' poker reference? although 300BB/600bb is usually the standard given mathmatically), but I can guarantee that your risk of ruin having only 11 buy-ins is WAY higher than 2%...

Also, note that multi-tabling should allow you to "see the long run" faster, thus reducing variance overall.

I'll add the links here and here.
 
Last edited:
zachvac

zachvac

Legend
Silver Level
Joined
Sep 14, 2007
Total posts
7,832
Chips
0
Also, note that multi-tabling should allow you to "see the long run" faster, thus reducing variance overall.

This is false. 12-tabling for one hour is equivalent to 1-tabling for 12 hours. Also note that as you play more the variance actually goes up. It's just that the mean winnings goes up faster thus RoR goes down.
 
aliengenius

aliengenius

Cardschat Elite
Silver Level
Joined
Jul 7, 2006
Total posts
4,596
Chips
0
This is false. 12-tabling for one hour is equivalent to 1-tabling for 12 hours. Also note that as you play more the variance actually goes up. It's just that the mean winnings goes up faster thus RoR goes down.

Of course 12:1 = 1:12 (excepting for the reduced win rate multi-tabling), so ok, perhaps I miss-phrased it:

but, you DO "see the long run faster" playing more tables, and thus an individual given bad beat will be more immediately offset by the overall volume (what I meant by "reducing variance").
 
zachvac

zachvac

Legend
Silver Level
Joined
Sep 14, 2007
Total posts
7,832
Chips
0
Of course 12:1 = 1:12 (excepting for the reduced win rate multi-tabling), so ok, perhaps I miss-phrased it:

but, you DO "see the long run faster" playing more tables, and thus an individual given bad beat will be more immediately offset by the overall volume (what I meant by "reducing variance").

Yes mentally. I think we both agree, just trying to say that in terms of bankroll needed and RoR, multi-tabling does not decrease RoR or BR needed. Nor does it increase it, as many seem to believe.
 
Status
Not open for further replies.
Bankroll Building - Bankroll Management
Top