Okay, I spent some time writing this, I hope it deepens your views on the subject and helps you understand why bankroll management is important and also to tailor a good bankroll management strategy for your game. I posted this at both my blogs since I think it's equally important everywhere (kekekekkekek).

Bankroll Management Explained

Foreword

This “article” is actually more of a guide to one of the most underrated and yet most important aspects of successful poker. It’s the second longer article I’ve written, first being about managing the highs and lows and how to keep on a good mood for playing poker. Obviously, I’m still learning in the game, so this article forced me to do some research as well and make my knowledge in this area deeper so that I (and soon you) could truly understand what’s it all about. I will mostly concentrate on making similar articles on not-directly-playing related, yet topics instead of going straight on to playing actual hands. There are a lot of better people to write about that. So let’s get started.

Introduction

As mentioned, bankroll management is one of the most underrated aspects of successful poker, not only from the beginning players, but some of the better ones too. Most players are given a strict rule to begin with, such as “You need to have X buy-ins to play at limit Y”. Why is it X? How does it differ from X-1? What is going on in here? People choose, or choose not to follow these restrictions and straying far from the path can result in a lot of tears. I will go into some of the math behind where these numbers come from and why you need to be properly rolled for the game.

Things to remember

Bankroll management is not there to compensate for bad play

This is not only for those beginning the game, but also for those playing higher, more successful, but still out of their bankroll. Many people often move up in limits thinking “Hey, I can beat the game at these limits, I don’t need good bankroll management”. While the first part of it might be true, the second isn’t. Bankroll management is there to negate the effects of hardcore variance. It all comes down to the numbers with this subject and don’t think you can beat the numbers because you can’t. Best you can do is adjust your bankroll management strategy to your winrate and standard deviation (more about those in later chapters) and you will be fine. Then again, if you’re not a winning player, there is no amount of bankroll management that can help you to not go broke.

Standard deviation

Let’s start with an encouraging thought: You can never be 100% certain that you won’t go broke because of bad luck. That being said, there are lots of programs out there to calculate your standard deviation. For example, PokerTracker is capable of doing so.

By definition, Standard Deviation is the measure of fluctuation from the average (mean) value across a range of samples. So basically, the lower the standard deviation is, the more consistent the players results are in that sample. And since calculating your standard deviation can be a pain in the ass, letting programs do it for you is generally the right way to go. Mathematically, it’s calculated by taking a square root of the variance (which is the statistical dispersion of a random variable). More information on how to come up with the standard deviation and related topics can be found here: http://en.wikipedia.org/wiki/Standard_deviation

Risk of Ruin

Also called ROR is what will ultimately decide how safe your bankroll will be. You can basically pick any number smaller than 100% to represent your risk of ruin, ie. How willing are you to go broke. When thinking of a number here, you should start low, lower than 1% because you really don’t want to hit that 1%. And also keep in mind that this does not include things you could possibly cause by yourself, such as tilting that really don’t go into category of variance. Later on, I’ll provide some tables with calculated optimal bankrolls that should suit your needs. It’s always better to have too much, than not enough.

Calculating your optimal bankroll

To the heart of the beast then. First off, you’ll need some statistics from your game. The larger the sample, the better. If you use PokerTracker, that’ll do just fine since you can get all you need from there. Also notice that to give an accurate estimation of what your bankroll should be, you also could need hundreds of thousands of hands to be sure. But few ten thousand should do fine.

The variables needed for the equation are SD (Standard Deviation), HWR (Hourly winrate, ie. BB/100) and ROR (desired Risk of Ruin). After you’ve come up with these numbers, you take the following formula:

The Required Bankroll = -(SD^2/2(*HWR))ln(ROR)

ln being the logarithm with e (2.71828...) as it’s base.

Designing an optimal bankroll management strategy

It is important to make a strategy that you’re comfortable with. Whilst the numbers might suggest a bit smaller number, if you feel uncomfortable playing under those circumstances, by all means, add a few buy-ins to your requirements. Also notice that the numbers that go to that formula are big bets for SD and HWR, instead of PokerTracker BBs (which is 2x BB for no limit). Later on, I will always assume to talk about Big Blinds rather than big bets, so don’t confuse them. I’ve picked a few “reasonable” examples on strategy.

Sample 1

Game: No Limit hold’em

ROR: 1%

HWR: 10 BB/100 (This would be 5 PTBB/100)

SD: 80 BB/100

Bankroll = -(80^2/(2*10))ln(0.01)

= 1473 BB

=~ 15 buy-ins

So this shows that being an okay winner with standard deviation of 80 BB/100, your risk of ruin with 15 buy-ins would be 1%. 1% can still be quite a lot so let’s look into a bit more secure example.

Sample 2

Game: No Limit Hold’em

ROR: 0.01%

HWR: 10 BB/100

SD: 80 BB/100

Bankroll = -(80^2/(2*10))ln(0.0001)

= 2947 BB

=~ 30 buy-ins

This shows that having 30 buy-ins is by the numbers a very safe bankroll to play with and even though the risk still exists, it’s very minimal. It can’t be stressed enough though that should the numbers go bad for you and you lose – say 15 buy-ins of 30 buy-in bankroll, that might really affect your game in a very very bad way, so again, having 30 buy-ins isn’t a guarantee you won’t go broke if you happen to run bad.

Let’s look at an example that goes vice versa. This is kinda for those who think “3 buy-ins is enough” or “I’m good enough to play with X buy-ins”. So we calculate ROR based on the requirements set for bankroll.

Sample 3

Game: No Limit Hold’em

HWR: 10 BB/100

SD: 80 BB/100

ROR: x

Bankroll: 1000 BB (10 buy-ins)

1000 = (-80^2/2*10))ln(x)

ln(x) = 1000/(-320)

ln(x) = -3.125

e^-3.125 = x

x = 4.4%

While this percentage might seem a bit low, take into consideration the times you’ve been runner runner flushed or runner runner rivered – that’s about the same probability. You don’t want that to happen. Granted it’s a risk that some people are willing to take in order to build up fast, but don’t be that person unless you’re willing to put in another 10 buy-ins, should you lose these (in which case you’d basically be playing with 20 buy-in bankroll). Also, the standard deviation in the equation is quite modest, with high fluctuation LAG styles, it can be even bigger and it affects the bankroll requirements.

So let’s take an example of more NL25 kind of approach to go in with $100 and calculate the risk of ruin for that.

Sample 4

Game: No Limit Hold’em (well this doesn’t actually matter, it just illustrates the class the winrates and standard deviations are in. For example SD is lower for Omaha Hi/Lo)

HWR: 10 BB/100 (This could probably be bigger on this level)

SD: 80 BB/100 (Since we’ve used it this far)

ROR: x

Bankroll: 400 BB (4 buy-ins)

ln(x) = 400/(-320)

ln(x) = -1.25

e^-1.25 = x

x = 28.7%

How about that! Doesn’t sound all that shibby anymore. By a bit more than halving the bankroll required for “relatively safe”, the risk of ruin has multiplied to seven times as big. So before thinking you’re good enough to play underrolled, know the risk you’re taking – even with what you’d consider perfect play. Better safe than sorry.

Now that you’ve been walked through the basics on how to calculate your required bankroll, I felt that I could do that for you too, so here are a few tables that show the amount of buy-ins (one buy-in being 100 BB) for different varieties of winrates, standard deviations and risk of ruins. Thank you for your time, I hope you learned something.

Charts

In all the following charts, the percentage on the left will show the ROR and the row name at the top indicates your standard deviation. The numbers in the tables are buy-ins (1 buy-in being 100 BB). Remember that these are all big bets, so if you see PokerTracker for your winrate and Standard Deviation, multiply them by two.

Bankroll chart for 5 BB/100 winrate:

Bankroll chart for 10 BB/100 winrate:

Bankroll chart for 15 BB/100 winrate:

Bankroll chart for 20 BB/100 winrate:

Bankroll chart for 25 BB/100 winrate:

Hard way to make an easy living

As "promised", here goes the article. A lot of questions go into all forums of this, especially from beginning players so I think this will serve as many answers to those players.

Managing the highs and lows

You wake up in the morning, let out a yawn. Sun is already shining and you take a shower. Birds are singing and life is good. Nothing could ruin your day and what would be better than taking a couple of hours to play some poker before heading to the beach. Life's good! Or is it.
You enter a table and get ravaged and even though you play perfectly, you take a swift hit. After that, you have a little trouble picking up the pace, you want to get up. Bit by bit, you get into the mode of wanting to "win it back". Soon you'll notice that the sun has set, it is dark and you're stuck 10 buy-ins.
Sound familiar? I can confidently say that I'm one of the pro-tilters in poker and mental state has a huge impact in my game. Lately though, I've managed to get to a point where it's not so much about the beats and such anymore. So how do you manage these high's and low's then?
Many things can set off a tilt. Many people seem to think that tilt is some rage that makes you go all-in every hand, like some good players have done (Say... B_Buddy is famous for this). That's not the case, it might be something smaller, spewing off chips here and there. It all adds up.
In the early days of my play, I was a bad beat maniac - each time I got a bad beat, I posted it in the forums and was crying and whining for ages. More recently I've learned that it's not the bad beats that matter, it's really all about bad plays. And thus nowadays I tilt more because of bad plays and not bad beats. But no matter what your trigger is, you have to be able to manage it.
Most people underestimate the impact of their personal life and state of mind into their game. It is very important to take care of these things and play when you're in the brightest of minds. So let's go into more specific ways to keep your mind clear.

Rule 1: Don't play tired.
And yet, you often feel like doing so. When your tired, your decision making isn't as sharp as it should be and you might end up doing sloppy decisions that cost you money.

Rule 2: Don't play long sessions while you're losing.
No matter what people say, most have the problem of not being able to quit while they're down. The more they play, the more they think it doesn't affect their game and the more they end up losing. For me, this was a problem for the longest time (just recently realized that losing sessions were my longest sessions). If you feel you're losing and not playing to make good decisions but rather to get even - just quit right away. There will be another day.
Although it doesn't always feel that way, you should also play longer sessions while you're winning. Sometimes you might feel you'd want to quit while you're up and it's true that you should the moment you start fearing you'll lose the amount you've won, but let not a doubt be in your mind. Know that you're winning and it doesn't matter if bad beat destroys part of (or all) your winnings. Just keep your good decision making shoes on.

Rule 3: Take a break after a very bad day.
Ironically enough, the next day after a huge losing day can often be (At some point) the time when you want to go play the most. Don't. This is for sure, one of the most important concepts of tilt management. You're still in the mood from last day's losses, thinking that you're probably running bad or whatever. You still want to get even and you still cloud your judgement by the bad streak you had the day before. Take a day off and you'll notice that the burning desire to play fades away by the next day and you'll be back to your good game again.

Rule 4: Eat healthy and steady.
Now this has a lot to do with keeping a clear mind. If you eat a huge meal, you'll go into a slower state of mind, which kinda is nature's normal response to when you've satisfied one of your basic needs. Keeping up a steady stream of nutrition, never overdoing it can help you sustain your stamina at the tables a lot better without having impact on your judgement. Eating healthy makes your mind work more clearly overall too.

Rule 5: Stay fit.
Although this is something I've somewhat managed to avoid a bit too much, it's very important to also exercise. Healthy body in a healthy mind and vice versa. Going to the gym after a bad session can also help get rid of the bad feelings as you can take it out on something or you can just go take a refreshing walk.

Rule 6: Take breaks when you need them.
It is not healthy to play 16 hours in a row. I've done it and I know of some people who can do it and still do well, but that's definitely not the case with most people. Take your breaks, to keep your state of mind as sharp as possible. Playing overly long sessions can eventually cause you play like a robot and thus, make you easier to read, maybe add some other leaks to your game as well.
It is also occasionally good to take some time off, even if you're winning. And to take off whole days every now and then to avoid "overdoing it", is definitely healthy.

Rule 7: "Morning Sickness"
I do not know if this is the case with all people, but I think many players underestimate the tiredness in the mornings. Don't go to the tables before having your morning coffee and preferably doing something else first (besides eating breakfast - it's the most important meal of the day you know). The early sessions can cause you to go down in 500mph vertical dive and then you'll end up spending the day, trying to win it back.

Rule 8: Only play when you feel like it.
There's no reason to play when you don't feel like playing - no matter what the reason is. You have to be concentrated to avoid making bad decisions and to capitalize on your opponents ones. Also Barry Greenstein suggests that having sex before the game is good for you since it releases anxiety and stress and makes you feel relaxed. It has been shown though that watching porn while playing can devastate your bankroll!

Rule 9: Work on your game.
Although this is not that directly related to tilt management, I still think it's an essential thing to mention. Most players, especially new ones only concentrate on improving their game while they're losing as the normal reaction of a human mind is that you must be doing something wrong when you're losing. But poker is a sick sport and there you can play perfect and still lose or play like shit and still win. What separates great players from the marginal winners is their ability to concentrate and improve their game also when they are winning. So you should also review the winning sessions so that you won't go blame tilt or bad play only when you're losing, you could be doing mistakes in the winning days too.

Rule 10: Don't let your ego get in the game.
This can often be a problem (to some people naturally or) after a big win. If you have huge winning session, you might end up going to the next day with the mentality of being invincible. You might soon be shown that's not the case and you end up beating yourself up with a large mallet, trying to pound some sense into your head. "How could I lose one week worth of winnings in one day?!", that's how. This is also related to rule number 9 - also work on your game while winning. Nobody plays perfect poker and although people generally play better when they're winnings, they still make mistakes. To identify those mistakes at the time will definitely help you improve your game.

So there were 10 rules to follow to avoid and manage your bad days as well as the good ones. Don't overdo it, it's often good to take a day break after a loong loong grind session the last day - even if you didn't lose. Work on your game on the good days and work on your game on the bad days and shrug all result orientation from your mind. Never let your ego to interfere and never underestimate your opponents.

I guess that's it for this time, I hope you took something out of it.

Cheers!~ <3

Into the Underdark

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Why do the pushin' when the donkey will do the pullin'

-Layne "Back-to-back" Flack

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I broke all my cardinal rules yesterday by playing dead tired after 26 hours up straight. I didn't lose that much, but I'm going to take today off from playing. I'm thinking of writing an article on arbitrary subject later today and posting it either here or Pathological Case (or both). I will do it mostly to get my ideas straight, probably post it to some forums too to get some feedback.

I know the biggest problems for me are still quitting when the pokerfairy is shoving his big black fist up my ever so bleeding anus. Chip Reese said in the quite fresh episode of CardPlayer.com's The Circuit that you the best advice he can give is to not play long sessions while you're losing. I guess that's when it occured to me that my longest sessions are always those I lose the most in. Mmmm... I guess result orientation pokes me in the eye and disturbs my views on the game and I'm off to a 1000 mph vertical dive into deep dark oblivion.

I will try to keep my eye more on this - like if I'm not making results after 2 hours, I should just quit before the frustration really settles in and pick my fight to be on the next day. Otherwise I'll end up pulling a bluff outta my ass on the wrong time. Although I think that was pretty well done bluff (and on turn, semi-bluff), I shouldn't have been in there in the first place.

I looked through the biggest losses for the day and like 80-90% of them were just big bluffs. Surprise, surprise. Like a friend of mine said "Muhweli's bluffing in the Special Olympics" - which is quite much what happened here. I managed to spew half a stack with 66 on 432 board against preflop raiser, turn was a 9 and on the river 4, the guy made an all-in reraise. I'm guessing he had either an overpair, 99 or A5. Overpair being the most likely one in my opinion as I had no other read on the guy.

Blibberblabber, yitter yatter, and ooga booga, tomorrow is a new day, today I'll do all kind of actually useful stuff. My Hand Reviewer is coming along fairly well and I think I'll have a beta version up for testing in a couple of weeks. So if you're interested in being a part of that, you can E-mail me at muhweli@gmail.com.

Cheers! <3

For the Love of GOD

Boya. I had some baddish sessions last week - I haven't really gotten into playing this week yet, but the little I played, I got like a bit over buy-in from a short NL25 session. I think I will now play NL25 for 6 more buy-ins, then play NL50 for 30 buy-ins (to prove myself I can win consistently god dammit). I will play shorter sessions when it seems I'm losing - having a good start for a session has a good impact on the mentality and having frustrating beginning can be a harbinger of doom in these things - it might mean I play a little worse until I lose the next big pot and it just goes down and down and down and down. But we'll see how this'll work out. Last time after making it out of a 2.5 buy-in hole at NL50, I just "knew" that if I kept on playing any longer, I'd take that huge losing session. Well within next 10 minutes, I got 3 sets, of which all got cracked.

But anyway, I feel comfortable with my game and despite the losing sessions, I know I was playing bad, I just didn't stop the session for the day. I guess I'm a bit of a gambling addict - so to fix this, if I feel I might be playing bad for some reason, I'll just quit playing for a while, maybe for a day.

There's nothing special to report I guess, I think I might mix in some small stake O8 cashgames as well as a) those have small variance, b) I'm a fucking hi/lo split god and c) the players are probably worst there are online - maybe with the exception of hi/lo stud.

To not make it all sound like whiney whiney bitchy bitchy, here's a quite sickish flop hand I won.

Improvements...

I've recently improved my game a lot. And by a lot I mean HUGE. Just greeeeat. My cashgames are improving and my MTTs are improving. I've only had minor cashes this far (one 6th in $11 Pot Limit Hold'em MTT), but I'm certain that I will make at least enough for the challenge before the end of the month... or die trying. Cash games, I've been running 15 PTBB/100 for 8k hands now, half NL50, half NL25 and it's lookin' good. NL50 winrate is around 9 PTBB/100 so it's the NL25 6-max (easiest game in the net) that gave me my huge winrate by running 4k+ hands 22 PTBB/100.

Okay so besides running good in cashgames and bad in tournaments, lemmey get back at why my game started improving again. First off, I did some research with PokerTracker to find out what my most losing hands are and why. After 40k sample, my top 10 biggest losers were all suited 1-gaps. That means I "might've" overplayed them a bit. I calmed down with those and *BOOM* my winrate started improving again. I'm still taking beats plenty and stuff so it's not just a good run (although obviously it's that too). I also overplayed some draws (semi-related to suited 1-gaps) and that was a huge leak for me. Some hands that weren't performing so well were something like QTo QJo, perhaps QJs. I've tried to be overly aggressive perhaps.

On complitely related sidenote, I also get LAG rating from PT now that I've been playing and I like it. I feel a bit loony at times for a reason, but I've also learned playing THE NUTS aggressively. Besides turning into a loonie, Sklansky's NL book seems to be quite good. It opened my eyes for some of the bigger betting styles. Also reading High Stakes Forum at 2+2 has helped great deal.

And for MTTs, I'm reading through the anthology of the 2+2 MTT wisdom and that has improved my game (all fronts) by huge leaps. And it feels good to know and notice you're improving.

Anyway, I've build back most of my NL100 losses now and I will grind it out to $2000+ and this time I won't take stabs. Been hammered too many times when I did that - this time I won't do it since it just screws me over... :[