To the untrained mind, mountains are just mountains. After a first glimpse into the truth, mountains are no longer mountains. After enlightenment, mountains are once again mountains.

-Unattributed Zen Proverb




THE UNTRAINED MIND

Student: How many buyins do I need to practice proper bankroll management?
Master: Twenty.

200BB if you're playing limit. Maybe 30 or 40 buyins if you're particularly risk averse or unsure of your skill. Maybe 50 or more if you plan to live off it. Its the generic "rule of thumb" and it should be fine.


MEDITATION AND STUDY

Student: What level should I be playing?
Master: What's your bankroll?
Student: Well, I loaded up $500 on PokerStars.
Master: I didn't ask how much money you had.

Bankroll management is risk management. You are asserting control over the factors you have influence upon while undertaking an endouvour with inherent risk in an effort to avoid, or at least reduce the chance of, ruin. Ruin is bad. Ruin is busto. Ruin is being unable to play poker.

You can calculate your risk of ruin (RoR) using the following formula:

RoR = e ^ (-2 * WR * BR / (SD * SD ) )

By pluggin in your expected winrate (in bb/100) , standard deviation (in bb/100) , and total bankroll (in bb) , you can calulate with great accuracy and precision the percent chance that you ever go busto. Ever.

So taking the example above and a generic micro-stakes player, let's calculate their RoR. They are playing 25nl with $500 and win at 2bb/100.

e ^ (-2 * 2 * 2000 / (50 * 50 ) )
4.1%

Is that good? Well, the general rule is to keep your RoR below 5%, though of course the actual value depends on each person's individual risk tollerance. But before we dive into that can of worms, let's pick apart the various elements that are used to calculate RoR.

What is your winrate? Your standard deviation? Well, both should be easily accesible from your poker database. But what do they tell you, how accurate are they, and how predictive are they? See the formula wants *expected* winrate and your tracker spits out *observed* winrate. But is there a difference? The first issue is sample size. I won't get into great detail, but we all know that short-run winrates have a lot of noise in them, so how many hands to get an accurate winrate? 10,000? BUZZ thank you for playing. 100,000? Now you're getting warmer. 1,000,000? That'll probably do it. But now how long did it take you to rack up a million hands... did you move up in that time, or change sites, did the old regulars move up and there are new players in the game, did you change anything about your play, do you see what I'm getting at? Any time you've racked up a significant sample such that you you have a high degree of confidence in your observed winrate, its almost impossible for the playing environment to have not changed. You're faced with the connundrum of ether a small sample in a static environment, or a large sample in a dynamic environment, neither of which is terrific at predicting what your winnrate will be in the future in games that haven't happened yet.

Oh, but it gets worse.

What exactly is your bankroll anyway? I say its "the amount you can lose before you quit poker". See, for the purposes of the formula, your bankroll is the amount of money available over your entire lifetime for betting on poker. So you've got $500 on PokerStars. That doesn't mean much regarding your bankroll. Do you have any other money, in a bank account, in cash, or in savings, that you would deposit if you had to? Well, you've got to count that. Oh, and if you have a nice job and could easily deposit $100 a month... well, you should count that money in your bankroll. Yes, even though you don't have it yet, and it might not even exist, you expect it will exist, and it should be counted in your bankroll. For the rest of your life? Ya, sure.

But let's say your income more than a year out is iffy: maybe you'll get laid off, or decide to quit your job, or buy a house and not have so much disposable income, so let's just count a year out. So you've got $500 in PokerStars, another $1000 in your checking account you could easily deposit if you wanted, plus $1200 from future income that isn't actually in your hands yet. You may have $500 in PokerStars, but your BANKROLL is $2700. Kinda over-rolled for 25nl, huh.

And lastly, the formula assumes you will obstinatly play the same level until busto if you hit a bad patch of variance. For those non-pros who don't have a nut, who don't have to make income from poker, you can double the effective size of you bankroll at any time simply by moving down to stakes half those you are playing now. If you can move down, are willing to move down, and do move down when on a bad run, you calculated RoR doesn't really apply. Because at any time you can re-asses and re-evaluate your situation and adjust your level of play to be more appropriate to your current situation.

And this, THIS, is the key to proper bankroll management. Playing with a 10 buyin bankroll isn't necessarily bad bankroll management. OK, if you're a beginner and unsure about your expectation in the game or a pro with a nut to make its a bad idea. But if your a casual player who is disciplined and willing to move down after losing as little as 2 buyins, an 8 buyin barnkroll could be a way to maximize your profits. And to other players in other situations, a 100 buyin bankroll might not be sufficient. More than anything else, good bankroll management is about constant evaluation of your game, your expectations, assessment of your environment, of your financial situation, and changing what you can to make sure you don't go busto, that you do not end up in ruin.

ENLIGHTENMENT

Student: But how many buyins do I need to practice proper bankroll management?
Master: Twenty.

Fifty if you've got a nut. Maybe double it if you're unsure of your skill or are particularly risk averse. Start there, and play it by ear. It won't be long until your gut will tell you when you're at risk and need to make a change. Best of luck at the tables.

I hope my meaningless chatter is useful to you.

First!! And damn you're early this week....COTW is usually 2 days late, lol

Also I would like to mention your "Emotional Bankroll". How much % of your bankroll do you have to lose before it really starts to affect you emotionally?

Say you have swings of being down 2-4 Buy-In's at 25NL. Can you lose $50-$100 with a $500(20xBI) bankroll and be ok with it? How high would your bankroll have to be for you to be ok with losing 2-4 buy-in's? (Of course you would move down levels when needed.)

Mainly I think your bankroll should be at whatever level it needs to be for you to be relatively comfortable losing.

How do you determine standard deviation?

Well done, Kurt. I know (or trust) you are exactly the right person to have written this so I was somewhat surprised you didn't emphasize two aspects.

Inquiring Mind

Student: How many buy-ins do I need to practice proper bankroll management?
Fellow Student: It depends.

Kurt did point out that by dropping down a level one effectively doubles their bankroll. There is a huge psychological effect at issue. When running bad, we're hemorrhaging money (even more than usual, as we all have leaks). It takes someone obscenely rich - or a pathological sociopath - to be able to completely ignore the constant bitch-slaps on one's bankroll.

So the question boils down to this: how many buy-in size hits can I take and still feel comfortable playing? That is the real low water mark when considering the number of required buy-ins for any given level. At some point the very fear of having to move down, even when it's the right thing to do, will cripple our game.

And then another thing, which I feel like dumping here.

Sample Size != Effective Sample Size

Without trying to hijack the discussion, let's just say that the quip about 10k hands not being enough is spot on. If we're playing a slightly tuned lag-tag 17/14 game, in 10k hands we have still only entered the pot with ~1700 hands. In full ring, that averages to less than 200 hands per position. Even if we played 50% of our hands (at 17/14 average) from the last three seats, we'd have less than a thousand hands worth of in-position experience.

A close-to-accurate winrate estimation will therefore take quite a lot of time and a remarkably big sample size to converge. As Kurt said, during that time both our play as well as the environment have very likely changed and evolved.

PT2: Look on the second tab along ("session details" I think it's called), then click the "more details" button in the top right of that tab.

+58

great post Kurt.

+1

I'm a big believer in the 20bi rule. Its practically impossible to go busto with this rule so long as you move down if and when needed.
Kurt covered all the ins and outs perfectly.

However I do make one exception to the rule - "LOL what is he doing there I gotta sit".
If a known mega-fish (like a 60+ vpip or something) sits at a level that you have 10bi for I think you should sit. Probably play just to have a shot at the fish, stay fairly tight otherwise (now is not the time for thin 5-bet bluffs) and you should have a nice positive expectation.

I wouldn't make it more than 1 table and the fish needs to be pretty bad, this is a situation that only comes up once in a while when a name in the lobby just catches your eye.

Totally true, I've had problems with this.

Great COTW.

Very nice, Kurt, well done.

I'm going to take a contrarian view to kinghyrule. If your emotional bankroll requirement is much different than the 20BI rule, then you have a significant leak in your game. The answer is not to have a huge enough bankroll to ignore it. Variance is one cause of a loss, but others include poor table selection (did you sit at a table with a couple of visitors from a couple of levels up) and playing your "C" game. If you keep hitting the top end of the villains' range, it may be that you have the range wrong, rather than variance.

I believe you need that emotional "pain" to improve your game. Too often factors we don't recognize are leaks we just classify as "variance." As Ray Zee said, "Show me a player that hasn't a significant down swing in the past year and I'll show you a player that hasn't improved." If you lose 4BIs in a session and you have such a bank roll you don't care about it after, it is unlikely you'll do the detailed session review to see what went wrong. Maybe you lost 2BIs because two idiots hit their 3 outers on the river. However, I'll guarantee that you probably didn't get full value out of them when you beat them either at showdown or failed to play a potential winning hand against them. As for the other 2BIs, based on my own experience, you'll find that in the cold light of the next day, you could have played hands better and made much of that up.

Finally, if losing 2BI makes you tilt, it will probably make you tilt no matter what the size of your BR is. If it doesn't because your bankroll is so large, you're probably not playing your "A" game.

As for the pro needing 50BIs, I think this is more of a matter of living expenses. Someone going "pro" needs 3-6 months of living expenses saved. Assuming a bare bones existence of $2000/month, that means having at a minimum of 120BI at 50nl, 60BI at 100nl and 30BI at 200nl just for living expenses reserved. If your living expenses are higher or lower, it would move the number up or down.

Finally, trying to guarantee you won't fail is a chimera. There are no guarantees in life. If you live your life so that you won't fail, you won't achieve meaningful success, either. Even a 20BI BR in the OP example means that out of 100 people trying, 4 will fail despite their efforts. Don't be a life nit. Live it.

If I get a chance to sit on the direct left of an uberfish, I'll happily sit down at a level where I have 4 buyins... it's just a great +EV proposition

Great post.

A great philosophy and one that I fully believe in!

HOLY ****, I LOVE THAT QUOTE YOU OPENED WITH!

Great post Kurt, I love your philosophy. Venice also has a really sick post here (as usual, and I'll be sure to give my gf your contact when I quit my job and she wants someone to yell at :P)

Hyrule also gets a huge +1 for the emotional bankroll reference. This is something I talk about in the psychology forum whenever questions arise about tilt, or being generally unhappy with losses. In most cases I think that people are over-extended on their emotional bankroll.

ChicagoJoey had a great line in reference to a sick sick pot by VI, "My heart never gets pounding anymore, but I can relate". It can then be implied that ChicagoJoey has a rather large emotional bankroll (if we are to extrapolate his heart-rate to his emotional involvement in pots), because he can afford to get sucked out on a 600BB pot without really caring about that isolated incident. On the other hand many players will go on super-monkey tilt when their Aces get cracked by Kings AIPF.

Learning to control your emotional bankroll management is almost as important as controlling your actual BRM.

Great post Kurt!

For those wondering and who don't have the function on their calculators, e = 2.71828183

Emotional bankroll is by far my biggest problem. My heart doesn't pound anymore either at anything below 200NL, but I start to tilt quite hard after 3 buyins at any level. Odd that one part of it does not affect me but the other part does.

If you pound the table, throw your mouse, curse at the screen,,,,,,,

...you are playing stakes beyond your BR. The above are signs that you are emotionally attached to the results which is almost always -EV.

And what if uberfish goes on a heater and stacks you 4 times?

Yes, this is what I touch on at the very end of my article, that once you know the math and understand the perturbations and implications, your gut will be a useful guide in determining your level of play.

You've got $500 so start at 25nl, sure, OK. A TRUE beginner (who studies the game and understands the math) will likely soon realize "this is ridiculous, I could go broke so easily! I'm dropping to 5nl until I have my sea legs." Someone for whom $500 is every cent they have in the world might feel 4% is too much RoR and drop down. And conversely an experienced, proven winning player who is short rolled might think "this is going to take forever, I'm starting at 50nl." They would all be right in doing what feels right, in following their emotional bankroll.

Very true. No matter the stakes, its important to be able to bring your A game. If you're so short rolled that you're playing scared money, or so over rolled that you're messing around and dropping buyins like water, you're not practicing good banrkroll management because you're setting yourself up to fail. It is important to play where you are comfortable.

This can be a problem at times. Take a college grinder, doing a workstudy job for $7 an hour with few expenses. They save up $600 in a month and deposit it and jump in. They feel they can't play their best, can't bring their 'A' game, unless the money "means something", so they jump right into 200nl. For this person, and many others, their gut is misleading them. First, it shows a basic misunderstanding of the math because it should be patently obvious that even Durrrr would go busto quickly if he played on a 3 buyin roll. But further, I question their ability to bring their 'A' game to the table when their entire net worth is on the table at one time.

I'm not advocating "do what you feel is best" with no strings attached; it requires mindfulness. Your self assessment must be valid and accurate, your estimation of game quality must be realistic, and your finances must be understood. Without a discerning and critical eye, following your emotions can be problematic.

Haha! I noticed this very dramatically when I took the 100vpip challenge. I played less than 2000 hands, but entering 95% of pots I believe my results were as significant as a 10,000 hand sample from a TAG. Food for thought.

What do you think is more likely, that or I pick up a few hands, value bet the crap out of him and win his stack, increasing my bankroll by 25% in the process?

It's a gamble totally worth taking imo

Good job, Kurt.


Nah, we have had 2 or 3 out of 20 that were late; we've just been running bad recently.

This is an example of your gut giving you good advice. You inherently realize that sitting to the left of a giant fish shoots your winrate through the roof, and when WR goes up RoR goes down, and you can correspondingly increase your stakes for this session without increasing your RoR.

A great post. I'm going to comment on the above paragraph.

First, the 3-6 months of living expenses saved up is not part of your bankroll. Much like I discussed in the article that many people are not counting all of their available money and underestimating their actual bankroll, this money should not be counted for fear of over-estimating your bankroll. This is because it will not be put on the poker table; you need it to eat and survive and will never put it in action, and therefore it is not part of your bankroll.

Further, I think a lot of the increased requirements (50 vs 20) for "pros" comes from the fact that they have a nut. They need to take $x out every month to pay bills, eat, etc. If they are just making their nut every month, they really can't drop down because their earn at the lower level won't be enough to sustain them. Therefore, while a hobbyist can drop down at will when they see events at the bottom 5% of expectation, a pro needs to weather that kind of variance and play on.

Oh, and I missed this the first go-around:

As a good friend of mine likes to say, poker rewards sociopathic thinking.

Also, I'm realizing in my ruminations that I left out some of the BRM basics. Notably that if you have a negative winrate, your RoR will always be 100%. You need to practice budget management, not bankroll management, until you improve and are confident you are a winner in the game.

Thank mpethy. And thanks everyone who has left positive feedback.

These articles always come out as so much less than what I planned in my mind, so its good to know that they are worthwhile.

vnh.

Sick insight ITT.

Anyone know how to view std dev in HEM? Thanks.

Under the reports tab, report by stakes, click the green plus sign (+). Add Std Dev BB, save and hit refresh.

The problem is the other player's at the table. Just because you have position on him doesn't mean you'll get the chance to isolate him whenever you want, expect to get 3bet and targeted by the regs at the table and while you have a big advantage over a fish you're the fish in the eyes of the reg so I think 4 buy-ins is pushing it a lot if you can't reload.