Jagsti
I'm sweet enough!
Silver Level
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.
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.
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.
I hope you find this post useful. GL all.
