Why Is Your Poker Bankroll Critical?

What is a poker bankroll for?

A bankroll serves to safely carry a player through variations in their poker performance.  We all go through our ups and downs.  Statistically, it is inevitable that we will all have winning AND losing streaks.  Because of these streaks, without a sufficient bankroll, even the top professional players would go broke on a regular basis.  In fact, one of the key distinctions between novice/intermediate poker players and professional players is that professionals realize how critical it is to obey the laws of the bankroll.  After you read this page, we hope you will appreciate why your bankroll is the most important part of your game.

Your Bankroll is Your Friend

The biggest mistake that you can make in poker is to not practice solid money management.  The most fundamental part of money management is "playing within your poker bankroll".  This refers to playing at stakes where, if you go on a losing run, you will NOT lose all of the money that you have to play with.

Before we get into a more in depth discussion of how to figure out what your bankroll should be, let's look at a very simple example of why your bankroll is critically important.

Imagine that you have a coin.  One side is heads, while the other is tails.  Someone has offered you the following proposition.  They will allow you to flip that coin...as many times as you would like as long as you still have money...and when the coin comes up heads...they will allow you to keep your coin and give you an additional $1.10...when it's tails, you lose $1.

So half the time you will make 110% on your toss...the other half you lose 100%.  The net expected value of this proposition is 5% in your favor

You have $1...should you accept the proposition?  $100?  $1,000?

If you accept this proposition with just $1 to your name, the chances are very good that you will go broke.  There's actually a 50% that you will lose all of your money on the first toss!  And even if you win, there's a 25% that you will lose all but $.10 on the next two tosses.  If you have $1 only to start, there is a great chance that you will end up broke within the first 20 tosses.

If you start this proposition with $100, there is a 0% chance that you will go broke in 20 tosses.  And with a net expected profit of $.05 per toss, you would expect to be positive $1.  (That assumes 10 head tosses and 10 tail tosses, which is a big assumption).

If you start with $1,000 you are even more comfortable that the math underlying this proposition will come out in your favor.  This is the value of having a bankroll in it's simplest form.  When faced with an opportunity where you have a proven edge, the bankroll allows you to act without fear of going broke.  Even if you are a winning player, to play outside of your bankroll is to take on too much risk.

So how big should your bankroll be?

Most poker players will track their performance using big bets/hour (BB/H).  A Big bet is the larger of the two bet amounts in a limit game.  For example, in a $3/$6 limit game, the big bet is $6.  In No Limit games, an hourly rate is sometimes used instead of big bets/hour...but you can also track it by big bets by doubling the value of the big blind.

Bankrolls are thus calculated as a multiple of big bets.  Most experts claim that a winning player should have a bankroll of approximately 300 times the big bet for the stakes that they are playing.  The mathematical derivative for this estimate is below for those interested in seeing it.

Given all of that, the following table gives a general guideline to use for determining bankroll requirements at the various levels of poker.

Aggressive play requires a slightly larger bankroll because it is, by its very nature, a more volatile type of play resulting in bigger swings of the bankroll.  Bankroll requirements decrease at higher limits because you should have developed better skill at poker at these levels.  If you find yourself losing money at an uncomfortable rate at a higher level of poker, drop back down and rebuild.  It may be that you just had an unlucky run.  Use Poker Tracker, Poker Office, the Party Poker Hand Replayer, or your own notes to go back and analyze your play.

Aside from that, your goal is to steadily increase in stakes as your bankroll steadily increases.  Pay attention to the health of your bankroll and it will last you a lifetime.

Do The Math and find YOUR optimal poker bankroll

There is a more precise, mathematical way to calculate how large your bankroll should be for a given level of stakes.  In order to use this method, you must already know something about your performance when playing poker.  Specifically, you need to know your hourly win rate.  It would also be ideal to know your standard deviation from this win rate, but since that is too tedious for most people to calculate, we'll use 10 times the win rate as an estimate.

Bankroll needed = -(SD^2/(2*HWR))*ln(risk aversion)

SD = standard deviation of win rate (10 times win rate is a good estimate)
HWR = Hourly Win Rate
ln = natural log function
Risk Aversion = represents your willingness to accept risk.  .1 corresponds to a 10% chance that you will go bust if you use the bankroll suggested.

As an example:
     Hourly win rate of 2 Big Bets (at $10/$20) = 40
     SD = 400
     Risk Aversion = 10%

    - ((400*400)/(80)) * ln(.1) = $4,605

This means that with a bankroll of $4,605, there will be a 10% chance that a player with these attributes will lose their entire bankroll.

If you had a 5% willingness to lose your whole bankroll, you would need a starting bankroll of:  $5,991  (It's not an accident that this is approximately 300 times the BB at the $10/$20 stakes.  This is where the 300x the big bet figure comes from.)