What is bankroll management?
Bankroll management are thoughts and rules you should keep in mind while playing any kind of poker (or any other game) for real money. Although it does not concern game strategy itself or ideas how to directly increase your profits it will help you with an equally important task – not to go broke.
As with almost every theoretical approach, especially the ones regarding poker, there are countless examples showing that even if you are unfamiliar with the theories you can be a successful player. However, examples of players who are unfamiliar and losing are much more frequent. If you don’t want to be one of them, read on.
Swings
Swings are a mathematical fact that cannot be avoided in any game that has at least some amount of luck involved in it. Even the best pros suffer from losing streaks from time to time and even the biggest fish in the game happens to win on an occasion. It is the existence of swings that makes thoughts of bankroll management a valuable asset. The best thing you can do is to learn to deal with them. Assess the decisions, not the results. If you lose a pre-flop Holdem all-in with AA – there’s obviously nothing you can do about that. It is important, however, to always keep an open mind. If there’s a leak in your game the worst thing you can do is to believe you are not responsible for it and keep repeating it. Always analyse your game and question your decisions. Besides improving your game and controlling the size and frequency of swings that befall you, it is an important aspect of increasing your bankroll.
What is bankroll?
Firstly, we need to define what bankroll is. For the purpose of this article we will define bankroll as the amount of money you have put aside with the intention to play poker with. This usually means the sum of money you currently have at your account plus an amount you are willing to deposit in case of losing streaks.
We will assume that not losing your bankroll and increasing it have the same priority. These may seem mutually exclusive but it merely means that we will try to avoid the choices which, although profitable, come with a high risk of decimating your bankroll.
Luck & skill
Poker is a game of skill. Poker is a game of luck. You may have heard both statements and may have even been a witness to lengthy discussions about which of them is true. As a matter of fact, they both are. Imagine two chess programs playing against each other. If one of them beats the other in every aspect of the game it will win 100% of the time. On the other hand, imagine two players guessing the result of a (perfectly random) dice roll. None of them is getting ‘the upper hand’ in this game, since there is no skill to master. They will both win and lose and there is nothing they can do to affect it.
Now imagine yourself playing poker. The game lies somewhere in between of the two aforementioned extremes. The good news is, however, that the ratio of skill/luck in the game can be affected.
Introducing variance (and expected value)
The quantity that we will use to describe the amount of luck involved in the game is called variance. Variance is high when the possible results differ greatly from the average result. Rather than bothering with a mathematical definition we are going to present several examples that illustrate its meaning. Imagine a coin flipping game with different rules:
Version 1: You win 3$ regardless of the coinflip’s result.
Version 2: You lose 10$ if the result is heads but win 20$ if the result is tails.
Version 3: You lose 100$ if the result is heads but win 98$ if the result is tails.
In the first game the variance is zero – all the possible results (i.e. the only one) are equal to the average result. In the second game the variance is non-zero, since the possible results differ from the expected value. In the third game the variance is the highest. The expected value is the lowest in the third game (−1$), followed by the first (3$) and the second (5$).
Risk aversion and game selection Which of the previous games should you choose? Obviously, if your bankroll is very large you should aim for the games that offer the highest possible expected value (game #2). However, the smaller your bankroll the higher the chance that it could be decimated even though the expected value of the game is positive. As an example, let’s suppose your bankroll is 30$ and you are playing game #2. If you lose three times in a row (which is likely to happen to one out of 8 players) you are broke and can no longer play the game. Playing game #1 seems like a better choice – although your bankroll will be only 39$ after three games (30+3×3), which is less than the expected value of playing three games of game #2 (30+3×5=45), you can be certain you will not go broke and can continue playing.
The third game is the worst choice by both criteria – not only is the variance significantly higher than in the other two games, but it also has a negative expected value. Don’t be fooled by the highest possible win. Even if your bankroll is large it will suffer in the course of time. This example resembles to many casino games like slot machines, roulette or lotteries. If you are aiming to be a profiting gambler, you should avoid these games at all costs.
Stakes, Style and Game
How do these theories apply to poker? There are three major aspects that affect the variance in poker – the bankroll/stakes ratio, game type and game style.
Stakes – this is the most obvious aspect. The size of your bankroll is always measured in multiples of stakes that are played (buyins, big blinds,…). If your bankroll is 30$ and you play a single 30$ SNG, the chance of going broke is very high – it is enough to lose the first game. On the other hand, if you play 1$ SNG, you would need to lose 30 games in a row to go broke, which is obviously far less likely to occur. Thus in order to decrease the chance of going broke and to avoid large swings choose lower stakes over the higher ones.
Style – there are countless ways to play poker and plenty of various strategies that can be applied. One of the basic characteristics of the game style is usually labelled as either conservative or aggressive. Conservative style prefers stricter pre-flop hand selection and often smaller pots. As a result, a conservative player usually wins a high percentage of small pots. On the other hand, aggressive style includes wide range of hands and, as the name suggests, sticking a lot of raises, re-raises and, inevitably, bluffs.
Consequently, an aggressive player loses a lot of small pots when the bluffs are unsuccessful but wins some huge pots when his loose table image pays off. This division is very basic and can easily be disputed. Nevertheless, it illustrates that your game style does affect the size and frequency of your bankroll swings and you should keep that in mind if your bankroll gets too small. If your bankroll is relatively large (compared to the stakes played) you are free to apply any style of play.
However, if your bankroll gets small, you need to avoid plays that jeopardize your bankroll. Risk aversion can potentially decrease the profitability of your play but cannot do the opposite. If this is the case (depending on the actual game style), you should move to lower stakes rather than playing higher stakes with lower or negative expectation.
Game – this is a non-variant parameter given by rules of a game. For example – in Holdem the range of winning percentages of individual hands is generally higher than in Omaha. In Holdem, AA is guaranteed to have 80% pre-flop, while 50-70% winning percentage is very common. In Omaha, AAKK usually does not have more than 75% and two random hands are likely to have 50-60% pre-flop odds. The smaller the winning percentages, the higher the amount of luck in every hand and therefore higher swings. Limit is also very important. No limit games allow huge pots and inevitably large swings. Fixed limit games have smaller average and maximum pots and hence smaller variance.
