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Poker Strategy | Advanced Poker

Bankroll Considerations for the Professional and Semi-Professional

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In a previous article in which my focus was moving up in limits, I addressed bankroll as it applies to the amateur player. The amateur does not need to make money playing poker and so can afford to take shots more aggressively than can someone who depends on poker income. In this article, I want to discuss several important features of bankroll management for semi-professionals and professionals, including the purpose of the bankroll, the relationship between bankroll and the limits that one can play, taking shots at higher limits, dropping limits, growing your bankroll, and setting goals for your play and income.

Let's begin with an examination of the purpose of your bankroll. What exactly is the point of having this thing and why does it matter? Essentially the bankroll allows you to "invest" in a particular level of play. The higher the level of play, the more income you can potentially make. Thus, the bankroll is what allows the professional to make money. Of course, you can sit with your entire bankroll in one game and have a high potential for profit, but you also have a high potential for losing it all and ending your career as a poker player.

The professional player must find the happy medium between maximum profit and minimal or at least acceptable risk. The bankroll, then, allows one to play almost indefinitely while maintaining a solid profit level. The bankroll is only a means to this real goal of earning income. The bankroll is not an end in itself and this fact must be kept in mind. Should your bankroll take a hit in the course of a bad week, this is not necessarily any reason to become upset or concerned. The bankroll is only a tool to be used in generating your income. Now, although it is only a means to the real end, it is a rather important tool and care must used in making decisions that impact it.

What exactly is the relationship between your bankroll and the level (or blind amounts) that you can play? As all poker players know, this game brings a certain amount of variance. Bad beats happen, and sometimes they can happen in rapid succession or for extended periods of times in big pots. This is the inherent risk of playing poker. Chance creates a risk of loss. You cannot do anything about the element of chance, but you can take steps to minimize its effect on your ability to earn an income playing poker. By having a bankroll large enough to absorb the downswings you can be relatively certain that you can play indefinitely and thus, indefinitely earn an income. A player with a $100K bankroll can almost certainly play a $1/$2 no limit hold'em game for as long as he/she would like. With a bankroll this large, however, the player could play at much higher levels, earning greater income while also being relatively certain of the ability to continue playing at that higher level indefinitely, but where exactly is that line?

This brings us to the more intricate question of how much bankroll one needs for a given blind level. There are several answers to this question, but I am going to limit my analysis to three or rather two and a half. The first is the conventional rule for big bets or buy-ins. In limit poker the conventional rule is 300 big bets (BBs). Thus, if you wanted to play a 5/10 limit game, you would need a bankroll of $3000. In a no limit game, the conventional rule is 20 buy-ins or 2000 big blinds (bbs). Thus, to play in a $2/$4 no limit game, you would need a bankroll of $8000.

Along these lines, Chris Ferguson has endorsed a 5% rule for no limit games. You should not have more than 5% of your bankroll on the table and if your stack reaches 10% of your bankroll then you should leave the table. This is quite similar to the conventional rule, since 5% of $8000 is $400, or one table buy-in. It could be used for limit poker also, but without a standard buy-in amount, it could be misused. For example, a player with a $100 bankroll might sit in a 1/2 game with $5. It is probably best to confine Ferguson's strategy to no limit. Ferguson's approach also reduces risk by limiting how much money you can have in front of you at a table, which is not something the conventional rule addresses.

A third strategy operates from a risk of ruin perspective. On this strategy one chooses an acceptable level of risk and determines the necessary bankroll given one's playing style. While the first two strategies appear sound, this final approach is more precise and can be tailored to your own game rather than a blanket rule that will not be appropriate for many players. How does this work? You will need to know your win rate and your standard deviation. I'll assume readers understand win rate, so I'll only explain standard deviation. Standard deviation is a measure of the distribution of your wins and losses in each session around your win rate. Thus, if you play five sessions of an hour each, your win rate would be $16/hr and your standard deviation would be $68.95/hr given the following results:

Session 1-won $30
Session 2-lost $50
Session 3-lost $100
Session 4-won $75
Session 5-won $125

How do we calculate the standard deviation? If you have a tracking program, it will probably do this for you, but if you do not have such a system you will need to calculate it yourself. Once you know how, it is relatively simple. You first need to standardize all session amounts into $/hr. In the example above I made this unnecessary by stipulating that each session was an hour in length. If, however, the first session were two hours in length, then you would refigure the amount as $15/hr for that session. Second, you determine the difference between each session result and your win rate. So, for example, you would subtract $16 from $30 for the first session to get $14, and so forth. You then square all of these numbers; i.e., $14 times $14 and so forth, and take the sum of each square. Finally, you will then average this sum.

So, in our example, you would divide 23,770 by 5 (number of sessions) to arrive at a variance of 4754. To determine the standard deviation you then take the square root of variance, which in this case is $68.95/hr. If you want to calculate your bankroll requirement, however, you only need the variance number. One final note: as a rule of thumb, you should have at least thirty sessions of data before you can expect a reasonably accurate standard deviation number. I've used only five to simplify the discussion.

Once we have these figures we can then determine our bankroll requirement. The bankroll formula is: -(SD*SD)/(WR*2)ln(risk of ruin). NOTE: standard deviation (SD) times itself (SD*SD) is simply variance. You can calculate for any risk of ruin you like, but if you are playing professionally you will want a minimum of 1% risk of ruin. With this number your chances of going bust are only 1 in 100. You could work with an even smaller risk of ruin, but this can get rather conservative. As a shorthand reference, the ln(1% risk of ruin) is -4.605 and for 0.1% it is -6.908. Now, if we continue with our example, a 1% risk of ruin requires a bankroll of: [(4754)/(16*2)](-4.605), which reduces to -[4754/32](-4.605), and this equals $3420.65. So, in our example the pro would need a bankroll of $684.13 to play in the current game with a 1% risk of ruin.

Now, that is the basic approach, but an important wrinkle must be borne in mind. If you were to withdraw all of your winnings, your risk of ruin would actually be 100%. Why is this? If you play indefinitely, never replenishing the bankroll, the natural variance of the game would gradually deplete the entire bankroll. It might take a long time for this to happen, but you can be reasonably certain that it would happen.

Professional players take a certain portion of their winnings for living expenses, but leave the remainder to grow the bankroll. The remainder is what I will refer to as the effective win rate. Thus, I will distinguish between the table win rate (i.e., what you make playing at the table) and the effective win rate (table win rate minus withdrawals for living expenses). For example, if a pro makes $20/hr playing at the table but withdraws $15/hr as her salary then her effective win rate is only $5/hr. This is rather important as the difference between the table win rate and the effective win rate generates vastly different bankroll requirements. Consider a pro who makes $20/hr at the table but whose effective win rate is only $5/hr and who also has a standard deviation of $100/hr. If we solve for a 1% risk of ruin with the table win rate, we get a bankroll requirement of $1151.25. If we solve for the effective rate, however, we get a bankroll requirement of $4605. Now that's quite a difference!

This difference underscores the advantage of this third bankroll strategy over the two previous strategies. Neither the conventional rule nor Ferguson's strategy accounts for the difference between a table win rate and the effective win rate. Moreover, neither strategy is equipped to take account of differing table win rates and standard deviation for varying players. Ferguson's strategy is conservative enough to keep one out of trouble, but it may also hold one back. The conventional rule may mislead players by requiring more bankroll than they actually need or by requiring too small a bankroll for what they need. Nevertheless, if your bankroll were to meet all three requirements, this should provide a good deal of psychological comfort.

Your comfort level is the final aspect of bankroll. I want to mention before getting into a more detailed analysis of how to use these bankroll requirements in actual practice. Part of the reason why you want to calculate your bankroll requirement is to know where you stand. If you know that you have a bankroll large enough so that your chances of going broke are only 1 in 100 or 1 in 1000, this provides the peace of mind to allow you to continue playing your A-game even if you lose a few buy-ins in the course of a session. Your own psychological comfort is important, and this is purely subjective. If, however, you understand the three basic rules and what they explain, this should give your subjective intuition some grounding in reality. This is important, particularly, for those who are more conservative and might hinder their development as players and consequently their ability to earn income by being overly cautious.

Continued in Part II

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