is an article you might find interesting:
- Chris "Fox" Wallace
It has occurred to me recently that many people have questions about bankroll management that aren't easily answered with just a simple number or a formula. This article should give you some ideas about how to think about your bankroll and what you need to know to come up with a reasonable bankroll strategy for yourself.
I'll start with a few numbers for reference. These aren't exact numbers, but they are a good place to start, and for our purposes they will do just fine. Below there are three columns. The numbers in the "Pro" column are for players who derive the majority of their income playing, and would be devastated financially if they lost their bankroll to a bad run of cards. Using these figures will yield a less than 1% chance of going broke over the course of a lifetime of play assuming that you are a solid winning player.
The numbers in the "Protected" column are for a bankroll that you are going to attempt to make a serious income from. If your bankroll will be tough to replace if you lose most of it then you should use these numbers.
The Unprotected" column is for people who are willing to play a little looser in an attempt to build a bankroll, and for those of you who could easily replace your bankroll if you were to lose it. Keep in mind that using these figures does yield a significant possibility of going broke or having to drop down levels if you get off to a rough start.
Now that we have these numbers, I can teach you how to modify them and how to use them. The practical application of these numbers also requires a basic understanding of variance and what kinds of things affect it, so we'll discuss that first.
Variance is a term used to describe the ups and downs you experience in a situation where results can differ from their average in the short term. It's also a nice way to describe a losing session.
Hatfield: "How'd you do today Fox?"
Fox : "Lots of statistical variance."
Hatfield: "How much are you stuck?"
Fox: "About $600"
Lots of things can increase or decrease your variance. If you read my previous bankroll article on limit Hold Em then you have seen some of the factors in the formula I presented. I'll do my best to present them in order of importance.
Your win rate is the single biggest factor in determining the variance that directly affects your bankroll. A solid 2BB/100 winner in a limit Hold Em game is not likely to see a downswing of more than 300 big bets very often, and (if he is lucky) may not see one in ten years. If that same player moves up to a tougher game where he is only winning half a big bet per 100 hands, a downswing of 300 BB's could occur every year or two. Hit the books and improve your game, and your variance will decrease as well.
Your mental stability will also affect your variance a great deal. That 60 BB downturn will turn into a 200 BB losing streak if it affects your mental state, and a small losing session can turn into a serious beating if you let it put you on tilt instead of getting up from the game.
Your playing style will affect your variance as well, though usually in small chunks rather than large ones. A very loose aggressive player who is winning at the same rate as a tight solid player will see more small ups and downs. Using limit Hold Em as an example, the loose aggressive player, no matter how good he is, will see more 50 BB swings than a tight solid player. If loose aggressive gets you a higher win rate then you shouldn't change your style, you simply need a little larger bankroll and the ability to deal with frequent swings.
Your opponents playing style can also affect your variance. If your opponents are loose and aggressive, or simply loose and unbluffable, then your variance will rise slightly. This is somewhat offset by the fact that your overly loose opponents will be idiots, and your win rate will be higher in these games.
In multi-table tournaments the payout structure and the size of the field will have a huge affect on your variance. The larger the tournament the less often you will make the top three where the big money is. Lots of misses and the rare big win is a recipe for high variance. The numbers in the chart above assume an average field size of 200. In the very large tournament fields, with buy-ins below $30 online your variance will be quite high, though your win rate against the donkeys who populate those tournaments will help offset the huge field size.
In a very steep payout structure tournament like the OWNS tournament on UltimateBet the variance is so high that 500 entry fees might not be enough, even for a very good player. For those of you who are unfamiliar with the OWNS, it's a $50 rebuy tournament where the winner takes the whole prize pool, and it is often filled with excellent players. Scary.
Keep in mind also that the number in the chart above is assuming regular freeze out tournaments. If the tournament is a rebuy you have to assume at least four times the initial buy-in as a your actual investment. If you play a lot of rebuy tournaments it would be wise to count the number of rebuys and the add-on for a few tournaments and come up with a good idea what your average investment really is for each tournament.
In a ring game the number of players has the opposite effect on variance. Playing shorthanded or heads up can increase your variance greatly because you are forced to play a looser and more aggressive style, and your opponents will usually play a little more reckless style as well.
Heads up sit and go tournaments are a variance monster all to themselves. Your win rate will have a massive effect on your variance in heads up play, and a player who is only winning 55% of his matches will have huge swings, while a really solid heads up player with a 70% win rate can get away with using numbers only slightly larger than the regular SNG numbers. The 55% player probably can't have a big enough bankroll no matter what he does; the variance is just too high.
That should give you a pretty good idea how high your variance is compared to most players and allow you to come up with a fairly accurate number that takes into account your personal variance, and the level of risk you are willing to take with your bankroll.
Now let's take a look at a few ideas for ways to take calculated risks without worrying too much about your bankroll disappearing.
A rolling bankroll is my own personal favorite. Pick a number that is when you will move up to the next level - we'll call it your ceiling - and a number at which you will have to move down a level because of a losing streak - we'll call that your floor. When you hit your ceiling you can move up a level, and when you hit your floor you must move down. Failing to move down immediately when you hit your floor is very risky, don't do it. I use numbers for my ceiling and floor that are similar to the "protected" and "pro" columns, so we'll use those in an example.
If you are a fairly standard variance player playing 10/20 Hold Em and you know you can beat the 15/30 games as well, then your floor would be 450 big bets (20*450) for a total of $9,000. Your ceiling to move up would be 750 big bets (20*750) for a total of $15,000. When you hit the ceiling and move up to 15/30 your numbers would change, and your floor would become 450 big bets at your new level, which comes out to $13,500. This means you move back down to 10/20 if you drop below $13,500. Hopefully with the information provided above you can come up with some good numbers for yourself.
Taking a shot at a big payday is nearly impossible to resist on occasion, especially for tournament players. If done judiciously, and in circumstances where your win rate is likely to be very high this won't increase your variance too terribly.
For ring game players I recommend that you never move up more than one level, and that you set yourself a specific number that you can lose at the higher level before you end your little adventure. This number should be less than 10% of your bankroll, and it is not a practice that you should engage in with any frequency. I will occasionally step up a level when I see one of my favorite fish at a table, but otherwise it's just too risky. Losing 5% of my bankroll ruins my day entirely and takes me a week to win back, making the risk only worthwhile if I can expect a much higher than average win rate at the higher table.
For tournament players taking a shot can be playing a tournament with an overlay even if it's twice your usual buy-in, or playing a few satellites to win your way into a big tournament. The BoDog 100k guarantee is a good example of a place to take an occasional shot. The terrible players, combined with a large overlay make this tournament very profitable, even if it is a little above your usual comfort level. No matter what your reasons are for taking a shot at a larger tournament, the buy-in should never exceed 5% of your bankroll, and these excursions into deeper water should remain few and far between.
Hopefully this article gives you all the tools you need to understand bankroll management. Feel free to email me at firstname.lastname@example.org
with any questions or suggestions you may have.
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