Bankroll Basics - How Much Do You Need?

Managing your money appropriately in poker requires, among other things, a good sense for what is an adequately sized bankroll, where "adequate" means you are unlikely to go broke over some period of interest. There have been some excellent technical discussions of bankroll size in the poker literature, some of the best of which can be found online in the archives of the newsgroup rec.gambling.poker.

My goal in this column isn't to delve into the mathematical intricacies of risk, ruin, and bankroll, or even to give you some ballpark estimates. Instead, I'd like to make some simple points that are usually assumed in the context of these discussions, but not always raised explicitly. These issues are masked in some common assumptions underlying questions about bankroll. For example, questions like "How much of a bankroll do you need to play game X?" are often assumed to refer to a player with a solid positive expectation (one big bet per hour), who neither extracts nor adds money to the bankroll, whose expectation and variance are stable, and who wants to know how much money he needs to keep in his shoebox in order to continue playing poker indefinitely. Although these assumptions provide a workable reference point, generic recommendations are rarely appropriate in practice. Unfortunately, people often repeat legitimate bankroll recommendations outside of the context in which they were sensible.

Before anything else, some terminology. People who ask bankroll questions may have little idea if they are winners or losers, and simply want to know how much money they need in order to play for a limited period of time: a session, the duration of their vacation, or until their next paycheck. These are all legitimately described as "bankroll" questions, even if the usual sense for poker players means, roughly, a lifetime bankroll. It's reasonable to use phrases like "monthly bankroll" to refer to the amount of money a given player would need to stay in action for an entire month. Another term that comes up often is "risk of ruin," a phrase that (not surprisingly) refers to the chance you'll run out of chips and be unable to continue playing. Since winning players are much more likely to run bad in the short run than in the long run, the critical bankroll question for many players is how much they need to play in a given game, minimizing their chances of running out of chips along the way.

The most important foundational concept in gambling and risk is variability of outcome. Some days you win, some days you lose. If there were no variability in your outcome over some small unit of time or play, bankroll issues would be simple. Winning players would not have to worry about going broke, and losing players would know exactly how many hours they could play on their available money. However, we all know that outcomes in poker are highly variable. Winning players may lose money in a given hour, day, week, month, or year. Losing players may win over similar intervals. In general, more variability increases your risk of ruin, and therefore increases your expected bankroll size. However, this is not uniformly true. Increased variability often comes with increased expectation. The balance depends somewhat on the specific details, but it's close enough that an extraordinarily bad player in your regular game can increase your variability while reducing your risk of ruin.

Another common assumption that goes with bankroll estimates is that you're a solid winner. It's surprising how often questions about bankroll are answered with the unstated assumption that the person asking is a one-big-bet-per-hour professional player, despite the fact that winning players shouldn't even have to ask these questions. Of course, bankroll considerations are very different for losing players. But even for winning players, risk of ruin depends critically on winning rate. A player whose expected win rate is one-tenth of a big bet per hour (0.1BB/hr.) would need a much larger bankroll than a 1.5BB/hr. player, even though both players have positive expectation. A player whose expectation goes from losing 0.1BB/hr. to winning the same (after fixing a leak) may have become a winner, but he will still require an enormous bankroll to enjoy a comfortable risk of ruin in the long run. The risk of ruin doesn't magically evaporate when you cross that line.

Of course, if you're a losing player, and don't expect to get any better, an adequate bankroll has to last your lifetime. If it can be replenished from other sources, then risk of ruin is only relevant over a limited duration of time – for example, until your next paycheck. In this case, two factors allow for a smaller bankroll. First, obviously, if your money has to last only a month, you don't need as much as you would for a year. Second, your tolerance for risk may be much higher than values usually given. If "ruin" for you means giving up poker indefinitely, you may want some assurance that your risk of ruin is less than 1 percent. If it only means taking some time off before you can play again, you may be comfortable with much more risk. Even for winning players, no amount of money guarantees you won't go broke. But it's important to consider, when making bankroll decisions, what you're really risking in the event you do run out of chips.

Taking shots at bigger games also can affect your solvency, even if you do it only when you're winning. While there may be lots of good reasons to do it, it certainly exposes you to more risk. That's the whole idea – take the risk when you can afford it. A simple solution to avoid undue adverse effects of taking shots is to pre-estimate your new risk of ruin, assuming the worst outcome at the bigger table. While doing this may mean that your earlier estimates of risk were based on some faulty assumptions (that is, that you were going to play the same game during the time period of interest), they're only faulty in the case where (a) you're out-earning your expectation and (b) you're happy with the revised level of risk.

In fact, it's often worth re-estimating your risk of ruin as you go, and if circumstances permit, adjusting your game selection appropriately. Although bankroll calculations are often made with the implicit understanding that you'll maintain a constant level of volatility, that's just an expedient step to make the calculations easier. Dropping down in limits when necessary, if your ego can take it, can help reduce your bankroll requirements dramatically if your main requirement is to stay in action. For example, if you have a monthly bankroll, and you take bad losses in your first three sessions, certainly your chances of ruin that month have gone up. This doesn't mean your calculations were wrong, it just means you have more information about whether the current month is one of the 95 percent or the 5 percent, and it's not good news. If your only concern is to stay in action, dropping down to a smaller game may have several positive effects. First, smaller games tend to be easier to beat, and many players would be well-advised to drop down anyway. Second, your expectation for the rest of the month may benefit from moving down if your risk of ruin is large enough. If you double your expected number of hours played while cutting your earning rate by a third, you'll do better in the long run.

I've avoided the mathematics of bankroll calculations for a few reasons, mainly because I think it's most important to think flexibly about bankroll and ruin, and only then to worry about numbers. It doesn't pay to do all the right arithmetic only to end up with the answer to the wrong question. However, in a future column I'll run over the differences between the available approaches to bankroll issues. As poker math goes, it's really not that difficult, and well worth the effort.