Bankroll management: What’s the big deal?

By Bernard Harris

Ask a hundred pros to list the top three most important aspects of poker and bankroll management (BRM) will make the list every time. Why is BRM so important? Simply put, if you are a breakeven or winning player and follow proper bankroll management, you will never go broke. This statement is not conjecture, hyperbole, or opinion but cold, hard, mathematical fact.

When most players think bankroll management they think “bankroll.” A bankroll is the money a player has allocated to play poker. If said player has $2,600 squirreled away for poker, then his bankroll is $2,600. If he has an initial poker roll of $1,400 and diverts $300 per week from his paycheck to poker, then his bankroll is $2,600 per month (adjusted as a function of his roll and paycheck). Most players compare their bankroll, in this case $2,600, to the game they wish to play. If said player wishes to play $2/5 no-limit and the minimum buy-in is $200, then he will often think his bankroll is sufficient. After all, he can buy into the game several times over. Surely, this is proper bankroll management?

Bankroll management is more than just having enough money to buy into a game for its minimum. BRM means having enough money to play optimally and weather the storm of variance (i.e., bad beats). So how much do you need to play a particular game? Assuming you are a breakeven or winning player, your bankroll needs to be at least 20 buy-ins for no-limit games (a buy-in is 100 big blinds) and 300 big blinds (BB) for limit games. So, if you play $1/2 no-limit, then you need a minimum roll of $4,000 and if you play $3/$6 limit then your roll should be $1,800.

The above buy-in requirements come from calculations based on variance. If you were to construct a no-limit (or limit) poker math model factoring in the rake, hero average equity advantage of 13 percent (heads up or adjusted for multiple players), and hero stepping on a land-mine eight percent of the time (i.e., villain flops a set to Hero’s over pair), then you would produce a chart that goes up and down like the Dow-Jones with a general upward trend.

However, despite the long-term up­trend you will see some downswings of 10, 15, and even 20 buy-ins; hence the requirement to have 20 buy-ins! Please note the above model does not include meta-game variables such as tilt, fatigue, and human error which can worsen a downswing.

When we play, we have no idea where we are sitting on the above curve. We could be on the verge of an epic 30 buy-in upswing or a tragic 20 buy-in death spiral. But if we are a breakeven or winning player and follow proper BRM then we can overcome all the negative variance we en­count­er and never go broke! Notice how despite the downswings, the chart’s general long term trend is upwards! Conversely, if we decide to play a game for which our bankroll is under 20 buy-ins (i.e., playing $2/5 no-limit with a bankroll of $3,000) then we become vulnerable to variance. If we are under-rolled, we could play 100 percent perfect poker, encounter a patch of bad variance (like hands 10K – 13K), and go bust.

Tournaments are another area in which bankroll management applies. Due to the top-heavy pay structure of tournaments, time constraints, and the escalating blinds, tournaments have tremendously more variance than cash games. As a result, proper BRM dictates that you should only spend two percent to four percent of your bankroll on a tournament. So, if your bankroll is $5,000, then you should only play tournaments with entry fees of $200 or less. The following poker math model shows how variance can impact tournament results for a winning player. The tournament in question is a $180 tourney (150 people) with the typical 10 percent top-heavy payout structure. We will assume hero finishes in the money 15 percent of the time and that out of that 15 percent he places in the top three places 30 percent of the time. The following graph shows hero’s results ran twice. As you can see from the graph, in the first simulation, hero got off to a good start. Unfortunately in the second simulation, hero went 36 tournaments without a major win. Both players experience 10, 15, and 20 game downswings but because they followed proper BRM they didn’t go broke before a major win replenished their rolls!

The mathematics behind bankroll management is based on the same principles that have built Las Vegas. Simply put, proper BRM means playing within your means and having a big enough bankroll to handle the negative variance which is inherent in poker. The variance lends itself to calculations which result in the accepted BRM requirements of 20 buy-ins for no-limit and 300 BB for fixed limit. Similarly, given the increased variance in tournaments, no more than two percent to four percent of your roll should be spent on a particular tournament. Follow the above BRM practices and you’ll never have to worry about going bust!