Bankroll Management II - Poker Bankrolls

Master gambler Mason Malmuth is the source of a large bit of my knowledge on the idea of bankroll management and using mathematics to very specifically calculate bankroll needs. In his book, Gambling Theory and Other Topics, Malmuth actually gives us a formula based in mathematics that can help to determine our minimum bankroll necessary to play at any particular stakes. This formula is described below:

B = (1.64sigma)^2/4u
where:
u is the hourly win rate
sigma is the standard deviation per hour
B is your required bankroll

This formula assumes you have a 5% risk of ruin tolerance. So, say for instance, we win $15 an hour on average, but can win or lose up to $300 an hour in any given hour. This gives us the condition of:

u = $15/hr, sigma = $300/hr
B = $4035

In other words, we would need to have a bankroll of over $4000 to successfully compete at the stakes where these are our statistics. This obviously means that I will be starting my project at stakes where the numbers are much smaller. In my next post, I will take into account my own numbers from the last 10,000 hands of $0.1/0.2 NL Hold 'Em that I've played on PokerStars and plugging them into this formula to see what kind of a bankroll I will need to play even at this super-micro limit. I will also be introducing PokerOffice, my preferred poker tracking software and discussing some of the features that I'll be using for my poker betting throughout this project.

However, until then I recommend that you get your own copy of Gambling Theory and Other Topics and read the much more detailed description and derivation of this formula for yourself. Malmuth's book is a must-own for anyone that intends to gamble seriously with any sort of theoretical or mathematical background knowledge.