The Poker Player’s Manifesto - Variance III

In the last two issues we have discussed everybody’s favorite friend, Variance. Some players are convinced that they cannot win because of variance, even though with that mindset variance is exactly what enables them to win. There are other players who are actually good enough to win, but variance has been against them for a while, and since they know poker is a skill game, they eventually assumed that they were wrong about how good they were and think they cannot win at poker, even though variance is exactly what has prevented them from winning. Variance is so great that there is no such thing as the long term in live tournament poker, thus all results must be taken with a grain of salt. Mark Newhouse and Leif Force and Maria Ho and Rep Porter and myself are good at the World Series of Poker main event, but not because of our successful results. We are good because of the way we approach that tournament. There are plenty of poker players out there that are better at poker than us who have never cashed in the WSOP main event, and that doesn’t make us better at the WSOP main event than them.

The long term is so much greater a spanse of time, measured in poker as hands, than most players can understand. Many think of a singular session as long term, and they somehow assume that all things should balance out by the end of the night. In a typical night of live poker, you should play a couple hundred hands depending on how fast the game is moving and how many hours you play. In the exercises we discussed last issue, we considered a sample size of 500,000 hands, equivalent to one year of online grinding, and equal to about 2,000 nights at the card room. We saw that variance rewarded one lucky guy with a great year while punishing an equally skilled player with a big losing year. Even though they had identical expectation, one year full time online was still not enough to balance the charts to expectation.

Bankroll management must be paramount when life is lived as a professional gambler. In our simulation of 1,000 years of an identical poker player, putting in equal volume with equal expectation as everybody else, our extremes were around $50,000 stuck and up $400,000. They all had expectations of $100,000 profit. Most important to me however was that nearly 30 percent of them experienced a downswing of 500 big bets. A dozen years ago when I became professional, it was popular opinion that 300 big bets was a sufficient bankroll for limit hold’em. In our model, about a quarter of those players would go broke before the end of the year, experiencing a natural downswing great enough to evaporate a 300 big bet bankroll.

So, how much of a bankroll do we need? Well, that depends on a lot of things mostly wrapped around win rate and standard deviation. The Kelly Criterion is the optimal model I know for structuring bet sizes based on expectation and bankroll. I’m not good at explaining it or utilizing it since bets within the context of poker is much more variable, but basically Kelly (a mathematician from the 50s) designed a formula to determine the fraction of a bankroll to bet given the odds received on the bet, odds of winning, and odds of losing. Simplified, the more likely you are to win your bet and the more money you will be be paid on your bet, then the more you should be betting.

Unfortunately, poker is much difficult to quantify; even if you are aware of your own personal win rate and standard deviation over a significant sample size of hands (thanks to Poker Tracker or HEM), it is still hard to apply the Kelly Criterion to deciding what stakes poker game to play, because your win rate and odds of winning are constantly changing in poker.

Start out bankroll management by betting less than you think you should be. Anybody can lose for twelve months straight. Since Kelly says that we should bet more when we have a better bet, that means that we should be willing to have more exposure to a tournament like the WSOP main event than any World Poker Tour main event. Furthermore, Kelly dictates that we should have more exposure when our probability of winning is higher, making us like the smaller field WPT events rather than the WSOP main event. Therefore, the crux lies in our win rate. The higher our win rate, the more we should bet, and with low win rates we should keep our exposure low.

So what does that mean in real numbers? I’m still not sure, but at this point in my career I get a little bit queasy having more than one percent of my bankroll on the line for any multi-table tournament. For the WSOP main event this year, I got in for a little over $2,000 of my own personal action which was about two percent of my bankroll. Twice my comfortable exposure, but it’s the WSOP main event. Colorado held a couple of $3,000 tournaments this year, the largest in the state’s history, and I played the first one twice entirely on my own roll. I was much happier getting in for three percent of my bankroll in a six-handed sit-n-go (twice) with good value than I was getting into the WSOP main event for 2 percent and six thousand opponents to defeat. Obviously, I wish I had all of my WSOP main event action over the years, but we can’t choose when variance decides to shine its winning light on us.

Bankrolls for cash games are less restrictive due to the balanced nature of the flow of money and win rates are much more predictable. At this point in my career, I am simply not comfortable sitting with less than 500 big bets in my bankroll for whatever game I am playing live, assuming a limit game. I have no idea what my win rate is online these days, if it even exists at all. For big bet games I need at least 40 buy-ins to even think about sitting in the game.

Lastly, bankroll requirements are dynamic with the quality of the game. You need less bankroll for shots at really good games with high win rates, but be aware of what a loss in a bigger game will do to your long term outlook of your regular game.

Accept variance and use it to your advantage. It isn’t going away and its existence will keep poker from going away too. ♠

Bryan Devonshire has been a professional poker player for nearly a decade and has more than $2 million in tournament earnings. Follow him on Twitter @devopoker.