Variance

In gambling, as in the stock market, you must consider two things when determining whether a game or portfolio is worthwhile: volatility and expected return. In gambling, these things are usually measured in hourly rate. Most gamblers underestimate the former and overestimate the latter. In fact, most gamblers I know probably have little concept of what volatility even is. According to Malmuth in Gambling Theory and Other Topics, an expert player may have to play over 4000 hours before he can be voer 99.8% sure to be above even (based on a standard devation of $650 and a win rate of $30). That's two full years of full-time playing before you can be assured of being in the black! How many pros would have the bankroll, patience, and psychological fortitude to play that long before throwing in the towel?

Volatility is a measure of the riskiness inherent in a game. The most common and useful measure is the standard deviation. If my standard deviation in a game were $300/hour and my expected return were $0/hour, then 68% I can expect to be within one standard deviation (-$300 to $300) after one hour of play. 95% of the time I can expect to be within 2 standard deviations (-$600 to $600).

Keeping these number in mind, I've found, is very useful for two reasons. First, it keeps me humble and prevents me from putting my bankroll at great risk. Usually, doubling stakes means more than doubling standard deviation, because competition tends to be better. Also expected return will be less than double for the same reason. Thus, if I were to move up from my usual $2-5NL game to the $5-10NL game, as I planned to do in January, I would have to accept a doubling of my standard deviation, while less than doubling my expected return.

Second, knowing about these standard deviation helps keep losses in perspective. A common question gamblers ask themselves (and others) when they are running badly is "Am I playing badly or am I just unlucky recently?" If you know your standard deviation, you can at least give yourself some idea by answering the question: "If I were playing as well as I normally do, what is the likelihood that I would have lost as much as I have over the past X hours?" Usually the number will be higher than you would have expected. This doesn't quite give you the answer you were looking for ("Bad or unlucky?"), but it does give you some perspective on how much luck really does play into results. For me, this can help me to regain my confidence during a losing streak.

Most people tend to attribute their good results to skill and their bad results to bad luck. I am just the opposite. In fact this post was inspired by a statistically unlikely session I had last night, where I came out almost 4 standard devation ABOVE my mean over the course of 7 hours. Boy, was I ever lucky!

By the way, the Rio games got good again and I'm going to qualify for the WSOP freeroll tournament. I sure hope volatility is on my side again that day.