I believe there is a major, possibly even fatal flaw with all the work currently done on gambling variance - the use of standard deviation as the measure of the variance being measured. SD assumes the distribution of observations is symmetrical around the mean; i.e., that the normal distribution is the correct statistical model to use. However, this is often not the case: a successful player will have a significantly positively skewed distribution of returns, and vice versa for the consistent loser. This means that even if the better player has a high SD, much of it will be "good" variance. Again, vice versa for the loser. The conclusion is that a better measure of this variance is the 2nd degree lower-partial moment (LPM2). LPM2 essentially captures just the variances below the mean and, since it is distribution-free it avoids the fatal flaw of SD in an asymmetric world. In the financial investment world where this measure has replaced SD, LPM2 is known as "Downside Risk", and has now become the risk measure of choice for the non-normal investment distributions that are typical for derivative and hedge fund strategies. For addition material on this concept see my website
www.investmenttechnologies.com.