I did not quite get the example with the bets. It is not clear what kind of problem the fat tails bring compared to normal as long as the distribution is symmet

I did not quite get the example with the bets. It is not clear what kind of problem the fat tails bring compared to normal as long as the distribution is symmetrical. There is a term for dealing with actual distributions that differ from the one you put as basis in your theory. http://en.wikipedia.org/wiki/Robust_statistics http://en.wikipedia.org/wiki/Robust_statistics Regression analysis and particulary ANOVA are sensitive to http://en.wikipedia.org/wiki/Heteroscedasticity http://en.wikipedia.org/wiki/Heteroscedasticity but may be less sensitive to fat tails as long as the standard deviation is independent from the mean.