Distribution of sample means explanation Say a casino has N slot machines all with the same expected value and standard deviation. Why is it when the standard deviation gets really large you end up with more machines under the expected value than over? I understand that the average of the samples will be approximately the expected value of the slot. But the samples means don't appear to be normally distributed. This seems not to be in line with the central limit theorem. I am wondering what bit I have confused. Thanks! 
 A: Having looked at the paper you linked, it comes down to a word that even they use - skewness. While some random distributions, like the normal distribution, are nice and symmetrical, many of them aren't. Often, especially when we look at things relating to money or other quantities, the distribution will have a big peak in small values, and a long tail of rare but large values. When that happens, the mean, or expected value, of the distribution will tend to be larger than the median, or middle value.
For example, consider a 6-sided die where 5 of the sides have one pip, and the remaining side has 16. The expected value of a single roll is $\frac{1}{6}(1 + 1 + 1 + 1 + 1 + 16) = 3.5$, just like a normal d6. But the probability that a single roll will be less than that value is $\frac{5}{6}$, because of the way the sides are distributed.
Similarly, poker machines are often designed so that the vast majority of their payouts are minimal, with a couple of very big, but very rare, jackpots. So if you measure "proportion of payouts less than the average payout", you're going to get a number bigger than 50%.
A: Continuing my Comment with a concrete example:
Suppose a slot machine pays \$1, \$10, \$100, and \$1000 with probabilities
proportional to .1, .01, .001, and .0001 respectively. (Approximate
probabilities  0.90009001, 0.09000900, 0.00900090, and 0.00090009 would 
accomplish that.) The average amount won 
in one play is \$3.60 and the SD is about \$31.42. 
Simulating the average winnings per session after 100,000 sessions
of 1000 plays each of such a slot machine, I
get the following histogram for the average winnings. The distribution
for one play is so extremely skewed that not even the average of 1000 plays is 
anywhere near normal.

