As a follow-up to this post, I found out why the same numbers were always coming up. It has to do with the sorting of the numbers and the distribution it produces.
(right-click and save image to view it at full resolution)
In a nutshell, if you simulate 1,000,000 lottery tickets and plot the frequency of the sorted numbers at each position, you get the graph as above. Increasing the number of simulated draws just improves the normality of the distribution at each position.
Not rocket science, but still a pretty picture :)