The point of the simulation portion was really to just explain that even though you know almost nothing about the theoretical behavior (from a probabilistic poi

The point of the simulation portion was really to just explain that even though you know almost nothing about the theoretical behavior (from a probabilistic point of view) you can just apply what happens at each time point over and over to get an idea of how it behaves. For example, using basically the same process of building from a base case to simulating a system, a few months ago, I was interested in determining roughly how many packs of cards from a certain game I would need to open to be reasonably sure I would have all card in the set. I took some probabilities that I'd gotten from other people opening hundreds of packs, and used that to simulate opening one pack. I then performed about a thousand runs of opening packs until I got every card and recorded the number of packs it took each time. In the end I got a really nice normal distribution of the estimate of the mean number of packs it would take to get every card (hooray for the central limit theorem!).