During the past twenty years, physicists have been using "chip-firing games" to model events in such naturally occurring systems as the earth's crust, snowfields, and the human brain. These chip-firing game models have been studied primarily via computer simulation. It is the purpose of my dissertation to investigate a chip-firing game using a strictly mathematical approach, thereby producing a method for analytically determining the probability distribution of the length of a game on a given connected graph. In this talk, I will introduce the audience to chip-firing games and contrast the simulation approach with the new analytical methods.