The Gambler's Ruin problem is a simple problem in probability which can be solved exactly. For this reason we can use the problem to illustrate simple relationships in probability and other areas of mathematics. In this chapter concepts from probability and statistics as well as ordinary differential and difference equations are presented in the solution of the Gambler's Ruin problem. The actual solution of the simplest case of the Gambler's Ruin problem can be obtained by solving a second order constant coefficient difference equation. This topic may not have been covered in a standard undergraduate curriculum. However, the extension of the solution technique for solving constant coefficient second order differential equations is easy. Students should be able to see that the techniques that have been learned in a standard ordinary differential equations course can be modified to solve new problems.
In addition, the use of simulation is presented as a means for approximately solving the problem. Code is developed that can be used to simulate the process related to a gambler playing a game many times. The results of the simulations will approximate the exact solution and can be compared to the exact solution.