Games have been of interest to mathematicians for many years because they can be mathematical models of simple, real life situations. This paper will explore various mathematical aspects of the game RISK. By using probability theory and Markov chains, the following two questions will be answered: 1) What is the probability that if you attack a territory, you will capture that territory? and 2) If you engage in war, what is the expected number of losses based on the number of defending armies?

Author Bio

I am currently a senior Mathematics major/Business minor at Elon University and will be graduating in May 2002. This work originally started in my Senior Seminar class under the mentorship of Dr. Crista Coles. After the class ended, I continued to do research because I truly enjoyed what I was doing and was supported by the Elon University A.L. Hook Endowment. This paper was presented at the Conference for Undergraduate Women in Mathematics at the University of Nebraska-Lincoln in February 2002 and at the Joint Meeting of the MAA and AMS in March 2002. My future plans consist of attending graduate school next year in an Applied Math or Operations Research program.