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?