Carcassonne in the Classroom

Document Type


Publication Date

September 2017

Journal Title

The College Mathematics Journal






“What is the probability of choosing a green ball from an urn with three blue balls,five green balls, and seven yellow balls?” Many students not only struggle to engage with this sort of question but are left wondering why the world of mathematics is obsessed with balls and urns. The variety of approaches to choose from makes probability a difficult subject for many students, yet probability is an important part of quantitative literacy since it is prevalent in everyday life. Finding ways to clarify probability for undergraduates is key to a successful mathematics experience. One strategy for increasing student engagement with probability concepts is to teach probability through its application to games. Many previous works have investigated the use of Markov chains to model board games, such as Chutes and Ladders [2, 4, 5], Monopoly [1, 3], and Risk [6, 7, 8]. While these works have primarily focused on understanding the various games for their own sake, in this article we focus on using the board game Carcassonne in the classroom as a path for students to learn about probability through a more interesting context. In particular, we give a sequence of increasingly difficult probability problems derived from Carcassonne that can be used in a wide range of undergraduate mathematics courses.