Caught “Red”-Handed? The Probability of Randomly Constructing a Legal Catan Board

Abstract

SummaryCatan is a dynamic property-building and trading board game in which players build a new board every time they play by arranging tiles, number tokens, and port markers. In the interest of creating an equitable board, the official Catan rules restrict how the number tokens are placed. In this paper, we use three techniques to count the number of nonequivalent boards satisfying this restriction, as well as determine the probability that a randomly generated board will be legal. AcknowledgmentWe thank the anonymous referees whose time and attention supported the publication of this work.Additional informationNotes on contributorsJathan Austin Jathan Austin (jwaustin@salisbury.edu) is an associate professor of mathematics at Salisbury University in Maryland. He earned a B.S. in mathematics from Salisbury, and both an M.S. in mathematics and a Ph.D. in mathematics education from the University of Delaware. In his spare time he enjoys doing jigsaw puzzles and watching classic sci-fi.Brian G. Kronenthal Brian G. Kronenthal (kronenthal@kutztown.edu) is a professor of mathematics at Kutztown University of Pennsylvania. He earned his B.S. in mathematics from Lafayette College (Easton, Pennsylvania), as well as his M.S. and Ph.D. in mathematics from the University of Delaware. His favorite research problems are combinatorial, often with an algebraic flair. In addition to teaching and research, he enjoys playing ping pong, watching movies, and rooting for Philadelphia sports teams.Jonathon Miller Jonathon Miller (jonathonamiller@gmail.com) is a software developer for Amazon. He earned his degree in mathematics and a minor in computer science from Salisbury University in Maryland. He also earned his MS in mathematics from The University of Delaware. In his free time Jonathon enjoys being a husband and father, playing board games, and serving as an excellent DM for Dungeons and Dragons.Susanna Molitoris-Miller Susanna Molitoris-Miller (susannamolitorismiller@gmail.com) earned her B.S. in mathematics from The University of Scranton, and M.S. in mathematics and Ph.D. in mathematics education from The University of Delaware. Susanna’s research focuses on how students learn mathematical concepts in creative ways. In her free time she enjoys spending time with her family, fiber arts, tea and, of course, game night with friends.