Mathematics of Tabletop Games (AK Peters/CRC Recreational Mathematics Series)

Mathematics of Tabletop Games provides a bridge between mathematics and hobby tabletop gaming. Instead of focusing on games mathematicians play, such as nim and chomp, this book starts with the tabletop games played by avid gamers and hopes to address the question: which field of mathematics concerns itself with this situation? Readers interested in either mathematics or tabletop games will find this book an engaging way to begin exploring the other topic or the connection between the topics. Features Presents an entry-level exposition of interesting mathematical concepts that are not commonly taught outside of upper-level mathematics courses Acts as a resource for mathematics instructors who wish to provide new examples of standard mathematical concepts Features material that may help game designers and developers make design decisions about game mechanisms Provides working Python code that can be used to solve common questions about games Covers a broad range of mathematical topics that could be used as survey material for undergraduates curious about mathematics. Cover Half Title Series Page Title Page Copyright Page Dedication Contents Preface Acknowledgment About the Author Image Credits CHAPTER 1: Combinatorics 1.1. SUM RULES 1.2. PRODUCT RULES 1.3. BINOMIALS AND MULTINOMIALS 1.4. STARS, BARS, AND GENERATING FUNCTIONS 1.5. COUNTING SUMMARY 1.6. LARGE NUMBERS CHAPTER 2: Geometry 2.1. REGULAR TILINGS 2.2. OFFSET REGULAR TILINGS 2.3. POLYOMINO TILINGS 2.4. REGULAR TILINGS OF SURFACES CHAPTER 3: Group Theory 3.1. GROUPS 3.2. THE LEMMA THAT IS NOT BURNSIDE’S 3.3. THE ORBIT STABILIZER THEOREM CHAPTER 4: Graph Theory 4.1. ADJACENCY IN GRAPHS 4.2. MATRICES OF GENERATING FUNCTIONS 4.3. DIRECTED GRAPHS CHAPTER 5: Probability 5.1. BASIC PROBABILITY 5.2. PARAMETERS 5.3. BINOMIAL DISTRIBUTION 5.4. MULTINOMIAL DISTRIBUTION 5.5. HYPERGEOMETRIC DISTRIBUTION 5.6. COMPARING DISTRIBUTIONS 5.7. MARKOV PROCESSES CHAPTER 6: Game Theory 6.1. RATIONALITY 6.2. SEQUENTIAL MOVE GAMES 6.3. SIMULTANEOUS MOVE GAMES 6.4. THREATS AND PROMISES 6.5. TWO WELL-STUDIED GAMES CHAPTER 7: Auctions 7.1. ENGLISH AND VICKREY AUCTIONS 7.2. BLIND AND DUTCH AUCTIONS 7.3. ALL PAY AUCTIONS 7.4. REVENUE EQUIVALENCE PRINCIPLE CHAPTER 8: Logic 8.1. COMPETITIVE DEDUCTIVE GAMES 8.2. COOPERATIVE DEDUCTION GAMES CHAPTER 9: Number Theory 9.1. THE FUNDAMENTAL THEOREM OF ARITHMETIC 9.2. MODULAR ARITHMETIC 9.3. MUXING IN GAMES 9.4. MUXING WITH SEVERELY RESTRICTED SIGNALS APPENDIX A: Resources Bibliography Referenced Games Index