The Way to Win: An Introduction to Game Theory

Mathematicians have studied games for over a century. How do they analyze them? In this course, we'll learn combinatorial game theory pertaining to games of perfect information, such as Go and chess. In these games, there are no dice or hidden cards; all game information is known to players except their individual strategies. In this introduction to combinatorial game theory, we'll learn mathematical concepts such as disjunctive sum and Grundy numbers, and use them to explore winning strategies in games such as Nim, Domineering, and Hackenbush. Between class meetings, students will also explore optional readings and resources, and dive deeper into the history and application of combinatorial game theory. Time Commitment: 2-4 hours per week (90-minute synchronous class times and 1-2 hours of independent work per week). Course will include 6 sessions over 6 weeks. Course Overview Learning Objectives: Define games of perfect information and their main types: impartial games and partizan games Apply basic terms and concepts in combinatorial game theory to games of perfect information Develop winning strategies for games of perfect information Identify winning and losing positions in impartial games such as Nim Distinguish between different types of positions in partizan games such as Domineering and Hackenbush Compute winners of simple disjunctive sums using Grundy numbers Test your strategies by playing games with classmates, family members, and friends