# Games without Chance: Combinatorial Game Theory

Georgia Institute of Technology

This course delves into the complex world of combinatorial game theory, offering a comprehensive understanding of mathematical strategies and analysis in games devoid of chance. Through a series of engaging modules, participants will explore the nuances of various game types, from simple two-player games to impartial games and infinite games. The course provides a deep dive into the mathematical theory behind these games, offering participants the opportunity to develop advanced problem-solving and strategic thinking skills.

Participants will embark on a journey through the following modules:

• Week 1: What is a Combinatorial Game?
• Week 2: Playing Multiple Games
• Week 3: Comparing Games
• Week 4: Numbers and Games
• Week 5: Simplifying Games
• Week 6: Impartial Games
• Week 7: What You Can Do From Here
• Resources

This course is designed for individuals with an interest in mathematics, logic, and game theory. It is particularly beneficial for students, mathematicians, and individuals interested in honing their strategic thinking and problem-solving abilities.

Certificate Available ✔

##### Course Modules

The course delves into various topics, including understanding combinatorial games, playing multiple games, comparing games, numbers and games, simplifying games, impartial games, and potential game outcomes.

#### Week 1: What is a Combinatorial Game?

Week 1 of the course introduces the concept of combinatorial games, focusing on the basic elements of two-player games without chance. Participants will explore the fundamental principles through engaging lectures, problem-solving exercises, and quiz reviews.

#### Week 2: Playing Multiple Games

In Week 2, participants will delve into the intricacies of playing multiple games, including Cutcake and Adding Games. The module provides in-depth insights into various game types and offers ample opportunities for practice and review.

#### Week 3: Comparing Games

Week 3 delves into comparing games, exploring the concept of ordering games and examining examples of games that are not numbers. Participants will engage in problem-solving activities and quizzes to reinforce their understanding.

#### Week 4: Numbers and Games

Week 4 focuses on numbers and games, delving into the relationship between numbers and games and exploring the concept of simplicity in game theory. Participants will engage in problem-solving activities and quizzes to test their knowledge.

#### Week 5: Simplifying Games

Week 5 explores the process of simplifying games, introducing new methods to simplify games and providing examples from Nim, Toads and Frogs, and General Reversible. Participants will engage in problem-solving activities and quizzes to reinforce their learning.

#### Week 6: Impartial Games

In Week 6, participants will delve into impartial games, exploring the strategies to win in games such as Nim and understanding the concept of Mex. The module offers problem-solving activities and quizzes to test participants' comprehension.

#### Week 7: What You Can Do From Here

Week 7 delves into advanced game concepts, including infinite games, loopy games, and mean values. Participants will explore these complex game types and engage in bonus quizzes and surveys to assess their learning outcomes.

#### Resources

The Resources module offers additional materials and references to further enhance participants' understanding of combinatorial game theory.

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