Games Without Chance: Combinatorial Game Theory

Open Online

Course Description

This course explores the mathematical theory of two player games without chance moves. We will cover simplifying games, determining when games are equivalent to numbers, and impartial games. Many of the examples will be with simple games that may be new to you: Hackenbush, Nim, Push, Toads and Frogs, and others. While this probably won’t make you a better chess or Go player, the course will give you a better insight into the structure of games.

How You Will Benefit

Upon successful completion of this course, participants will be able to understand:​

  • Definition of game inequalities in terms of who does better; problem and solution.
  • Simplicity and numbers; how to play win numbers; students will be able to determine which games are numbers and if so what numbers they are.
  • Simplifying games: dominating moves, reversible moves.


This is a university level mathematics course. While there are no specific mathematics prerequisites, it is highly recommended that students have taken rigorous college level mathematics courses (AP calculus counts as such).

Ready To Get Started?

This Open Online course is brought to you in partnership with Coursera, an online learning platform. If you’re ready to register now, you will be directed to the Coursera website.


Register on Coursera


  • What is a Combinatorial Game?
  • Playing Multiple Games
  • Comparing Games
  • Numbers and Games
  • Simplifying Games
  • Impartial Games
  • What You Can Do From Here


Technology Requirements

Verify you meet the minimum technology requirements for this section.

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Course Info

Course ID: DL 0010M
Course Format: Online