Education Technology

Great Expectations

Activity Overview

This activity uses a combination of simulation and simple probability tree diagrams to explore a set of dice with some very unusual characteristics. Grime Dice, created by Dr. James Grime are used in the initial investigation, however Efron dice and other non-transitive dice can be explored in the extension section of the investigation.


  • Use simulation to estimate probabilities;
  • Use probability tree diagrams to determine exact solutions;
  • Understand the limitations of the expected value;
  • Discover the non-transitive property of different sets of dice;
  • Establish strategies for exploring chance events.


  • Tree diagram
  • Simulation
  • Transitive
  • Expected Value

About the Lesson

Two people select one of the three special dice on offer in this activity,. All dice have the same expected value. The person rolling this highest number is the winner. Is the game fair? Explore this activity: "Great Expectations" to reveal the answer, then explore different dice. The results will amaze and are guaranteed to challenge your thinking.