Efron's Dice
Mathematical Modeling
The idea for non-transitive dice has been around since the early 1970s
Introduction
"However, the remarkable reversing property is not true for all sets of non-transitive dice, for you do need to pick your values carefully. For example, here is another famous set of non-transitive dice; it is a set of four non-transitive dice known as `Efron Dice' and invented by the American statistician Brad Efron" James Grime
Guiding Questions
- What is the sample space for this scenario?
- How can you calculate the theoretical probabilities?
- What simulation methods could you use to verify your results?
- How does changing parameters affect the expected outcomes?
- What are the limitations of your probability model?
Key Mathematical Concepts
Game Theory
Probability Theory
Randomness
Statistical Analysis