Playing with Probability - Efrons Dice/teaching approach

We are used to the idea of transitivity, where we can ascribe an order to events. Efron’s dice are non-transitive and probability methods that the pupils are familiar with can be used to explore how to play a game using them. This provides a discussion⁽ⁱ⁾ topic for joint reasoning⁽ⁱ⁾ - whole class⁽ⁱ⁾ or in group work⁽ⁱ⁾. Pupils can explore aspects of mathematical thinking⁽ⁱ⁾ particularly with relation to probability.