Grime Dice
Dr. James Grime has created a fascinating set of unusual dice which are pictured above.
They are examples of “Non-Transitive Dice” and we’ll explore later on just what is meant by “Non-Transitive Dice”
The dice are arranged in alphabetical order.
Here is a game you can play with a friend. It is a game for two players, with this set of five dice.
Your friend picks a die and you pick another. The two dice are then rolled together and whoever gets the highest value wins. Seems fair enough yet, in a game of say ten rolls, you will always be able to pick a die with a better chance of winning - no matter which die your friend has chosen.
Let’s explore some possible outcomes.
Let’s summarise the results so far.
It appears that Blue is the “strongest” die and Yellow is the “weakest”.
This would appear to be a case of the dice being “Transitive” because the winning property is transferred in a linear, finite manner.
But let’s just check this by playing the Yellow Die against the Blue Die.
Now let’s update the summary.
The winning property is no longer transferred in a linear fashion but instead loops round.
This is why we call the dice “Non Transitive”.
Bizarre! But we’ve done the Maths….
Here are some more ideas to explore.
Based on what you have just seen, can you find a strategy which will ensure that when you play against your friend in a game of say, ten rolls, you are always more likely to win?
And what happens if you arrange the dice according to word length?
Or change the game so that each player picks two dice of the same colour?
Have fun!