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More than a year after I first met Doctor James Grime and his non-transitive dice I had the idea to combine his mathematical discovery with his love of juggling and create a set of juggling balls.

The free pattern also contains instructions for making the dice in plastic canvas.  

Grime Dice are a set of five dice with the numbers arranged so that you can always choose a dice that will, over time, beat the dice chosen by your opponent. They are known as non-transitive dice. Using dice A, B and C, A will beat B, B will beat C and, amazingly, C will beat A. Several sets of non-transitive dice have been documented. Grime Dice are slightly different because you can use a set of 3 or a set of 5 and you can also change the order in which they work by choosing to use two sets of dice. There are several different tricks that can be employed to beat the opposition. If the opponent works out the trick you are using you can use different rules to ensure that you will still win. You can even play against two opponents at the same time - and beat both of them.

The chances of winning rely on the probability of the score of each dice. The names of the colours are very important to learning the tricks to enable you to win.

Click to download the pattern

The pattern does not include information about the mathematics or about how to choose a dice that will win. This information is available on the internet in videos and other resources created by James and other mathematicians.

In this video James is juggling with the dice and includes some information about them.

Be aware that there are some older web pages where you might find dice with different colour/number combinations from those shown here. The colours used in this pattern are the same as those used for the ‘official’ Grime Dice that you can buy from Maths Gear.