Physicopoeia

φυσικοποιΐα
THINGS I WISH I'D KNOWN WHEN I STARTED TEACHING PHYSICS

What should the 'Half Life' of my dice be?

Rolling a number of dice and removing those which turn up a certain face on each throw is a very popular and worthwhile activity for pupils getting to grips with the idea of radioactive decay, randomness and half-life. You should find that the half-life of a set of dice in this activity is a bit less than four throws.

 

Once you've taught the idea of half-life, you might get pupils asking what the 'half-life' of a set of dice should actually have been in theory. Depending on how you try to get an answer to this question, though, you might get one of two apparently contradictory results. The pdf below sets out the apparent paradox, whilst the Excel file contains data that I'd ended up keeping (for no particular reason) over ten years of classes doing this experiment. It's interesting to compare the half life from this aggregate of results with the two seemingly contradictory theoretical results:

Rolling Dice totaliser.xlsx

Dice Half-life problem.pdf

Murray and Hart's (2012) paper examined the mathematics behind this 'paradox' in more detail. Some related points about exponential decay models can come out of discussing iterative methods of capacitor discharge, especially the graphs that result.