OK, so they are not really dice, just wooden cubes with one side painted a darker colour. And they are not actually radioactive. But we use them to show what happens during radioactive decay. We say that the dice represent the NUCLEI of unstable radioactive atoms. We gather up 30 dice and drop them onto the table all at once. Any that come dark side up are said to have decayed. There are 4 in this picture. They are taken out and put on one side, The other 26 are scooped up and dropped again. The process can be repeated until only one of the dice is left in. You can plot dice left in against throw number. With only 30 dice there is a lot of scatter but you can put a best fit line through. The number of throws for the number of dice left to halve is thus the half life. More advanced theory notes that the probability of any one cube being dark side up and thus decaying is 1/6. Eaach time we'd expect (1/6 x number dropped) to be taken out. The rate at which the number drops each throw dN/dt = - 1/6 x number left in. This can be integrated to give number left in N=N0exp(-1/6xt). For any radioactive isotope, there is a different probability of a nucleus decaying. Instead of 1/6, this is called the decay constant lambda. Half life = Ln2/lambda.
