The distributions of the run occurrences for a sequence of independent and identi cally distributed (i.i.d.) experiments are usually obtained by combinatorial methods and the resulting formulae are often very tedious, while the distributions for non i.i.d.experiments are generally intractable.It is therefore of practical interest to find a suitable approximate model with reasonable approximation accuracy.In this talk, we demonstrate that the negative binomial distribution is the most suitable approximate model for the number of runs: it outperforms Poisson approximation and general compound Poisson approximation.Moreover, we show that the accuracy of approximation in terms of the total variation distance improves when the number of experiments increases, in the same way as the normal approximation does in the Berry-Esseen theorem.This is a joint work with Xiaoxin Wang.