I want to know how well the normal distribution explains the sum of rolls with n dice with s sides.
The mean value and the variance of the dice rolls are
$$\mu=n\frac{s+1}{2}$$ and $$\sigma^2=n\frac{s²-1}{12}$$
How many dice does it take for this to be a good approximation and is it equally good everywhere between the max and min values of the dice distribution(outside of which the probability is obviously zero while the normal distribution will approach zero)? What would this function look like?