You can calculate the mean μ and the standard deviation σ of a dice roll. You get μ=3.5, σ=sqrt(105/36)~=1.707... . It's not very similar to a Gaussian, but sometimes these numbers are useful anyway.
It's more interesting if you calculate the distribution of the sum of rolling 100 dices. It's easy to calculate, becuase μ=100*3.5=35, σ=sqrt(100*105/36)~=17.07... But now the distribution is very similar to a Gaussian with μ=100*3.5=35 and σ=sqrt(100*105/36)~=17.07... https://en.wikipedia.org/wiki/Central_limit_theorem They are not equal because the sum of the roll of 100 dices is bounded between 100 and 600 and the Gaussian is not bounded. For most applications, you can just use the Gaussian instead of the exact distribution.
