Sum of roll of N dice

[Jim Horn]

One minor issue for using a single random number to simulate rolling N dice which each have S sides: if S^N > 10^(number of significant digits), then the simulation fails in that not all possible dice rolls can be represented (the pigeonhole principle). After all, any random number function can only attain a finite number of output values but a large number of dice could exceed that number of states.

I'm sure the statistics of such a limited situation wouldn't be far off of theory, though.