Re: Throwing dice

Roberto Avanzi wrote:
The Qurqirish Dragon wrote:
It seems that you should be able to do this as a sum of multinomials.
The problem is that there will be a huge number of terms, since there
are six possibilities.

Yes, that's the approach I have been using.
It works only for small values of the parameters,
then it becomes rapidly non manageable. If I have
150 20-face dice then you can see which way the
complexity is going. I can of course get good
approximations by averaging on a few millions
of random experiments - the C code can be written
in a few minutes. But it is not satisfactory.

With many faces, a normal approximation should work ok, and the
order statistics can be modeled with beta distribution. Order
statistics will apply easily to your problem if the following
have the same probability distribution: (a) the largest count
of any particular pip when n dice are thrown at once, or (b) the
maximum count of 1's among m trials of throwing n dice at once
(where n = number of dice and m = equally-probable faces per die).

-jiw
.