[OT] Generating distribution of N dice rolls

[Sergey]

On Thursday, 10 November 2022 at 02:10:32 UTC, H. S. Teoh wrote:
> This is technically OT, but I thought I'd pick the smart brains 
> here for my project, which happens to be written in D. ;-)
>
> Basically, I want to write a function that takes 2 uint 
> arguments k and N, and simulates rolling N k-sided dice and 
> counting how many 1's, 2's, 3's, ... k's were rolled. Something 
> like this:
>
> 	uint[k] diceDistrib(uint k)(uint N)
> 		in(k > 0)
> 		in(N > 0)
> 		out(r; r[].sum == N)
> 	{
> 		uint[k] result;
> 		foreach (i; 0 .. N) {
> 			result[uniform(0, k)]++;
> 		}
> 		return result;
> 	}
>
> The above code works and does what I want, but since N may be 
> large, I'd like to refactor the code to loop over k instead of 
> N. I.e., instead of actually rolling N dice and tallying the 
> results, the function would generate the elements of the output 
> array directly, such that the distribution of the array 
> elements follow the same probabilities as the above code.
>
> Note that in all cases, the output array must sum to N; it is 
> not enough to merely simulate the roll distribution 
> probabilistically.
>
> Any ideas?  (Or links if this is a well-studied problem with a 
> known
> solution.)
>
> <ObDReference> I love how D's new contract syntax makes it so 
> conducive to expressing programming problem requirements. ;-) 
> </ObDReference>
>
>
> T

They should have uniform distribution with well known mean and 
std. To have exactly N rolls you can estimate with distribution 
function numbers for (k-1) sides (let their sum will be M), and 
the rest (N-M) put into k’s side

https://scientificgems.wordpress.com/2015/11/03/mathematics-in-action-probability/