Randomize values without exceeding a value?

Question

I have some time thinking the following, I want to make a button to randomize whole values of some skills. The question is that I have 10 points to distribute between 4 skills, the idea is to have selected randoms numbers without exceeding 10 points.

I had thought in this

public int startPts = 10, usedPts = 0;
public int skill1 = 0, skill2 = 0, skill3 = 0, skill4 = 0;

public void ButtonRandom(){
   startPts = 10;
   usedPts = 0;

   skill1 = Random.Range( 1, 10 );
   usedPts += skill1;

   skill2 = Random.Range( 1, usedPts );
   usedPts += skill2;

   skill3 = Random.Range( 1, usedPts );
   usedPts += skill3;

   skill4 = startPts - usedPts;
   usedPts += skill4;

   startPts = startPts - usedPts;

 }

I also try with several conditionals and repetitive methods, but I do not get the desired result. Since sometimes it surpasses the 10 points, leaves points without using or only changes the first 2 values when I put the conditions.

Thank you, guys.

Answer 1

If what you want is for every possible distribution to be equally likely, then none of the solutions presented so far work. The solutions presented so far pick 3, 3, 2, 2 much more often than 7, 1, 1, 1. Do you see why?

If your desired distribution is uniform over possibilities, this algorithm gives you that:

using System;
using System.Collections.Generic;
using System.Linq;

public class Program
{
    // Partition n into m summands
    static IEnumerable<IEnumerable<int>> Partitions(int n, int m)
    {
      // There is no partition of n into zero summands for any value of n other than zero.
      // Otherwise, give the partitions that begin with 0, 1, 2, ... n.
      if (m == 0) 
      {
        if (n == 0)
          yield return Enumerable.Empty<int>();
      }
      else 
      {
        for (int nn = 0; nn <= n; ++nn)
            foreach(var p in Partitions(n - nn, m - 1))
                yield return (new[] { nn }).Concat(p);
      }
    }

    public static void Main()
    {
        // Divide up six points into four buckets:
        var partitions = Partitions(6, 4).ToArray();
        // Now choose a random member of partitions, and 
        // add one to each element of that sequence. Now
        // you have ten points total, and every possibility is 
        // equally likely.

        // Let's visualize the partitions:
        foreach(var p in partitions)
            Console.WriteLine(string.Join(",", p));

    }
}