Simulate coupon collection with trading of doubles; see http://math.stackexchange.com/questions/1825418.

Question1825418.java

import java.util.Random;

public class Question1825418 {
	final static int ntrials = 1000000;
	final static int n = 10000;
	
	final static Random random = new Random ();
	
	public static void main (String [] args) {
		long count = 0;

		for (int i = 0;i < ntrials;i++) {
			int nmissing = n;
			int ndouble = 0;
			int npairs = 0;
			
			while (npairs != nmissing) {
				int next = random.nextInt (n);
				if (next < nmissing)
					nmissing--;
//					nsingle++;
				else if (next < nmissing + ndouble) {
					ndouble--;
					npairs++;
//					nsingle++;
				}
				else
//					nsingle--;
					ndouble++;
				count++;
			}
		}
		
		System.out.println (count / (double) ntrials);

		count = 0;
		
		for (int i = 0;i < ntrials;i++) {
			int nmissing = n;
			int ndouble = 0;
			
			while (nmissing != 0) {
				int next = random.nextInt (n);
				if (next < nmissing)
					nmissing--;
//					nsingle++;
				else if (next < nmissing + ndouble) {
					ndouble--;
					nmissing--;
//					nsingle += 2;
				}
				else
//					nsingle--;
					ndouble++;
				count++;
			}
		}
		
		System.out.println (count / (double) ntrials);
	}
}