Compute the entropy of cards shuffled using a primitive shuffling method; see http://math.stackexchange.com/questions/1684658.

Question1684658.java

import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;

public class Question1684658 {
	final static int n = 8;
	
	static class Permutation {
		int [] p = new int [n];
		
		public int hashCode () {
			return Arrays.hashCode (p);
		}
		
		public boolean equals (Object o) {
			return Arrays.equals (((Permutation) o).p,p);
		}
		
		public String toString () {
			return Arrays.toString (p);
		}
	}
	
	static class Distribution extends HashMap<Permutation,Double> {
		public Double put (Permutation p,Double d) {
			Double old = get (p);
			return super.put (p,old == null ? d : d + old);
		}
	}
	
	static Distribution distribution = new Distribution ();
	
	public static void main (String [] args) {
		Permutation id = new Permutation ();
		for (int i = 0;i < n;i++)
			id.p [i] = i;
		distribution.put (id,1.);
		
		double lim = 0;
		for (int i = 2;i <= n;i++)
			lim += Math.log (i);
		
		for (int k = 0;k < 50;k++) {
			System.out.println (Math.log (lim - entropy (distribution)));
			Distribution newDistribution = new Distribution ();
			for (Permutation p : distribution.keySet ()) {
				double weight = distribution.get (p) / n;
				for (int i = 0;i < n;i++) {
					Permutation q = new Permutation ();
					for (int j = 0;j < i;j++)
						q.p [j] = p.p [j];
					q.p [i] = p.p [n - 1];
					for (int j = i + 1;j < n;j++)
						q.p [j] = p.p [j - 1];
					newDistribution.put (q,weight);
				}
			}
			distribution = newDistribution;
		}
	}
	
	static double entropy (Map<Permutation,Double> distribution) {
		double entropy = 0;
		for (Double d : distribution.values ())
			if (d != 0)
				entropy -= d * Math.log (d);
		return entropy;
	}
}