% L3B empirical study
% If we roll a fair die n times, how often does it happen
% that every result (1,2,3,4,5,6) appears equally many times?
% Default n=6.

function L3Bdicestats(n, rep)

  if nargin<1, n=6; end
  if nargin<2, rep=1e3; end

  tic
  cpu0 = cputime;
  nsuccess = 0;
  
  for i=1:rep
    emp = hist(dice(n), 1:6);
    if all(emp == emp(1))
      nsuccess = nsuccess + 1;
    end
    if mod(i,10000)==0
      fprintf('%d trials in %.2f s...\n', i, cputime-cpu0);
    end
  end
  toc
  
  fprintf('%10d trials (of rolling a die %d times)\n', rep, n);
  fprintf('%10d successes (all bars same height)\n', nsuccess);
  fprintf('%10.5f success rate\n', nsuccess/rep);
  
end