% L3B empirical study
% If we roll a fair die 12 times, how often does it happen
% that every result (1,2,3,4,5,6) appears exactly two times?

function L3Bdicestats(rep)

  if nargin<1, rep=1e3; end

  tic
  cpu0 = cputime;
  nsuccess = 0;
  
  for i=1:rep
    emp = hist(dice(12), 1:6);
    if all(emp == 2)
      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 12 times)\n', rep);
  fprintf('%10d successes (all bars height 2)\n', nsuccess);
  fprintf('%10.5f success rate\n', nsuccess/rep);
  
end