% Lecture #0: Monte Carlo
% Roll six dice
% Count how many times you get 3 of a kind
% xxx a b c
% xxx aa b
Pair3 = 0;
for games = 1:1e4
   Dice = ceil( 6*rand(1,6) );
   Dice = sort(Dice);
   % check for pairs
   N = zeros(1,6);
   for i=1:6
      for j=1:6
          if(Dice(j) == i)
              N(i) = N(i) + 1;
          end
      end
   end
   [N,b] = sort(N, 'descend');
if ( (N(1) == 3) & (N(4) < 3)) 
    Pair3 = Pair3 + 1;
    end
end
% probability:
disp('3 of a kind odds')
Pair3 / 1e4