1 function Aufgabe3
   2 %Aufgabe3 - Simulate Monty-Hall-Problem and plot empirical evidence.
   3 %
   4 %usage
   5 %  Aufgabe3
   6 %
   7 %description
   8 %  Aufgabe3 simulates the Monty-Hall-Problem 10000 times and plots are pie-chart
   9 %  which indicates whether it is wise to switch doors or not.
  10 %
  11 %author
  12 %  buenau@cs.tu-berlin.de
  13 
  14 N = 10000;
  15 
  16 who_won = zeros(2, N);
  17 
  18 for i=1:N
  19   % Put price behind a random door.
  20   price = zeros(1,3);
  21   price(randint(1, 1, [1 3])) = 1;
  22  
  23   % Strategy 1: Choose door at random. 
  24   strat1_sel = randint(1, 1, [1 3]); 
  25 
  26   % Strategy 2: Switch to other door.   
  27   host_opens = randomchoice(setdiff(1:3, [ strat1_sel find(price) ]));
  28   strat2_sel = randomchoice(setdiff(1:3, [ strat1_sel host_opens ]));
  29 
  30   who_won(1, i) = price(strat1_sel);
  31   who_won(2, i) = price(strat2_sel);
  32 end
  33 
  34 pie(sum(who_won, 2) / N, { 'Strategy 1: Do not change', 'Strategy 2: Change doors' });
  35 title(sprintf('Frequency of wins for the two strategies in %d simulations', N));
  36 
  37 % Choose an element of vector a at random.
  38 function c = randomchoice(a)
  39 c = a(randint(1, 1, [1 length(a)]));