Data update

Task/Monty-Hall-problem/Chapel/monty-hall-problem-2.chapel

@@ -0,0 +1,21 @@
+use Random;
+
+config const numGames = 100_000_000;
+
+var switch, stick: uint;
+
+// have a separate RNG for each task; add together the results at the end
+forall i in 1..numGames
+  with (var rand = new RandomStream(uint, parSafe = false), + reduce stick)
+{
+  var chosen_door = rand.getNext() % 3;
+  var winner_door = rand.getNext() % 3;
+  if chosen_door == winner_door then
+    stick += 1;
+}
+
+// if you lost by sticking it means you would have won by switching
+switch = numGames - stick;
+writeln("Over ", numGames, " games:\n - switching wins ",
+        100.0*switch / numGames, "% of the time and\n - sticking  wins ",
+        100.0*stick  / numGames, "% of the time");

Task/Monty-Hall-problem/EasyLang/monty-hall-problem.easy

@@ -0,0 +1,21 @@
+max = 1000000
+for i = 1 to max
+   car_door = random 3
+   chosen_door = random 3
+   if car_door <> chosen_door
+      montys_door = 6 - car_door - chosen_door
+   else
+      repeat
+         montys_door = random 3
+         until montys_door <> car_door
+      .
+   .
+   if car_door = chosen_door
+      stay += 1
+   .
+   if car_door = 6 - montys_door - chosen_door
+      switch += 1
+   .
+.
+print "If you stick to your choice, you have a " & stay / max * 100 & " percent chance to win"
+print "If you switched, you have a " & switch / max * 100 & " percent chance to win"

Task/Monty-Hall-problem/MATLAB/monty-hall-problem-1.m

@@ -1,56 +1,2 @@
-function montyHall(numDoors,numSimulations)
-
-    assert(numDoors > 2);
-
-    function num = randInt(n)
-        num = floor( n*rand()+1 );
-    end
-
-    %The first column will tallie wins, the second losses
-    switchedDoors = [0 0];
-    stayed = [0 0];
-
-
-    for i = (1:numSimulations)
-
-        availableDoors = (1:numDoors); %Preallocate the available doors
-        winningDoor = randInt(numDoors); %Define the winning door
-        playersOriginalChoice = randInt(numDoors); %The player picks his initial choice
-
-        availableDoors(playersOriginalChoice) = []; %Remove the players choice from the available doors
-
-        %Pick the door to open from the available doors
-        openDoor = availableDoors(randperm(numel(availableDoors))); %Sort the available doors randomly
-        openDoor(openDoor == winningDoor) = []; %Make sure Monty doesn't open the winning door
-        openDoor = openDoor(randInt(numel(openDoor))); %Choose a random door to open
-
-        availableDoors(availableDoors==openDoor) = []; %Remove the open door from the available doors
-        availableDoors(end+1) = playersOriginalChoice; %Put the player's original choice back into the pool of available doors
-        availableDoors = sort(availableDoors);
-
-        playersNewChoice = availableDoors(randInt(numel(availableDoors))); %Pick one of the available doors
-
-        if playersNewChoice == playersOriginalChoice
-            switch playersNewChoice == winningDoor
-                case true
-                    stayed(1) = stayed(1) + 1;
-                case false
-                    stayed(2) = stayed(2) + 1;
-                otherwise
-                    error 'ERROR'
-            end
-        else
-            switch playersNewChoice == winningDoor
-                case true
-                    switchedDoors(1) = switchedDoors(1) + 1;
-                case false
-                    switchedDoors(2) = switchedDoors(2) + 1;
-                otherwise
-                    error 'ERROR'
-            end
-        end
-    end
-
-    disp(sprintf('Switch win percentage: %f%%\nStay win percentage: %f%%\n', [switchedDoors(1)/sum(switchedDoors),stayed(1)/sum(stayed)] * 100));
-
-end
+wins = ceil(3*rand(1e8,1)) - ceil(3*rand(1e8,1))
+mprintf('chance to win for staying:  %1.6f %%\nchance to win for changing: %1.6f %%', 100*length(wins(wins==0))/length(wins), 100*length(wins(wins<>0))/length(wins))

Task/Monty-Hall-problem/MATLAB/monty-hall-problem-2.m

@@ -1,3 +1,2 @@
->> montyHall(3,100000)
-Switch win percentage: 66.705972%
-Stay win percentage: 33.420062%
+chance to win for staying:  33.334694 %
+chance to win for changing: 66.665306 %

Task/Monty-Hall-problem/MATLAB/monty-hall-problem-3.m

@@ -0,0 +1,56 @@
+function montyHall(numDoors,numSimulations)
+
+    assert(numDoors > 2);
+
+    function num = randInt(n)
+        num = floor( n*rand()+1 );
+    end
+
+    %The first column will tallie wins, the second losses
+    switchedDoors = [0 0];
+    stayed = [0 0];
+
+
+    for i = (1:numSimulations)
+
+        availableDoors = (1:numDoors); %Preallocate the available doors
+        winningDoor = randInt(numDoors); %Define the winning door
+        playersOriginalChoice = randInt(numDoors); %The player picks his initial choice
+
+        availableDoors(playersOriginalChoice) = []; %Remove the players choice from the available doors
+
+        %Pick the door to open from the available doors
+        openDoor = availableDoors(randperm(numel(availableDoors))); %Sort the available doors randomly
+        openDoor(openDoor == winningDoor) = []; %Make sure Monty doesn't open the winning door
+        openDoor = openDoor(randInt(numel(openDoor))); %Choose a random door to open
+
+        availableDoors(availableDoors==openDoor) = []; %Remove the open door from the available doors
+        availableDoors(end+1) = playersOriginalChoice; %Put the player's original choice back into the pool of available doors
+        availableDoors = sort(availableDoors);
+
+        playersNewChoice = availableDoors(randInt(numel(availableDoors))); %Pick one of the available doors
+
+        if playersNewChoice == playersOriginalChoice
+            switch playersNewChoice == winningDoor
+                case true
+                    stayed(1) = stayed(1) + 1;
+                case false
+                    stayed(2) = stayed(2) + 1;
+                otherwise
+                    error 'ERROR'
+            end
+        else
+            switch playersNewChoice == winningDoor
+                case true
+                    switchedDoors(1) = switchedDoors(1) + 1;
+                case false
+                    switchedDoors(2) = switchedDoors(2) + 1;
+                otherwise
+                    error 'ERROR'
+            end
+        end
+    end
+
+    disp(sprintf('Switch win percentage: %f%%\nStay win percentage: %f%%\n', [switchedDoors(1)/sum(switchedDoors),stayed(1)/sum(stayed)] * 100));
+
+end

Task/Monty-Hall-problem/MATLAB/monty-hall-problem-4.m

@@ -0,0 +1,3 @@
+>> montyHall(3,100000)
+Switch win percentage: 66.705972%
+Stay win percentage: 33.420062%

Task/Monty-Hall-problem/Standard-ML/monty-hall-problem.ml

@@ -0,0 +1,23 @@
+val pidint = Word64.toInt(Posix.Process.pidToWord(Posix.ProcEnv.getpid()));
+val rand = Random.rand(LargeInt.toInt(Time.toSeconds(Time.now())), pidint);
+
+fun stick_win 0 wins = wins
+  | stick_win trial wins =
+  let
+    val winner_door = (Random.randNat rand) mod 3;
+    val chosen_door = (Random.randNat rand) mod 3;
+  in
+    if winner_door = chosen_door then
+      stick_win (trial-1) (wins+1)
+    else
+      stick_win (trial-1) wins
+  end
+
+val trials = 1000000;
+val sticks = stick_win trials 0;
+val stick_winrate = 100.0 * Real.fromInt(sticks) / Real.fromInt(trials);
+(* if you lost by sticking you would have won by swapping *)
+val swap_winrate = 100.0 - stick_winrate;
+
+(print ("sticking = " ^ Real.toString(stick_winrate) ^ "% win rate\n");
+ print ("swapping = " ^ Real.toString(swap_winrate)  ^ "% win rate\n"));