% Ph = [1/3 1/3 1/3 % 1/3 1/3 1/3 % 1/3 1/3 1/3] %__________________________________________________________________________ % % CASE 1A: Host always hides the car behind one particular door. % Pc = [1 0 0] or [0 1 0] or [0 0 1] %__________________________________________________________________________ % 1. Pc = [1 0 0], D = 1, H = 3. % The host always hides the car behind door 1. % Consequently, a player with an initial door choice of D = 1 cannot win % by switching doors after the host opens door H = 3 i.e. Psw = 0. D = 1; H = 3; Ph = ones(3)/3; Pc = [1 0 0]; Pws_correct = 0; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) % 2. Pc = [1 0 0], D = 1, H = 2. % The host always hides the car behind door 1. % Consequently, a player with an initial door choice of D = 1 cannot win % by switching doors after the host opens door H = 2 i.e. Psw = 0. D = 1; H = 2; Ph = ones(3)/3; Pc = [1 0 0]; Pws_correct = 0; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) % 3. Pc = [0 1 0], D = 1, H = 2. % The host always hides the car behind door 2. % Consequently, a player with an initial door choice of D = 1 does not % have the option to switch doors after the host opens door H = 2. D = 1; H = 2; Ph = ones(3)/3; Pc = [0 1 0]; Pws_correct = NaN; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) % 4. Pc = [0 1 0], D = 1, H = 3. % The host always hides the car behind door 2. % Consequently, a player with an initial door choice of D = 1 can only win % by switching to door 2 after the host opens door H = 3. i.e. Psw = 1. D = 1; H = 3; Ph = ones(3)/3; Pc = [0 1 0]; Pws_correct = 1; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) % 5. Pc = [0 0 1], D = 1, H = 2 % The host always hides the car behind door 3. % Consequently, a player with an initial door choice of D = 1 does not % have the option to switch doors after the host opens door H = 2. D = 1; H = 2; Ph = ones(3)/3; Pc = [0 0 1]; Pws_correct = 1; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) % 6. Pc = [0 0 1], D = 1, H = 3 % The host always hides the car behind door 3. % Consequently, a player with an initial door choice of D = 1 does not % have the option to switch doors after the host opens door H = 3. D = 1; H = 3; Ph = ones(3)/3; Pc = [0 0 1]; Pws_correct = NaN; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) %__________________________________________________________________________ % % CASE 1B: Host hides the car behind two particular doors with equal probability. % Pc = [0 0.5 0.5] or [0.5 0.5 0] or [0.5 0 0.5] %__________________________________________________________________________ % 1. Pc = [0 0.5 0.5], D = 3, H = 1. % The car is either behind door 2 or 3. If the host opens door H = 1, the % player's chance of winning by switching from door D = 3 to door 2 is % equal i.e. Psw = 0.5. D = 3; H = 1; Ph = ones(3)/3; Pc = [0 0.5 0.5]; Pws_correct = 0.5; Pws = MontyHall3(D,H,Ph,Pc); assert(isequal(round(Pws,4),Pws_correct)) % 2. Pc = [0 0.5 0.5], D = 3, H = 2. % The host never hides the car behind door 1. Hence, the player can never % wi by switching to door 1. D = 3; H = 2; Ph = ones(3)/3; Pc = [0 0.5 0.5]; Pws_correct = 0; Pws = MontyHall3(D,H,Ph,Pc); assert(isequal(round(Pws,4),Pws_correct)) % 3. Pc = [0.5 0.5 0], D = 3, H = 1. % The host never hides the car behind door 3. Hence, the player can only % win by switching to door 2. D = 3; H = 1; Ph = ones(3)/3; Pc = [0.5 0.5 0]; Pws_correct = 1; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) % 4. Pc = [0.5 0.5 0], D = 3, H = 2. % The host never hides the car behind door 3. Hence, the player can only % win by switching to door 1. D = 3; H = 2; Ph = ones(3)/3; Pc = [0.5 0.5 0]; Pws_correct = 1; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) % 5. Pc = [0.5 0 0.5], D = 3, H = 1. % The host never hides the car behind door 2. Hence, the player can % never win by switching to door 2. D = 3; H = 1; Ph = ones(3)/3; Pc = [0.5 0 0.5]; Pws_correct = 0; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) %__________________________________________________________________________ % % CASE 1C: Hosts hides the car behind any of the three doors with equal probability. % Pc = [1/3 1/3 1/3] %__________________________________________________________________________ % The host does not manipulate the game. Hence, it is a fair game. D = 1; H = 3; Ph = ones(3)/3; Pc = [1 1 1]/3; Pws_correct = 0.5; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) %__________________________________________________________________________ % % CASE 1D: Host hides the car with a pre-determined probability. % Pc = [0.26 0.43 0.31] %__________________________________________________________________________ D = 1; H = 3; Ph = ones(3)/3; Pc = [0.26 0.43 0.31]; Pws_correct = 0.6232; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 1; H = 2; Ph = ones(3)/3; Pc = [0.26 0.43 0.31]; Pws_correct = 0.5439; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 2; H = 1; Ph = ones(3)/3; Pc = [0.26 0.43 0.31]; Pws_correct = 0.4189; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 2; H = 3; Ph = ones(3)/3; Pc = [0.26 0.43 0.31]; Pws_correct = 0.3768; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 3; H = 1; Ph = ones(3)/3; Pc = [0.26 0.43 0.31]; Pws_correct = 0.5811; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 3; H = 2; Ph = ones(3)/3; Pc = [0.26 0.43 0.31]; Pws_correct = 0.4561; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct))

% Marilyn vos Savant. % Ph = [ 0 1 0 % 1 0 0 % 0.5 0.5 0] %__________________________________________________________________________ % % CASE 2A: Host always hides the car behind one particular door. % Pc = [1 0 0] or [0 1 0] or [0 0 1] %__________________________________________________________________________ D = 3; H = 1; Ph = [ 0 1 0; 1 0 0; 0.5 0.5 0]; Pc = [1 0 0]; Pws_correct = NaN; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 3; H = 2; Ph = [ 0 1 0; 1 0 0; 0.5 0.5 0]; Pc = [1 0 0]; Pws_correct = 1; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 3; H = 1; Ph = [ 0 1 0; 1 0 0; 0.5 0.5 0]; Pc = [0 1 0]; Pws_correct = 1; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 3; H = 2; Ph = [ 0 1 0; 1 0 0; 0.5 0.5 0]; Pc = [0 1 0]; Pws_correct = NaN; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 3; H = 1; Ph = [ 0 1 0; 1 0 0; 0.5 0.5 0]; Pc = [0 0 1]; Pws_correct = 0; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 3; H = 2; Ph = [ 0 1 0; 1 0 0; 0.5 0.5 0]; Pc = [0 0 1]; Pws_correct = 0; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) %__________________________________________________________________________ % % CASE 2B: Host hides the car behind two particular doors with equal % probability. % Pc = [0 0.5 0.5] or [0.5 0.5 0] or [0.5 0 0.5] %__________________________________________________________________________ D = 3; H = 1; Ph = [ 0 1 0; 1 0 0; 0.5 0.5 0]; Pc = [0.5 0.5 0]; Pws_correct = 1; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 3; H = 2; Ph = [ 0 1 0; 1 0 0; 0.5 0.5 0]; Pc = [0.5 0.5 0]; Pws_correct = 1; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 3; H = 1; Ph = [ 0 1 0; 1 0 0; 0.5 0.5 0]; Pc = [0 0.5 0.5]; Pws_correct = 0.6667; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 3; H = 2; Ph = [ 0 1 0; 1 0 0; 0.5 0.5 0]; Pc = [0 0.5 0.5]; Pws_correct = 0; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 3; H = 1; Ph = [ 0 1 0; 1 0 0; 0.5 0.5 0]; Pc = [0.5 0 0.5]; Pws_correct = 0; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 3; H = 2; Ph = [ 0 1 0; 1 0 0; 0.5 0.5 0]; Pc = [0.5 0 0.5]; Pws_correct = 0.6667; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) %__________________________________________________________________________ % % CASE 2C: Hosts hides the car behind any of the three doors with equal % probability. % Pc = [1/3 1/3 1/3] %__________________________________________________________________________ D = 3; H = 1; Ph = [ 0 1 0; 1 0 0; 0.5 0.5 0]; Pc = [1 1 1]/3; Pws_correct = 0.6667; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 3; H = 2; Ph = [ 0 1 0; 1 0 0; 0.5 0.5 0]; Pc = [1 1 1]/3; Pws_correct = 0.6667; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) %__________________________________________________________________________ % % CASE 2D: Host hides the car with a pre-determined probability. % Pc = [0.26 0.43 0.31] %__________________________________________________________________________ D = 1; H = 2; Ph = [ 0 1 0; 1 0 0; 0.5 0.5 0]; Pc = [0.26 0.43 0.31]; Pws_correct = 0.3735; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 2; H = 1; Ph = [ 0 1 0; 1 0 0; 0.5 0.5 0]; Pc = [0.26 0.43 0.31]; Pws_correct = 0.2650; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 3; H = 1; Ph = [ 0 1 0; 1 0 0; 0.5 0.5 0]; Pc = [0.26 0.43 0.31]; Pws_correct = 0.7350; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 3; H = 2; Ph = [ 0 1 0; 1 0 0; 0.5 0.5 0]; Pc = [0.26 0.43 0.31]; Pws_correct = 0.6265; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct))

%__________________________________________________________________________ % % CASE 3A: Host always hides the car behind one particular door. % Pc = [1 0 0] or [0 1 0] or [0 0 1] %__________________________________________________________________________ D = 2; H = 1; Ph = [0.3333 0.3651 0.3016 0.4646 0.2283 0.3071 0.2926 0.4043 0.3032]; Pc = [1 0 0]; Pws_correct = NaN; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 2; H = 3; Ph = [0.3333 0.3651 0.3016 0.4646 0.2283 0.3071 0.2926 0.4043 0.3032]; Pc = [1 0 0]; Pws_correct = 1; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 2; H = 1; Ph = [0.3333 0.3651 0.3016 0.4646 0.2283 0.3071 0.2926 0.4043 0.3032]; Pc = [0 1 0]; Pws_correct = 0; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 2; H = 3; Ph = [0.3333 0.3651 0.3016 0.4646 0.2283 0.3071 0.2926 0.4043 0.3032]; Pws_correct = 0; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 2; H = 1; Ph = [0.3333 0.3651 0.3016 0.4646 0.2283 0.3071 0.2926 0.4043 0.3032]; Pc = [0 0 1]; Pws_correct = 1; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 2; H = 3; Ph = [0.3333 0.3651 0.3016 0.4646 0.2283 0.3071 0.2926 0.4043 0.3032]; Pc = [0 0 1]; Pws_correct = NaN; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) %__________________________________________________________________________ % % CASE 3B: Host hides the car behind two particular doors with equal probability. % Pc = [0 0.5 0.5] or [0.5 0.5 0] or [0.5 0 0.5] %__________________________________________________________________________ D = 3; H = 1; Ph = [0.3333 0.3651 0.3016 0.4646 0.2283 0.3071 0.2926 0.4043 0.3032]; Pc = [0 0.5 0.5]; Pws_correct = 0.6136; Pws = MontyHall3(D,H,Ph,Pc); assert(isequal(round(Pws,4),Pws_correct)) D = 3; H = 2; Ph = [0.3333 0.3651 0.3016 0.4646 0.2283 0.3071 0.2926 0.4043 0.3032]; Pc = [0 0.5 0.5]; Pws_correct = 0; Pws = MontyHall3(D,H,Ph,Pc); assert(isequal(round(Pws,4),Pws_correct)) D = 3; H = 1; Ph = [0.3333 0.3651 0.3016 0.4646 0.2283 0.3071 0.2926 0.4043 0.3032]; Pc = [0.5 0.5 0]; Pws_correct = 1; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 3; H = 2; Ph = [0.3333 0.3651 0.3016 0.4646 0.2283 0.3071 0.2926 0.4043 0.3032]; Pc = [0.5 0.5 0]; Pws_correct = 1; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 3; H = 1; Ph = [0.3333 0.3651 0.3016 0.4646 0.2283 0.3071 0.2926 0.4043 0.3032]; Pc = [0.5 0 0.5]; Pws_correct = 0; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) %__________________________________________________________________________ % % CASE 3C: Hosts hides the car behind any of the three doors with equal % probability. % Pc = [1/3 1/3 1/3] %__________________________________________________________________________ D = 3; H = 1; Ph = [0.3333 0.3651 0.3016 0.4646 0.2283 0.3071 0.2926 0.4043 0.3032]; Pc = [1 1 1]/3; Pws_correct = 0.6136; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 3; H = 2; Ph = [0.3333 0.3651 0.3016 0.4646 0.2283 0.3071 0.2926 0.4043 0.3032]; Pc = [1 1 1]/3; Pws_correct = 0.4745; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) %__________________________________________________________________________ % % CASE 3D: Host hides the car with a pre-determined probability. % Pc = [0.26 0.43 0.31] %__________________________________________________________________________ D = 1; H = 2; Ph = [0.3333 0.3651 0.3016 0.4646 0.2283 0.3071 0.2926 0.4043 0.3032]; Pc = [0.26 0.43 0.31]; Pws_correct = 0.5690; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 1; H = 3; Ph = [0.3333 0.3651 0.3016 0.4646 0.2283 0.3071 0.2926 0.4043 0.3032]; Pc = [0.26 0.43 0.31]; Pws_correct = 0.6274; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 2; H = 1; Ph = [0.3333 0.3651 0.3016 0.4646 0.2283 0.3071 0.2926 0.4043 0.3032]; Pc = [0.26 0.43 0.31]; Pws_correct = 0.3123; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 2; H = 3; Ph = [0.3333 0.3651 0.3016 0.4646 0.2283 0.3071 0.2926 0.4043 0.3032]; Pc = [0.26 0.43 0.31]; Pws_correct = 0.3726; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 3; H = 1; Ph = [0.3333 0.3651 0.3016 0.4646 0.2283 0.3071 0.2926 0.4043 0.3032]; Pc = [0.26 0.43 0.31]; Pws_correct = 0.6877; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct)) D = 3; H = 2; Ph = [0.3333 0.3651 0.3016 0.4646 0.2283 0.3071 0.2926 0.4043 0.3032]; Pc = [0.26 0.43 0.31]; Pws_correct = 0.4310; Pws = MontyHall3(D,H,Ph,Pc); assert(isequaln(round(Pws,4),Pws_correct))