function montyHall2(n,d,o)
%montyhall(n,d,o) Simulates n rounds of the Monty Hall problem and
%                 gives win/loss ratio
%
%                n   : Number of rounds to simulate (Any positive integer)
%                d   : Number of doors (Positive integer >= 3)
%                o=0 : Show final win/loss score and estimated probability
%                o=1 : Show win/loss tally chart and estimated probability
%                o=2 : Show results for each round
%
% All parameters are optional, by default they will take the values:
% n=1, d=3, o=0.
%
% The Monty Hall problem is a probability puzzle based on the American
% television game show Let's Make a Deal. The name comes from the show's
% host, Monty Hall. The problem is also called the Monty Hall paradox,
% as it is a veridical paradox in that the result appears absurd but is
% demonstrably true.
%
% Reference: http://en.wikipedia.org/wiki/Monty_Hall_problem

win=0;
lose=0;
tally=[0;0];
Monty=0;

% Check for nonexistent variables and set to defaults
if exist('n')~=1
    n=1; 
end

if exist('d')~=1 || d<3 || d~=round(d) 
    d=3; 
end

if exist('o')~=1 
    o=0; 
end

if o==2
    for i = 1:n
        % Picks a random door for the car to be behind
        Car = randi(d)-1;
        % Player picks a random door
        Choose = randi(d)-1;
        % Monty recursively picks a random door until he has chosen
        % the door that neither has the car behind it or has been
        % chosen by the player
        
        while (Monty==Car || Monty==Choose)
            Monty=randi(d)-1; 
        end
        
        % If you originally choose the car, no matter what door Monty
        % opens, you will lose by switching.
        % If you originally choose a goat, Monty has to open a door to
        % reveal the other goat, and switching will switch to the car
        % meaning you win.
        % Simply put, if you originally choose the car, switching wins
        % and if you don't, switching loses.
        % This is the basis of the score tally system
        
        if Choose==Car 
            lose=lose+1; 
        else
            win=win+1; 
        end
        
        % Display round results after game has been played.
        disp(['Round ',num2str(i)]);
        disp('Chosen door:');
        disp([zeros(1,Choose),1,zeros(1,(d-1)-Choose)]);
        
        if Car<Choose
            disp('Monty opens:');
            disp([ones(1,Car),0,ones(1,Choose-Car-1),0,ones(1,(d-1)-Choose)]); 
        end
        
        if Car>Choose
            disp('Monty opens:');
            disp([ones(1,Choose),0,ones(1,Car-Choose-1),0,ones(1,(d-1)-Car)]);  
        end
        
        if Car == Choose
            if Car<Monty
                disp('Monty opens:');
                disp([ones(1,Car),0,ones(1,Monty-Car-1),0,ones(1,(d-1)-Monty)]); 
            else
                disp('Monty opens:');
                disp([ones(1,Monty),0,ones(1,Car-Monty-1),0,ones(1,(d-1)-Car)]);
            end
        end
        
        disp('Car is behind:');
        disp([zeros(1,Car),1,zeros(1,(d-1)-Car)]);
        
        if Choose == Car
            disp('Switching loses'); 
        else
            disp('Switching wins'); 
        end
        
        disp(' ');disp('   Win | Lose');disp([win,lose]);
        disp('---------------------');
    end
else
    for i = 1:n
        % When detail~=2, the next few lines simulate the game
        % instead. This is a lot simpler as all unnecessary commands are
        % removed. In the original block of code (where detail=2), the
        % code can be summarised as;
        % Pick 2 random numbers (Car and Choose), pick a random number
        % not equal to those numbers (Monty) and finally check if the two
        % original numbers are equal.
        % The number that is chosen for Monty does not affect whether a
        % win or a loss is tallied, so it is not needed for the simulation.
        Car = randi(d)-1;
        Choose = randi(d)-1;
        % Defining 'Monty' is not needed to decide a win or a loss.
        % while (Monty==Car || Monty==Choose), Monty=randi(d)-1; end
        
        if Choose == Car 
            lose=lose+1; 
        else
            win=win+1;
        end
        tally = [tally, [win;lose]];
    end
end

if o==1
    disp(['W: ',num2str(tally(1,1:n+1))]);
    disp(['L: ',num2str(tally(2,1:n+1))]);
else
    disp(['Won  ',num2str(win)]);
    disp(['Lost ',num2str(lose)]);
end

if n>=10
    disp(['Estimated Chance Of Winning After Switch: ',num2str(win/n)]); 
end

end