%%% *****************************************
%%% The MONTE HALL Problem
%%%
%%% Author: James Beck
%%% Date: Dec 2, 2006
%%% *****************************************

% THE QUESTION
% Say you're on a game show where they have three doors. 
% One door has a car behind it, and the other two of the 
% doors have goats. You randomly choose a door and the 
% host opens one of the OTHER doors, and shows you that 
% there is a goat behind it. Then he says, 'Do you want 
% to pick the third door, or do you want to keep your 
% origional choice?'. What do you pick and why?

% Number of times the situation is repeated
% -------------------------------------------
runs = 100000;

% SOLVE
% -------------------------------------------
% Carry out the situation over and over, and
% keep track of the results.

picked = 0;
for j=1:runs,
	% Randomly pick a door for the car to be in
	doors = [0,0,0];
	[j,i] = max(rand(1,3));
	doors(i) = 1;

	% Randomly pick a door to go first
	[j,pick] = max(rand(1,3));
	
	% If the door you picked has the car, add one to the counter
	if doors(pick)==1,
		picked = picked + 1;
	end
end

% DISPLAY STATISTICS/RESULTS
% -------------------------------------------
disp('---------------------------------------');
disp(['First Pick has the car: ',num2str(picked)]);
disp(['The other door has the car: ',num2str(runs-picked)]);
disp('---------------------------------------');
disp(['The ratios are: [',num2str(picked/runs),'] (picked) and [',num2str((runs-picked)/runs),'] (the other).']);