runMontyHallSim.matlab

% Run a Monty Hall problem simulation with the following parameters:
% 
% changeDoors: boolean determining whether the contestant should change
%              doors
% 
% doors:       the number of doors in the problem, with a minimum of 2
% 
% N:           the number of problem simulations to perform, with a minimum 
%              of 1
%
% returns [runs, Pr], where runs is an array with N rows, each with the 
% following columns:
%   1) the door originally picked
%   2) the other door left closed
%   3) the door finally picked
%   4) the door the prize was behind
%   5) a boolean representing whether the contestant won
%
%  and with Pr being the proportion of games won by the contestant

function [runs, Pr] = runMontyHallSim(changeDoors, doors, N)

% Minimum of 1 run with 2 doors
N = max(N, 1);
doors = max(doors, 2);

% Allocate runs array
runs = zeros(N, 5);

for i = 1:N
    prizeDoor = randi(doors);
    originalDoorPicked = randi(doors);
    
    % What would Monty Hall do? If the contestant picks the prize door, 
    % leave one of the other doors closed, chosen at random.
    if (prizeDoor == originalDoorPicked)
        otherDoorLeftClosed = randi(doors);
        while (otherDoorLeftClosed == originalDoorPicked)
            otherDoorLeftClosed = randi(doors);
        end
        
    else % Otherwise, leave the prize door closed  
        otherDoorLeftClosed = prizeDoor;
    end
    
    if (changeDoors)
        doorFinallyPicked = otherDoorLeftClosed;
    else
        doorFinallyPicked = originalDoorPicked;
    end
    
    contestantWon = (doorFinallyPicked == prizeDoor);
    
    runs(i,:) = [originalDoorPicked, otherDoorLeftClosed, ...
        doorFinallyPicked, prizeDoor, contestantWon];
end

Pr = sum(runs(:,5))./N;

Here is an overview of the problem. MacKay's excellent Information Theory, Inference, and Learning Algorithms, which is freely downloadable, has an in-depth discussion of the problem in the solutions to Exercises 3.8 and 3.9 (pages 57, 60, and 61).

By the way, this is Matlab or Octave code.