thief_of_baghdad.m

totalDays = 0;
nTrials = 100000;

for null = 1 : nTrials
    
    days = 0; % he starts in jail on day 0
    free = 0; % he is not free

    % inner loop is one prison term
    while(~free)
        % choose a door
        door = floor(rand(1)*3); % uniformly distributed random number [0,2]

        if door == 0
            days = days + 1;
        elseif door == 1
            days = days + 3;
        else % door must be 2
            free = 1; % he is free, end
        end

    end % while(~free)

    totalDays = totalDays + days;

end %for null = 1 : nTrials

fprintf('On average, a thief is in prison for %i days\n', totalDays/nTrials)