Compare the KFY shuffle with naive shuffle by a=[1,2,3]. There are 6 combinations. The experiment result shows that KFY shuffle is unbiased and the number of distinct combination closes to round(max_iter/6). But naive shuffle is biased. Refer to http://blog.codinghorror.com/the-danger-of-naivete/

KFY_shuffle_vs_naive_shuffle.matlab

%% KFY shuffle
n = 3;
max_iter = 1e5;
count = zeros(17,1);
for iter = 1:max_iter
    a = 1:n;
    for i = n:-1:2
        j = randi(i,1,1);
        t = a(i);
        a(i) = a(j);
        a(j) = t;
    end
    key = a(1)*4+a(2)*2+a(3)*1;
    count(key) = count(key)+1;
end
idx = [11,12,13,15,16,17];
disp(count(idx));
figure; barh(count(idx));


%% naive shuffle
n = 3;
max_iter = 1e5;
count = zeros(17,1);
for iter = 1:max_iter
    a = 1:n;
    for i = 1:n
        j = randi(n,1,1);
        t = a(i);
        a(i) = a(j);
        a(j) = t;
    end
    key = a(1)*4+a(2)*2+a(3)*1;
    count(key) = count(key)+1;
end
idx = [11,12,13,15,16,17];
disp(count(idx));
figure; barh(count(idx));