I think there's a minuscule probability that this RNG leaves (at least) one number never to generate, shortening its ideal cycle. Potential fix:

sub generate_rng {
    my $seed = shift;
    my $count = 0;

    return sub {
        $seed = sha384_hex($seed . $count++);
        my $rnd = hex(substr($seed, 0, 4));
        return $rnd;
    };
}
[download]

Take my methods with a grain of salt since I'm an amateur at best in this subject -- I wouldn't know a bad RNG from a good one.

Anyway, it appears that the OP is trying to increase the randomness of rand() by various voodoo methods. This is a futile task and he's much more likely to worsen it by making it more biassed. For example, a lot of newbies try to out-random random by saying rand() + rand() and getting a triangular distribution as a result.