Possibly related to the number of random numbers - first from the built in rand and then with rand from Math::Random::MT::Auto. I generated 2 ** 25 random numbers and the code and results are below.

#!/usr/bin/perl
use strict;
use warnings;
use 5.014;

my %rand;

for (1 .. 2**25) {
    my $r = rand;
    $rand{ $r }++;    
}

say scalar keys %rand;

use Math::Random::MT::Auto qw(rand);
%rand = ();
for (1 .. 2**25) {
    my $r = rand;
    $rand{ $r }++;    
}

say scalar keys %rand;
[download]

Results:

C:\Old_Data\perlp>perl t.pl
32768
33554432

C:\Old_Data\perlp>perl -E "say 2**25"
33554432

C:\Old_Data\perlp>perl -E "say 2**15"
32768

C:\Old_Data\perlp>
[download]

You can see that for 2**25 == 33_554_432 the built in rand only produced 2**15 == 32768 random numbers but the module produced an entire range of random numbers equal to 2**25.

Update: perl version -
C:\Old_Data\perlp>perl -v This is perl 5, version 14, subversion 1 (v5.14.1) built for MSWin32-x64-multi-thread

Windows version - 7