Just for fun I made a copy of the chisquare() function in S::CS, that returns the number it calculates, rather than its string assessment of what that value means:

sub chisquaredVal {
    my @data = @_;
    @data = @{$data[0]} if(@data == 1 and ref($data[0]));
    return "There's no data!" if(!@data);
    return "Not enough data!" if(@data == 1);
#    return "Malformed data!" if(grep { /\D/ } @data);

    my $degrees_of_freedom = scalar(@data) - 1;
    my ($chisquare, $num_samples, $expected, $i) = (0, 0, 0, 0);
    if (! ref($chitable[$degrees_of_freedom])) {
        return "I can't handle ".scalar(@data)." choices without a bet
+ter table.";
    }
    foreach (@data) { $num_samples += $_ }
    $expected = $num_samples / scalar(@data);
    # return "There's no data!" unless $expected;
    foreach (@data) {
        $chisquare += (($_ - $expected) ** 2) / $expected;
    }
    return $chisquare;
}
[download]

I also had to disable the "Malformed data" tests, as they reject floating point numbers!)

Then I wrote a script that repeated the test a hundred times on the F-Y shuffle using MT rand(), and gathered the numerical values it produces into an array:

#! perl -slw
use strict;
use Statistics::ChiSquare qw[ chisquare chisquaredVal ];
use Math::Random::MT;
use Data::Dump qw[ pp ];

my $mt = Math::Random::MT->new();

our $N          //= 1e6;
our $ASIZE      //= 4;
our $T          //= 4;

sub     shuffle {
        $a = $_ + $mt->rand( @_ - $_ ),
        $b = $_[$_],
        $_[$_] = $_[$a],
        $_[$a] = $b
                for 0 .. $#_;
        return @_;
}

my @data = ( 1 .. $ASIZE );
my @chi;
for( 1 .. $T ) {
    my %tests;
    ++$tests{ join '', shuffle( @data ) } for 1 .. $N;
    push @chi, chisquaredVal( values %tests );
}
[download]

And finally, ran the original chisquare() function on its own output for assessment:

print chisquare( @chi );

__END__
C:\test>chiSquareChiSquare -ASIZE=7 -N=2e2 -T=1e2
There's a >99.5% chance, and a <100% chance, that this data is random.

C:\test>chiSquareChiSquare -ASIZE=7 -N=2e2 -T=1e2
There's a >90% chance, and a <95% chance, that this data is random.

C:\test>chiSquareChiSquare -ASIZE=7 -N=2e2 -T=1e2
There's a >99.5% chance, and a <100% chance, that this data is random.
[download]

Finally, I think it got something right!

Its own output is truly random :)

(Sorry. I was bored :) )