Maybe this explains it better?

The following program uses this heavily biased PRNG:

sub badRand($) { rand() < 0.5 ? 0 : rand( $_[0] ) }
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which is designed to produce 0, 50% of the time. That means that when asked for numbers 0-9, it produces '0', 10 times more often than any of the other values:

[549637, 50008, 50261, 50195, 50365, 49871, 50000, 49692, 49768, 50203
+]
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And when asked for 0..23, produces '0' 25 times more often than any other number:

[ 521654, 20747, 20716, 20614, 20914, 20740, 20906, 20580, 20625, 2107
+7, 20736, 20912, 20835, 20820, 20958, 20818, 20866, 20818, 20969, 206
+46, 20749, 20953, 20454, 20893, ]
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But when that biased PRNG used within a standard Fisher Yates shuffle, the shuffles are fair, no matter how many times you run it:

{
  ABCD => 67436,
  ABDC => 67742,
  ACBD => 67990,
  ACDB => 68277,
  ADBC => 68018,
  ADCB => 67846,
  BACD => 67766,
  BADC => 67859,
  BCAD => 68598,
  BCDA => 68919,
  BDAC => 69172,
  BDCA => 67870,
  CABD => 67755,
  CADB => 67192,
  CBAD => 67657,
  CBDA => 67731,
  CDAB => 67793,
  CDBA => 67680,
  DABC => 67755,
  DACB => 68016,
  DBAC => 68098,
  DBCA => 67988,
  DCAB => 67666,
  DCBA => 68408,
}
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The test code:

#! perl -slw
use strict;
use Data::Dump qw[ pp ];

sub badRand($) { rand() < 0.5 ? 0 : rand( $_[0] ) }

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

my @rands; ++$rands[ badRand( 10 ) ] for 1 .. 1e6; pp \@rands; <STDIN>
+;

my @vals = ( 'A' .. 'D' );
my %tests;
my $c = 0;
while( 1 ) {
    ++$tests{ join '', shuffle( @vals ) };
    unless( ++$c % 576 ) {
        system 'cls';
        pp \%tests;
    }
}

__END__
c:\test> junk77
[549637, 50008, 50261, 50195, 50365, 49871, 50000, 49692, 49768, 50203
+]
{
  ABCD => 67436,
  ABDC => 67742,
  ACBD => 67990,
  ACDB => 68277,
  ADBC => 68018,
  ADCB => 67846,
  BACD => 67766,
  BADC => 67859,
  BCAD => 68598,
  BCDA => 68919,
  BDAC => 69172,
  BDCA => 67870,
  CABD => 67755,
  CADB => 67192,
  CBAD => 67657,
  CBDA => 67731,
  CDAB => 67793,
  CDBA => 67680,
  DABC => 67755,
  DACB => 68016,
  DBAC => 68098,
  DBCA => 67988,
  DCAB => 67666,
  DCBA => 68408,
}
[download]