Why is that a favorite? I get it'll shuffle anything correctly, but trading O(NlogN) for O(1) is painful:

#! perl -slw
use strict;
use Benchmark qw[ cmpthese ];
use List::Util qw[ shuffle ];
use Data::Dump qw[ pp ];

sub buk1 { $a = $_ + rand @_ - $_ , $b = $_[$_], $_[$_] = $_[$a], $_[$
+a] = $b for 0 .. $#_; return @_; }
sub buk2 {
    die 'Need array reference' unless ref( $_[0] ) eq 'ARRAY';
    our( @aliased, $a, $b ); local( *aliased, $a, $b ) = $_[0];

    $a = $_ + rand @aliased - $_,
    $b = $aliased[ $_ ],
    $aliased[ $_ ] = $aliased[ $a ],
    $aliased[ $a ] = $b
        for 0 .. $#aliased;
    return;
}

sub tybalt {
    map $_->[0],
    sort { $a->[1] <=> $b->[1] }
    map [ $_, rand ], @_;
}

our $SANITY //= 0;

if( $SANITY ){
    my %tests;
    my @test = 1 .. 4;

    buk2( \@test ),
    ++$tests{ buk2     }{ join ' ', @test            } for 1 .. 10000;
    ++$tests{ buk1     }{ join ' ', buk1( @test )    } for 1 .. 10000;
    ++$tests{ tybalt   }{ join ' ', tybalt( @test )  } for 1 .. 10000;
    ++$tests{ ListUtil }{ join ' ', shuffle( @test ) } for 1 .. 10000;

    pp \%tests;
}

our $SIZE //= 100;
our @array = 1 .. $SIZE;

cmpthese -1, {
    buk1    => q[ my @shuf = buk1( @array ); ],
    buk2    => q[ buk2( \@array ) ],
    tybalt  => q[ my @shuf = tybalt( @array ); ],
    ListUtil=> q[ my @shuf = shuffle( @array ); ],
}
[download]

Benchmark:

           Rate   tybalt     buk1     buk2 ListUtil
tybalt    224/s       --     -65%     -70%     -97%
buk1      644/s     187%       --     -14%     -91%
buk2      746/s     233%      16%       --     -90%
ListUtil 7342/s    3176%    1040%     884%       --

C:\test>shufflesBenchmark2018.pl -SIZE=1e3
           Rate   tybalt     buk1     buk2 ListUtil
tybalt    229/s       --     -66%     -70%     -97%
buk1      675/s     195%       --     -13%     -91%
buk2      776/s     238%      15%       --     -89%
ListUtil 7339/s    3102%     987%     846%       --

C:\test>shufflesBenchmark2018.pl -SIZE=1e4
           Rate   tybalt     buk1     buk2 ListUtil
tybalt   17.2/s       --     -75%     -78%     -98%
buk1     67.5/s     292%       --     -13%     -90%
buk2     77.2/s     349%      14%       --     -89%
ListUtil  704/s    3992%     944%     812%       --

C:\test>shufflesBenchmark2018.pl -SIZE=1e5
            (warning: too few iterations for a reliable count)

           Rate   tybalt     buk1     buk2 ListUtil
tybalt   1.21/s       --     -81%     -84%     -98%
buk1     6.40/s     430%       --     -15%     -89%
buk2     7.53/s     523%      18%       --     -87%
ListUtil 56.4/s    4566%     781%     649%       --
[download]