P1 P2 P3 P4 P5 P6

 P1       1  2  3  4  5
 P2    1     4  5  3  2
 P3    2  4     1  5  3
 P4    3  5  1     2  4
 P5    4  3  5  2     1
 P6    5  2  3  4  1

##</code><code>##

Rd 1: (P1,P2), (P3,P4), (P5, P6)
Rd 2: (P1,P3), (P2,P6), (P4, P5)
Rd 3: (P1,P4), (P2,P5), (P3, P6)
Rd 4: (P1,P5), (P2,P3), (P4, P6)
Rd 5: (P1,P6), (P2,P4), (P3, P5)

##</code><code>##

  factorial[ ((n/2)-1) * (n-1) ] / [ factorial((n/2)-1) ]^(n-1)

##</code><code>##

Round 1:
match 8 with 1, then pair up the rest
symmetric to that line..

             1                       
             |                       
         7---|----2                  
             8                       
        6----------3                
                                    
           5----4                  

Round 2:
match 8 with 2, then pair up the rest
symmetric to the line..

             1                        
         7    \  2                  
          \    \^                     
           \ 8^ \                     
       6    \    3                
        \    \                        
         \    \                       
          5    4    

Round X: ... keep rotating around the circle, etc

##</code><code>##

my @players = qw/Frodo Sam Merry Pippin Strider Gandalf Legolas Gimli/;

########
my $num = @players;
die "must have even number of players" if $num % 2;

for my $partner (0 .. $num-2) {

  print "Round #" . ($partner + 1) . ":\n";
  print "  $players[-1] vs $players[$partner]\n";

  for my $pair (1 .. ($num-2)/2) {
    my $p1 = ($partner - $pair) % ($num - 1);
    my $p2 = ($partner + $pair) % ($num - 1);
    print "  $players[$p1] vs $players[$p2]\n";
  }
}