Rather than 'Global symbol "@array of lists" requires explicit package name...' I get the error 'Global symbol "$array_of_lists" requires explicit package name...'. When you reference the index in your loops, you are referencing it as a reference to a hash and not the hash itself. (ie $var->{$a} for a reference, $var{$a} for a hash). There was also an index typo fixed below. On the other hand, when selecting an array element, use [] instead of {}.

Update

my %array_of_lists = (1 => \@list3, 2 => \@list4, 3 => \@list899);
  #my @array_of_lists = (@list3, @list4, @list899);
  ##Set my hand
  my $my_pocket = "AcAs";
 
 #printf("\n\n@array_of_lists\n\n");
  #My cards
  my $my_card1 = substr($my_pocket, 0, 2);
  my $my_card2 = substr($my_pocket, 2, 2);
  printf("$my_pocket");
  
  #for (my $z = 0; $z <= 100; $z++
  #{
  for my $a ( 0 .. scalar(keys %array_of_lists))
    {
        #The loop will iterate through each element (hand of current h
+andlist)  of the current row and remove any
        #hand that contains the cards assigned randomly above.
        for my $b ( 0 .. $#{$array_of_lists{$a}} )
        {
            #If the first card of the random hand above equal the firs
+t card in the element I am currently on, then remove the element from
+ this handlist by
            #splicing it out. Or if the first card of the random hand 
+above equal the second card of the element (hand) I am currently spli
+ce it out.
            if (substr($my_pocket, 0, 2) eq substr($array_of_lists{$a}
+[$b], 0, 2) || substr($my_pocket, 0, 2) eq substr($array_of_lists{$a}
+[$b], 2, 2))
            {
                $array_of_lists{$a} = splice(@{$array_of_lists{$a}}, $
+b, 1);
            }
            elsif (substr($my_pocket, 2, 2) eq substr($array_of_lists{
+$a}[$b], 0, 2) || substr($my_pocket, 2, 2) eq substr($array_of_lists{
+$a}[$b], 2, 2))
            {
                $array_of_lists{$a} = splice(@{$array_of_lists{$a}}, $
+b, 1);
            }
        }
    }
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