Instead of calculating I wrote a little script counting the probabilities of group combinations.

Roboticus was right, you need about 14,05 characters per line plus "\n"

Only 1 + 8 + 21 + 20 = 50 combinations are possible per group, resulting in a conservative compression of 50.79 bits = 6.34 bytes per line, which already means a compression to 42% = 58% win.

But if you look into the likelihood of those combinations you clearly see that a Huffman encoding would result in an even better ratio.

I think that's then near the theoretical optimum. (further reading Huffman_coding_with_unequal_letter_costs )

All this supposing your input was real... ;-)

 
use strict;
use warnings;
use Data::Dump qw/pp/;

my %count;

for my $c0 (0..9){
   for my $c1 (0..9){
      for my $c2 (0..9){
         for my $c3 (0..9) {
            my @c = sort {$a <=>$b} ($c0,$c1,$c2,$c3);
            #print "@c\t:\t";
            my @allowed;
            for my $i (1..3) {
               if ( $c[$i] != $c[$i-1]    &&   $c[$i] != $c[$i-1]+1 ) 
+{
                  push @allowed, $c[$i] 
               }
            }
            #print "@allowed\n";
            $count{join "",@allowed}++
         }
      }
   }
}



my @length;
my $average;
for my $k (keys %count){
   my $len = length $k;
   $length[$len]++;
   $average+= $len* $count{$k}/10000;
}

warn '@length: ', pp \@length;
warn 'average #characters: group/line',pp [$average,$average*9];


my  $combies =0;
$combies+= $length[$_] for 0..3;
#$combies=93;

warn "# possible combinations: ", $combies;


my $upper_bound= log($combies)/log(2)*9;
warn 'Upper bound bits, bytes', pp [$upper_bound, $upper_bound/8];

#warn "ranking", pp [ sort {$b <=>$a} values %count ];

warn 'probabilities: ',pp \%count;

[download]

@length: [1, 8, 21, 20] at /tmp/compress.pl line 36.
average #characters: group/line[1.5624, 14.0616] at /tmp/compress.pl l
+ine 37.
# possible combinations: 50 at /tmp/compress.pl line 44.
Upper bound bits, bytes[50.7947057079725, 6.34933821349656] at /tmp/co
+mpress.pl line 48.
probabilities: {
  ""    => 592,
  "2"   => 74,
  "24"  => 60,
  "246" => 24,
  "247" => 24,
  "248" => 24,
  "249" => 24,
  "25"  => 84,
  "257" => 24,
  "258" => 24,
  "259" => 24,
  "26"  => 84,
  "268" => 24,
  "269" => 24,
  "27"  => 84,
  "279" => 24,
  "28"  => 84,
  "29"  => 60,
  "3"   => 208,
  "35"  => 144,
  "357" => 48,
  "358" => 48,
  "359" => 48,
  "36"  => 192,
  "368" => 48,
  "369" => 48,
  "37"  => 192,
  "379" => 48,
  "38"  => 192,
  "39"  => 144,
  "4"   => 366,
  "46"  => 228,
  "468" => 72,
  "469" => 72,
  "47"  => 300,
  "479" => 72,
  "48"  => 300,
  "49"  => 228,
  "5"   => 524,
  "57"  => 312,
  "579" => 96,
  "58"  => 408,
  "59"  => 312,
  "6"   => 682,
  "68"  => 396,
  "69"  => 396,
  "7"   => 840,
  "79"  => 336,
  "8"   => 830,
  "9"   => 508,
} at /tmp/compress.pl line 52.

[download]

Cheers Rolf
(addicted to the Perl Programming Language :)
Wikisyntax for the Monastery FootballPerl is like chess, only without the dice

update

I just realized that Roboticus already had the same basic ideas here: Re: Data compression by 50% + : is it possible?

In reply to Re^3: Data compression by 50% + : is it possible? by LanX
in thread Data compression by 50% + : is it possible? by baxy77bax

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