my $min = 1;  # Min die value.
my $max = 6;  # Max die value
my $numdice = 4;

my $dice;  # ref to the table with dice.
my $num;  # number of combinations.
my $hist; # histogram

sub High_one;

prepare_dice();
# print "@{$dice}" . "\n";
# for (my $i=1; $i<216; $i++)
# { forward_dice();
# }
do
{
#  print "@{$dice}" . "\n";
  $$hist{High_two()} += 1;
} while (forward_dice());
# print "@{$dice} Num: $num\n";
print_hist();


# Init $dice to $numdice dice with value $min.
sub prepare_dice
{ $dice = undef;
  $num = 1;
  for (my $i=0; $i<$numdice; $i++)
  { push (@{$dice}, $min);
  }
}

# Forwards dice by 1 and takes care of overflows.
# Returns 0 when there are no more combinations, 1 otherwise.
sub forward_dice
{ my $ind = $numdice -1;
  my $ovf = 0; # Overflow
  do
  { $ovf = 0;
    $$dice[$ind] += 1;
    if ($$dice[$ind] > $max)
    { $$dice[$ind] = $min;
      $ind--;
      $ovf = 1;
    }
  } while ($ovf and ($ind >= 0));
  if ($ind >= 0)
  { $num++;
    return 1;
  }
  return 0;
}

# Return the highest die.
sub High_one
{ my @sorted = sort { $b <=> $a}  @$dice;
  return $sorted[0];
}

# Return the sum of two highest dice.
sub High_two
{ my @sorted = sort { $b <=> $a}  @$dice;
  return $sorted[0] + $sorted[1];
}


# Print histohram.
sub print_hist
{ my %upto = ();  # Number of this or lower.
  foreach my $i (sort { $a <=> $b} keys %$hist)
  { $upto[$i] = $$hist{$i};
    $upto[$i] += $upto[$i-1] if (defined $upto[$i-1]);
  }
  my %gteq = (); # Number of this or higher
  foreach my $i (sort { $b <=> $a} keys %$hist)
  { $gteq[$i] = $$hist{$i};
    $gteq[$i] += $gteq[$i+1] if (defined $gteq[$i+1]);
  }

  my $avg = 0;  	# Compute average and standard deviation.
  my $stdev = 0;
  foreach my $i (keys %$hist)
  { $avg += $i * $$hist{$i};
  }
  $avg /= $num;
  $avg = sprintf '%2.4f', $avg;
  foreach my $i (keys %$hist)
  { $stdev += ($avg - $i) * ($avg - $i);
  }
  $stdev /= keys (%$hist);
  $stdev = sprintf '%2.4f', sqrt($stdev);

  print "Dice: Highest 2 of $numdice, combinations: $num, Average: $avg, Stdev: $stdev \n";
  print "Outcome, Probability, LowerOrEqual, HigherOrEqual \n";
  foreach my $i (sort { $a <=> $b} keys %$hist)
  { my $ind = sprintf "%2d", $i;
    my $prob = sprintf '%.6f', $$hist{$i}/$num;
    my $lowEq = sprintf '%.6f', $upto[$i]/$num;
    my $gtEq = sprintf '%.6f', $gteq[$i]/$num;
    print "$ind, $prob, $lowEq, $gtEq \n";
  }
  #print "@{$hist} \n";
}



# Sortowanie takie jak potrzebuję, z zachowaniem tablicy źródłowej i od największej liczby do najmniejszej:
# my @sorted = sort { $b <=> $a}  @$aref;
# Wystarczy wtedy wziąść pewną część liczb od początku.
# Ewentualnie obciąć:
# my @third = splice(@sorted, 0, 2);  // Pierwsze 2.