Chainmail post melee morale probabilities for 6 LF vs 6 LF

#!/usr/bin/perl
# Chainmail post melee morale probabilities for 6 LF vs 6 LF

sub nFactorial { # Factorial n!
    my $n=shift;
    my $product = 1;
    while($n>0) {
        $product *= $n--;
    }
    $product;
}

sub nCr { # Combinations of n out of r
    my ($n,$r) = @_;
    int nFactorial($n) / int nFactorial($r) * int nFactorial($n-$r);
}

# Probability of 6 LF scoring n kills against 6 LF, n in 0..6
sub prob {
    my ($n) = @_;
    nCr(6,$n) * (1/6)**$n * (5/6)**(6-$n);
}

foreach $lA (1..6) {
  foreach $lB (1..6) {
    foreach $m (1..6) { # Morale die
      # Step 1: Compute fewer casualties
      $dA = 6 - $lA; # A's casualties
      $dB = 6 - $lB; # B's casualties
      $p = (prob($dA) * prob($dB))/6; # Probability of this outcome
      if( $dA < $dB ) {
        $r1A = $m * ($dB - $dA);
        $r1B = 0;
      } elsif( $dB < $dA ) {
        $r1B = $m * ($dA - $dB);
        $r1A = 0;
      } else { # $dA == $dB
        $r1A = 0;
        $r1B = 0;
      }
      # Step 2: Compute greater survivors
      if( $lA > $lB ) {
        $r2A = $lA - $lB;
        $r2B = 0;
      } elsif( $lB > $lA ) {
        $r2B = $lB - $lA;
        $r2A = 0;
      } else { # $lA == $lB
        $r2A = 0;
        $r2B = 0;
      }
      # Step 3: Surviving figures
      $r3A = 4*$lA;
      $r3B = 4*$lB;
      # Step 4: Morale scores
      $sA = $r1A + $r2A + $r3A;
      $sB = $r1B + $r2B + $r3B;
      # Difference
      $d = abs($sA - $sB);
      # Double difference because no. figures per side < 20
      $d *= 2;
      $prob{$d} += $p;
    }
  }
}

foreach $d (sort {$a <=> $b} (keys %prob)) {
  #print $d, " ", $prob{$d}, "\n";
  if( $d >= 0 && $d <= 19 ) {
    $meleecontinues += $prob{$d};
  } elsif($d >= 20 && $d <= 39) {
    $backhalfgoodorder += $prob{$d};
  } elsif($d >= 40 && $d <= 59) {
    $backonegoodorder += $prob{$d};
  } elsif($d >= 60 && $d <= 79) {
    $retreatonemove += $prob{$d};
  } elsif($d >= 80 && $d <= 99) {
    $routoneandhalfmove += $prob{$d};
  } else { # $d >= 100
    $surrender += $prob{$d};
  }
  $total += $prob{$d};
}

# 13 special cases where we do not need to check post melee morale
# Probability A wipes out B
for $dA (0..5) { $p0Bs += prob($dA) * prob(6); }
# Probability B wipes out A
for $dB (0..5) { $p0As += prob($dB) * prob(6); }
# Probability A & B wipe out each other
$p0 = prob(6) * prob(6);
# Add these special cases to the total probability mass
$total += $p0 + $p0As + $p0Bs;

print "Outcome:                           Probability\n";
print "=======================================================\n";
print "A and B wipe out each other:       ", $p0, "\n";
print "A wipes out B:                     ", $p0Bs, "\n";
print "B wipes out A:                     ", $p0As, "\n";
print "Melee continues            (0-19): ", $meleecontinues, "\n";
print "Back 1/2 move, good order (20-39): ", $backhalfgoodorder, "\n";
print "Back 1 move, good order   (40-59): ", $backonegoodorder, "\n";
print "Retreat 1 move            (60-79): ", $retreatonemove, "\n";
print "Rout 1 1/2 move           (80-99): ", $routoneandhalfmove, "\n";
print "Surrender                  (100+): ", $surrender, "\n";
print "Total:                             ", $total, "\n";