Cool. One remark: using int rand() instead of your random() sub should make it more efficient, and IMHO more readable:

#!/usr/bin/perl
my $wins = 0;
my $lose = 0;
my $goat;
for (my $i=0;$i<1000000;$i++) {
  my $car = int rand(3);
  my $choice = int rand(3);
  do {
    $goat = int rand(3);
  } while (($goat != $car) && ($goat != $choice));
  if ($choice != $car) {$wins++} else {$lose++};
}
print "WINS = $wins!\nLOSE = $lose!\n";
[download]

takes about 10 wallclock seconds at my machine, while the original takes more than 70 seconds.