Simple implementation of the statistics Monty Hall problem.

monty.pl

#! /usr/bin/perl

# implement the monty hall problem, run it a while, calculate percentages

sub make_doors {
  my($car, @door, $i);

  $car = int(rand(3));
  for ($i = 0; $i < 3; $i++) {
    $door[$i] = ($i == $car);
  }
  $car_door[$car]++;    # keep some additional stats
  return(@door);
}

sub guess1 {
  my($pick);

  $pick = int(rand(3));
  $guess_door[$pick]++;
  return($pick);
}

sub guess2 {
  my($oldpick, $montyshow) = @_;
  my($i);

  for ($i = 0; $i < 3; $i++) {
    return($i) unless $oldpick == $i or $montyshow == $i;
  }
}

sub monty {
  my($pick, @door) = @_;
  my($i, @montyshow, $montyshow);

  for ($i = 0; $i < 3; $i++) {
    next if $i == $pick;
    push(@montyshow, $i) unless $door[$i];
  }
  $montyshow = $montyshow[int(rand($#montyshow))];
  return($montyshow);
}

sub find_car {
  my(@door) = @_;
  my($i);

  for ($i = 0; $i < 3; $i++) {
    return($i) if $door[$i];
  }
}

sub play_one {
  my(@doors, $mypick, $monty, $mynewpick, $car);

  @doors = &make_doors;
  $mypick = &guess1;
  $monty = &monty($mypick, @doors);
  $mynewpick = &guess2($mypick, $monty);
  $car = &find_car(@doors);
  if ($car == $mynewpick) {
    $pick = "NEW";
    $newct++;
  } else {
    $pick = "OLD";
    $oldct++;
  }
  $totalct++;

  # columns are:  first pick, monty's show, second pick, car location
  printf "%10d: %2d %2d %2d %2d %s\n", $totalct, $mypick+1, $monty+1,
    $mynewpick+1, $car+1, $pick;
}

$max = shift;
$max = 20 unless defined($max);

print "this is the monty hall problem.  FP is the player's first pick,\n";
print "MP is what door monty shows you, SP is the player's second pick,\n";
print "AT shows which door the car is actually behind.  also shown is\n";
print "if the player SHOULD have kept their OLD choice or gone with the\n";
print "NEW one.\n\n";

print " trial num: FP MP SP AT\n";
for ($i = 0; $i < $max; $i++) {
  &play_one;
}

printf "played %d games:  NEW: %d (%2d%%) OLD: %d (%2d%%)\n",
  $totalct, $newct, int($newct * 100 / $totalct),
  $oldct, int($oldct * 100 / $totalct);

monty_output.txt

3812 bash$ ./monty.pl
this is the monty hall problem.  FP is the player's first pick,
MP is what door monty shows you, SP is the player's second pick,
AT shows which door the car is actually behind.  also shown is
if the player SHOULD have kept their OLD choice or gone with the
NEW one.

 trial num: FP MP SP AT
         1:  3  2  1  1 NEW
         2:  1  2  3  3 NEW
         3:  2  1  3  2 OLD
         4:  1  3  2  2 NEW
         5:  1  3  2  2 NEW
         6:  3  1  2  2 NEW
         7:  2  1  3  2 OLD
         8:  2  1  3  2 OLD
         9:  2  3  1  1 NEW
        10:  2  1  3  3 NEW
        11:  2  3  1  1 NEW
        12:  1  3  2  2 NEW
        13:  3  1  2  2 NEW
        14:  2  3  1  1 NEW
        15:  3  2  1  1 NEW
        16:  3  1  2  2 NEW
        17:  2  1  3  3 NEW
        18:  1  2  3  3 NEW
        19:  2  3  1  1 NEW
        20:  2  1  3  3 NEW
played 20 games:  NEW: 17 (85%) OLD: 3 (15%)
3813 bash$ ./monty.pl 100000 | grep played
played 100000 games:  NEW: 66606 (66%) OLD: 33394 (33%)