Get Next Post or First Post

I have the following code which should display the next post or the first post if it is the last post.

<?php
$next = next_post_link('%link', 'Next Game');

  if($next == null){

	echo '<a rel="first" href="'.get_permalink(4).'">Next Game</a>';

  }else{

	 echo next_post_link('%link', 'Next Game');
  }
?>

It works well except on posts where it is NOT the last post t displays two links: NextGameNext Game

linking to both the next post and the first post!

On the last post it correctly displays a link to the first post. I can’t understand how it is pulling two links for posts that are not the last post.