How do you know if your ex is serious about wanting you back or if he is just playing games?

You cannot know what your ex actually intends to do. What you can do is act in the way that best serves your own needs. If you want to put the relationship back together then you should act as if your ex is serious about wanting you back. Your ex may change his/her mind even if that was not their original intention. On the other hand, if you do not want the relationship to continue then act so as to end it now.