Ouch! That doesn't sound like much fun! The problem may be that you're using your fingers as toys. If so, this sends a message to your cat that it's OK to bite flesh. Even if you're holding a small toy as you play, your cat won't know where the toy ends and your fingers begin.
To avoid this biting problem, engage your cat in play using a fishing-pole type of toy. This toy puts a very safe distance between the cat's teeth and your hand. Be sure to put the toy away after playtime to keep the cat from chewing the stringy parts, which would be unsafe.
Parenting 
