Sometimes when I am petting my 3-year-old cat she will roll over on her back and stretch out. At this point, if I bring my hand near she will try to grab it with her claws or mouth. I think she is just being playful, but my hand is not the ideal playmate for a ten-pound predatory animal. However, I don't want to just leave her hanging if she wants to play. Is there some kind of toy I can substitute for my cat to play with, or should I just leave her alone when she does this?
I've found that when my cats want that kind of play, I get the best results by substituting a decent-sized stuffed toy (catnip is optional). I don't mean one of the tiny mice designed for batting around, but, rather, a toy that's at least 3-4" around, something that the cat can reasonably hold onto with both front paws and/or its mouth while rolling around on its back. (I don't know where to buy toys of this sort commercially; mine are hand-made. If you want to make your own, a rectangular stuffed toy is pretty easy.)
I've tried offering a thing on a string, but when my cats want to wrestle they don't seem to want to chase an airborne object. They want to grab something and hold on; the key is for that thing that they grab to not be a body part or anything else that is Not A Toy.
Our dogs (when we had dogs) used to like "tug of war" with a cloth knotted on both ends. I've never tried this with a cat, but that might work too -- it gives the cat something to grab onto (unlike the thing on a string) and allows you to put a little more distance between your hands and the cat.
Playtime is an important bonding experience between you and your cat so you should take the opportunity to play!
However, if you let her play with your hand, you will teach her that hands are acceptable playtoys, and it will become difficult to later teach her not to bite or claw at your hands.
I would also recommend staying away from any toys that are hand shaped, such as padded gloves (some people will play with their cats using oven mitts or specially designed cat toy gloves). These items will also teach the cat that your hand is a toy.
A better idea is to use a toy that will establish a clear distance between your hand and her. Interactive wand toys such as Da Bird are usually a good choice.
I have in the past used 8-12" stuffed animals (usually tigers). I'm not sure how much difference it makes to the cat whether you use a kicker (stuffed rectangle) or a stuffed animal toy, but I enjoy making the stuffed animal lash its tail and make stalking movements toward my cat, and I think that my cat gets more enjoyment out of this sort of play, since when I do so my cat often switches from defensive fighting positions (lying on back) to offensive ones (jumping on the toy and chewing/kicking the heck out of it).
I think the hand attacking/kicking behavior is play for the purpose of learning how to fight large opponents (like other cats), while chasing a cat teaser or laser pointer is play for the purpose of learning to catch prey. I try to think about how to make my cat's pretend opponent more realistic since this seems to make my cat enjoy play more. So when I use a laser pointer, I will make the dot scurry along walls, duck around corners, and run and hide inside paper bags as though it were a small frightened prey animal, rather than just wriggle it back and forth in front of my cat, and she seems to become much more focused on catching the dot when I do this.
I let my cat grab and bite my hand. I tease her a little by rubbing her belly and she will try to attack my hand. But when she hurts me I say "a-a-a-ah" loud enough. At first it was not intentional, I just screamed because of pain and noticed that it made her stop. So whenever I show that I'm hurt, she will leave my hand alone and can even start to lick it.
I got is as she understands that she must be gentle with my hands. Don't know how, but she also figured herself that attacking my feet or legs must be done without claws. Maybe because she learnt that my hands don't like to be scratched.
Not sure if I'm just lucky to have a clever and caring cat or that I've found a good way to teach her.