I have gotten bitten several times - twice by Jack Russells whose owners though asked failed to tell me their dogs were aggressive. Now I just assume the worst of these dogs and don’t touch them.
The worst was when I stuck my hand in to break up two pits. I knew I was going to get bitten but I felt I had to intervene to prevent serious injury to one of the dogs. Sure enough, in the heat of the fight, I was bitten. It was inadvertent and the dog immediately let go, but the bite was hard.
A good hard kick in the @$$ works wonders in breaking up a dog fight. A swift kick in the belly if it's a dangerous dog. They forget all about biting when you knock the wind out of them.