How do you discourage a dog from biting while playing?

I've always trained dogs not to bite by firmly saying "Ow! No bite." They have to learn that we are more delicate than other dogs. It's also very important to provide them with an alternative.

So I make a noise like it hurt, say no bite, and then give them a toy immediately after. This promotes what I call 'substitute biting,' where I'll rile one of my dogs up with a little rough housing, and they'll grab a toy and start chomping down and shaking that while looking at me.

I fostered a stray who I basically had to train all the puppy phases out of when he was about 1 year old and as big as my wife (GSD mix/mut). Even tho he was starved of human contact, he too learned not to bite with this method. Took longer than most puppies.. but when I'd say "Ow! No bite." he'd stop and look at me trying to figure out what prompted it. If toy substitution didn't work, I'd stop playing. He learned that if he wanted to play, he couldn't bite the fragile humans.

Also worth noting that some dogs (common with GSD for instance) like to engage in a sort of handholding, especially as a puppy. It may seem like they're wanting to chew on you if you don't know better, but if they kinda just get your hand in their mouth it could be the 'handholding.' I break that habit because it can still scratch and I don't want someone to claim a dog of mine 'bit' them by doing it.