I am going through this right now with my puppy. He bites harder than any of the others when he plays. I am not sure why some bite hard and others seem to know from the start tohold back. I thought maybe he bit harder because he never had a mother to nip gently when he got too rough within the litter. I hand-raised this litter. But since others go through the same thing, maybe it is just a case-by-case trait.
I find Chachi's advice is working best for me so far. At least when I yell like I am hurt, Rocky stops biting and just looks at me. Then he starts licking so I know he is not meaning to hurt -- he just has to learn how hard he can bite without hurting. I have also been using the "No Bite" sternly spoken and the distraction with a toy. He still keeps doing the same thing on each play time. But I am sure with persistence he will lighten up.
I agree about not using the crate as a punishment place. You want him to like his crate. I would also get an exercise pen or a play yard. That way he has some place to play and get some of that energy out. Mine now has run of half of the house -- just not down the hall to the bedrooms. That way he is pretty much in my sight at all times, but is not penned up. I also have the advantage of other dogs to help work out some of the extra energy -- they chase each other in a big figure eight through out house. Hilarious unless you are trying to concentrate on something.
I had also read about one behavior modification practice, especially for my situation with no momma dog to teach....the idea was to nip gently with your fingers right around the top of the puppies neck, like a momma dog would with her teeth when she wanted to correct a behavior. Since yours is so young it might work. I did not have much luck with it, probably because I was too reluctant to make the little nip hard enough to do more than make the puppy think I was playing more. But I can follow the logic of why it would work.
The biting when playing is really a pretty common thing to deal with -- I won't even call it a problem. It is just that some seem to instinctively know how hard they can go better than others. Good luck!