Let's pretend that you have to photograph a martial arts black belt test in a studio with roughly 1600 square feet of mat space.
Of course, the subjects are going to be throwing kicks, punches, and so on (need to freeze action) and the studio is rather poorly lit by overhead florescent lights.
I don't want to have to pump up the ISO too much because I want to make sure the photos are sell-quality as this is a very memorable event.
I have three AB800s to work with and a 430ex that can be tripped via slave or triggered remotely.
I'd probably do this the same way I do christmas morning, where the kids are running all over the place and I need good light everywhere. I use the ceiling as a huge softbox. I put 2-3 remotely triggered strobes out of the way, near the sides of the room, angled up toward the ceiling, so that I get some good diffused light no matter where I am. Do some test shots to set a reasonable manual exposure, and shoot in RAW to give me some fudge factor. Here's an example shot with this setup:
Assuming this martial arts studio has those fluorescent lights in a normal height, suspended ceiling, this ought to work for you as well. It won't be the most creative light, but it will be decent.
I don't think they will want strobes going off during a test. I think you need to approach it much the way you would for shooting a basketball game (there are several helpful threads about shooting sports) -- rely on anticipating the action, pre-focusing, open aperture and the highest ISO setting you can get away with, and hope this allows a fast-enough shutter speed. Don't shoot at maximum zoom so you have some room for the participants to move; you can always crop later.
One other possible workaround is to convert to grayscale; at any given ISO level, I find the Green Channel is often smoother than the image as a whole (I think the sensors have twice as many green-detectors as red or blue), and I will just copy that to a graysscale image and adjust from there.
I face much the same situation/conditions at Isaac's dojo -- as you can see, I only get middling results, but you should be able to do better with a dSLR.
