I did a walk up on a Friday in mid-July last year for an overnight permit. About 10 overnight permits were available, and I was the 11th so it looked like I would miss out. Then someone gave up a permit, so I was golden.
When you do the walk up, they basically do a mini lottery that morning. So, if you were the first to be picked on the day I showed up, and you needed 10 permits, you would have gotten all of them (and everyone else would have been out of luck). Obviously, the fewer permits you need, the more likely you will be able to get all the permits you need....
