The no-shows and group-size reductions show up the day before, sometimes two days before. As I write this, there is one Day Use available for tomorrow, but no overnights. You have to keep checking the site to catch one when they pop up.

Any slots farther out are way more scarce, and show up infrequently.

If they would start refunding some of the permit fees for early cancellations, there would probably be more available, but giving back money is apparently a really difficult thing to do.