LarryD, if you go to the unused permits pages, each one has a link to the unused permits page for the prior year, so you can see the trends for yourself, back as far as 2007. Mondays are good, but my feeling is that Tuesdays are even better.
Also, please understand, the unused numbers are after ALL activity is completed at the end of that date. If you go in at 11 AM, your chances of getting a no-show or cancellation permit is even better than those unused numbers.
This year, if you go in at 8:30 or so, as people are coming in and picking up their permits, they often shed a few slots due to some party members dropping out. So THOSE permits become available immediately, even before the 11 AM time when no-shows become available.
The other thing to try is to watch the Recreation.gov site for the date you want, and keep checking several times each day. People do cancel their reservations, so those permits become available sometime within 24 hours after the cancellation.
...and you didn't say whether you are looking for day hike or overnight permits. The links to whichever permit you want are in the 2012 unused permits page.
