Early to mid-June, mid-week lottery slots are truly easiest to get. Only you need to understand, if we have above average snowfall, the switchbacks are often covered with snow in June.
However, pretty much anytime mid-week, you can get walk-in (free) permits. If you have the time, go on a Sunday or Monday, get into the line and ask for a next-day permit. The best times are at 11 AM for overnight permits, and 2 PM for day hikes. But any time during the day, as people with permits check in and drop off a few slots, those slots become available.
Note that the
Unused Permits numbers are the numbers from the end of the day, after anyone and everyone looking for the walk-ins has been given permits.
Now that the permit season is over, I hope to get the numbers for the 2015 season up pretty soon.