i usually run mine around 10-12 on hard/soft loomy tracks, and if is kind of rocky i usually put 15, just cuz im cheap and i dont wanna burst the tire haha. But usually the less air pressure the better traction, this only applys until a cirtain pressure, if its to low, the tire will actually slide on the rim, which will cause lose of traction, if its to high, there wont be enough tire on the ground and will slide alot, giving less traction. thats just wat i kno, hope it helps.
Riding conditions, tire size, tire brand/, model, and your riding style all come into play for what's "best".
Depends on the air gauge you use as well. I have three, they all read differently. If one says I have 12 psi in, the others will read 11.5 and 13.5 psi or so. I stick with one gauge now, and have a good feel for how changes in pressure effect the bike. On that gauge I run 10-12 psi in the rear and 13-15 up front. Depending on the terrain it can make a big difference. One of my first rocky rides I ran 15 psi and struggled everywhere. A local told me to try 10 psi in my Maxxis IT rear, then it was a whole different story!
Hard pack is dirt that's packed about as hard as pavement, you know, dirt roads and such. The hard pack trails I ride have a lot of square edged holes. The extra pressure helps reduce the risk of pinch flats.
The very first time I had a new tire put on a dirtbike, I had no idea what the pressure should be and just assumed the Mensa guys at the shop knew what they were doing. I cussed that darn rear tire for two months because I couldn't take a turn at anything over 10 mph without my rear end sliding out from me. I can't even tell you how many times I ended up running off the bike on my feet as it slid sideways. I finally just checked the pressure on both tires for no real reason I can remember. The front was 13. The new tire was 27!!!
I ride on all sorts of terrain and generally try to keep my pressure at 13-14 and it seems to work pretty well everywhere.