as little as necessary :idontknow:
You want the tire soft enough to conform to the terrain, and provide traction, but still hard enough to keep it on the rim (Purpose of beadlocks), and keep the rim from pinching the tire/hitting the ground. What that magical point is, is going to be different jeep to jeep, and tire to tire... So YOU NEED TO AIR DOWN. to what point is the question. how much air can YOU keep in the tire and still get the grip you need??? :idontknow:
It takes about 6-8psi to get the tread flat on the ground with my jeep. but again, this is MY jeep, nearly empty (unloaded), on 10 ply Toyos.
When I'm wheeling, It really depends on what I am doing. If its sandy/Rocky, I'll get a little more aggressive with the air, but otherwise, 15psi give or take is plenty soft for a good day in the dirt. even WITH beadlocks and my *hard as F *10 ply toyos...