Why a "reverse" grip I see so much, one palm facing in, other out? I was told it was for *balance*, but didn't quite understand what it does. And, if it is a good, recommended grip, should one be switching sides; right palm inward - left palm out first set, right palm outward left palm in second, and so on?
A mixed grip doesn't necessarily improve your grip strength, but it makes the mechanics of gripping easier.
The problem with the double overhand grip is that that bar wants to roll out of your hands. When you get to heavier weights this becomes more noticeable. I try to stick with double over hand (DOH) as long as possible to stimulate strength gains in the forearms, but switching to a mixed grip is often necessary when you progress to heavier weights.
When you switch to a mixed grip, gripping is easier because when the bar rolls OUT of one hand, it rolls INTO the other. This offers a counter-force that makes gripping the bar easier.
My max DOH pull is 405 lbs for a single, and I can't lift anything beyond that with that grip style. I've pulled 315x30 (I probably can't lift >10 reps with DOH), 405x8 and 485x1 with a mixed grip, and grip was never an issue. For me, switching to a mixed grip makes a HUGE difference and it is totally necessary if i want to increase my deadlift strength.
I've always read to stick with the double overhand grip until you can no longer hold the weight your deadlifting for reps without losing grip, then switch over to the mixed grip. Seeing how I'm just getting started lifting again, I don't think I'll be needing to switch anytime soon.