It's a scary situation for reaction.
I nearly was hit last weekend by a headon Ford F250. I saw him about 1/4 to 1/8 mile away as we both came over a crest in the road and he stayed in my lane for several seconds. At first I thought he was just passing something, but there wasn't anybody around him on a 4 lane rural highway with divider turning lane.
He finally returned to his lane, but it left me in a dilemma as to what the best response to take. If the driver had drifted asleep, veering right might place you into his ultimate path. If remain steady, reaction distance/time is half your perceived safe distance and time to take action. If you veer to the left, then that is the path he would take if he was avoiding me.
I braked repeatedly, but it has to be one of the more easily encountered but deadliest situations out there.
I've read that one should not go left, as the natural reaction of the drunk is to drift right as he or she sees your lights approaching, figuring that you are just another vehicle he must pass to the right.