2 miles passing distance is a good guide between ships. It also depends on who's on the bridge of the other ship! some of these guys rely heavily on GPS plotters & ECDIS and don't like straying off the track.
I've heard of masters on some FOCs coming onto the bridge and checking the course recorder, then give the 3rd Mate a clip over the ear for altering course and wasting fuel!
Not sure how true it is, but experience tells me some don't like altering in head-on situations, if you alter course 4-6 miles away, they will maintain course and not reciprocate the action.