As a practical matter, I recorded this rule of thumb for containerships at sea at night seen from deck of a yacht.
10 miles--one dim white light on horizon, may be mistaken for a rising star.
8 miles -- Unmistakably one bright white light.
6 miles -- Color appears, red or green, in confusing diffusion of whiteness.
5 miles -- Very clear identification of colored light. "Larger" than any white lights. First certainty of both red and green.
4 miles --No doubt about it.
3 miles--Bleedin' circus of deck lights, looks like Memorial Day at a used car lot approaching rather fast.
2 miles--If both red and green observed, 90-degree turn away already instituted. Bible out and open. Do not spill Jack Daniels on Bible. Our speed 6 knots. Containership speed 20 knots.
1 mile--a floating city passes with stupendous sound of throbbing engines, lit like Times Square and considerably more conspicuous that my LED running lights burning half an amp.
The numbers may seem conservative, but are made so by the interference of an active seaway and a low topsides (trough and mist obscure the view). But AIS gives a reliable record of what is seen at what distance. It also provides collision-course warning far in advance, before the sight of red and green approaching. An actual collision course at sea is a defiance of odds, since there are 360 points on the compass. Yet twice the AIS warned that a ship 5 miles away would come within .10 nm of us. Time to alter course.
Of course a yacht, unlike a ship, can yaw through 20 degrees in a seaway, one's "course" is not good data. But a "Collision Alarm", as my AIS calls a .10 nm "Closest Point of Approach, " does successfully win the attention.
Yacht running lights? Not very important offshore. Previously it was the odds that got us there (except for Slocum and all the other disappearances). With AIS there is no reason to get run down, and it's easy to know when to get out of the way.