RSW

Is there a setting that will guarantee that all homeworlds have the same number of adjacent planets? It seems that a disparity on the first turn really snowballs and makes a significant difference in the size of one's empire.

Hmm, no, but it sounds like a good idea. Presently, the RSW server does make an attempt to guarantee that the number of worlds that all players can reach within the first three turns is similar.

David

Does it determine this by just taking the number of planets within 3 steps of the homeworld, or does it actually consider factors like what fleets you'd pick up on the way and therefore how much you'd be able to explore within 3 turns?

A little of both. It's not sophisticated enough to consider the number of fleets, but instead assumes you'll be able to explore every connection you discover until you encounter other players. However, it does consider the implicit borders created by the other players' simultaneous expansions as well.

David

Will it make sure there are no black holes within 3 worlds of your homeworld? I'd hate to start 1 hop or 2 hops away from a black hole.

No such guarantees. It does know about black holes and doesn't count them towards the worlds you can reach, though; and it knows that you can't fly through a black hole.

As to placement, though, the only guarantee is that there will not be a black hole immediately adjacent to your homeworld. You might discover a black hole on turn 2, though, if you are really unfortunate. On the other hand, a black hole in such proximity to your homeworld might be a useful defensive advantage as well.

David