A very simple examination of capital placement:
 

Using a hexagonal map, and making it "wrap around", in order to have four moves between everyones capital it requires 18 provinces per players.

What I mean by four moves is:
<Capital>-<Province>-<Province>-<Province>-<Capital>
Thus it would take four moves to go from one capital to another.

If someone wants to work with a hexagonal map-pad, or make their own, this can be verified fairly quickly.

For three moves, you require 9.33 provinces per player.

Now, most Dominions maps have less connections per province, so that would tend to drop the 18 provinces per player count down quite a bit. Making the map not-wraparound would lower the required number of provinces per player further

Most players find 15-16 provinces comfortable, and following the four moves to enemy capital is relatively easy, on a non-wrap around map . BUT, if one makes the map wrap-around, then the number of provinces required to have four moves to enemy capitals GOES UP. It may still be POSSIBLE to follow the four move rule, but it becomes MUCH MUCH MORE DIFFICULT.
This is because a capital in the northeast corner now "touches" a capital in the southwest corner, and so provinces must be added between them.

For that reason, I think maps with wrap-arounds should have an additional province added per player to adjust for the increased closeness that losing the borders causes.

Re: A very simple examination of capital placement:
 

I think that the start locations should be assigned automatically by a script that requires 4 provinces between starts.

If it doesn't find good starts with 4 provinces between each pair, generate a new random map.

Re: A very simple examination of capital placement:
 

I was hoping for some insider information on some stocks.

Re: A very simple examination of capital placement:
 

I don't think Illwinter is a publicly traded company. Shrapnel might be.