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To put the rule precisely, for each of your worlds, count the number of steps from that world to the nearest world not owned by you. That's the number of D-Ships that world will produce each turn.
Consider the following sample map:
In this map, you own all of the magenta worlds. Worlds 2 and 7 are owned by one of your opponents, and worlds 21 and 16 are owned by another opponent. World 12 is not owned by anyone.
Worlds 24, 26, 14, and 4 all connect directly to a world not owned by you. These worlds will therefore produce just one D-Ship next turn.
However, worlds 9, 22, and 23 will produce two D-Ships next turn, because they connect only to worlds that you own--from these worlds, you must travel two hops to reach a world you don't own.
Furthermore, worlds 19 and 27 will produce three D-Ships next turn, because they are three hops away from the nearest world that you do not own.
If you were to successfully capture both worlds 12 and 16, then worlds 19 and 27 would start to produce four D-Ships per turn, because that would be the new minimum distance to a world you don't own.
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