Kazarp (DavidG) vs. Stone Mill:
It is never a good thing to have a big fleet of enemy ships pounding your homeworld.
DavidG certainly had me in a very bad position; annoyingly used mines (or the threat of mines) against me and continued to control key positions. He expolited the fact I was very late in researching mines 2; it is tough to counterattack when you don't have enough sweepers.
So I pull back the fleet guarding the warp point in my home system for training. Almost on cue, he came through soon after with a fat fleet and cleared my minefield.

The sad thing was that I could not readily counter attack and risk being baited into a fresh minefield. I knew it would take him at least 2 turns to reach the homeworld, so I patiently waited, knowing he could have his way with all the planets in the system.
On the second turn he fragged a great planet, and moved into striking range. I guessed that he could not resist gunning for my homeworld; so I moved my fleet there for defense.
At this point in the game, things looked grim.

But I guessed right

(for once); my fleet routed his ships over my homeworld. My home planet took a pounding, but survived. A painful result was that he destroyed my Space Port, which sent my economy crashing. I halted my empire's production for a few turns to build a new one; all the minesweepers needed for a counterattack sat in queue and waited. Unfortunately, this gave him valuable turns to generate a defense fleet.
I finally got things together and plowed through. He generated a surprisingly big fleet at the warp point, but they were no match.
What a relief. I was really sweating.
As it stands now, a bell is tolling in his home system. And do not ask for whom the bell tolls...