First of all, I apologize if there are any typos. I'm writing this at a hospital's e-cafe, and these "sanitary keyboards" are the most godawful thing ever invented. I have to slam every freaking key down.
Ok, so yesterday my friend and I played a LAN on a medium map with one solar system, 20 or so planets, and pirates. I played Advent, he played TEC. The game went pretty well... lots of bidding wars with the pirates as we teched up and expanded. Towards the end we both had pretty good sized fleets, 7 caps at least and lots of lesser ships. Mainly it was a matter of one of us breaking the others' fleet, and then rolling up planets. (We had a gentleman's agreement to pretend that you had to break a planet before jumping past it.)
So, I had a small battle group of Drone Hosts, fully upgraded. With it I was harassing his frontier worlds, jumping in and sending bombers after a mine or other structure, then jumping out and hitting somewhere else. I had a clever plan for victory that involved him being enraged by my raids. I had researched the upgrade to allow me to see fleets jumping up to 2 wells away, which made a big difference.
Here is a laughably crude layout of the planets involved in the final battle.

1 - A well defended core TEC system
2 - A frontier TEC world I had recently bombed into oblivion
3 - A dead asteroid I had colonized very sneakily and placed a PJI in
4 - Space Junk
5 - One of my frontier worlds... prety well defended.
So here's how it went down. After taking out 2, I moved half my fleet to 3 and colonized, building a PJI. The other half went to 4. I had seen with my psychic upgrades that his fleet was in 1. I moved my Drone raiders from 5 through 2 and into 1, where he became very excited, thinking he had caught me at last. He had a PJI in 1, so my jump out was slow and he took out a couple of my drones. When my raiders reached 2, I swung them to jump to 3. He thought he was going to catch them in a dead end, and gave chase with his whole fleet, even taking the time to do a group jump. My caps with radial damage were all waiting on the other end, and I began jumping the rest of my fleet from 4 to 2 at the same time he jumped to 3. After taking severe damage in 3, he took a slow jump (PJI) back to 2, where he met my 2nd fleet blocking his retreat. While this happened, the pirates were at the end of their countdown and I bribed them with around 14000 credits (more credits = bigger raid) so they sent an enormous attack at one of his core worlds.
His crippled fleet managed to escape with one cap (I had focused all my fire on those) and lots of lesser ships. Trusting his defenses to hold me, he had to scramble to reinforce and fight off the pirates. In the meantime, I brought up a small group of Purge vessels and started wasting his planets. The game took another hour, and at one point he almost pushed me out of his empire, but once I cut his trade route in half and started pushing out some culture, it was game over.
I truly, truly love this game.
Except for the auto focus when I zoom in. I hate getting stuck on stupid fighters. 
-zenchronus