I just finished a 3 player (1 of each race, 2 AIs, I was Advent) game that was interesting. My opponents had a better start then I, and quickly had me on the ropes. Then I got some missions from green as red attacked me. I unintentionally completed the mission by killing off reds' ships. I was able to repel the assault (it was pretty pathetic, actually, but my scouts showed a red vs green battle elsewhere).
A little while later, almost the same thing occurs, but with the other players: green attacks me, red sends me a mission, i repel the invasion, gain a better standing with red. Now, these 2 assaults were on opposite ends of my empire and it took quite a haul to get from the one planet to the other. I've been trapped in this situation in the previous versions where the AI just pinballs my fleet the whole game between the 2 ends of my tiny empire, completely stalling any expansion I might hope to have. This time, because each time I was attacked and not the attacker, and I recieved and completed missions.... both enemies started to like me... Not a huge, hey-let's-be-friends like, but enough that they stopped attacking me to focus on fighting each other (which they really hated by now).
This meant that green, who was by far the dominant player, left a mostly undefended world right next to me. This world also had a fairly straight shot at his homeworld. His fleet was on the other side of the solar system in a viscious battle vs. red. I had shored up my defenses and had all the tools I needed should there be a counterattack, so I attacked. It was a pretty rough battle, as green eventually came back to defend his planet, but his capitals had significant damage and were taken out fairly quickly. Red saw an oppertunity and tried to attack me on the other end of the empire during his break vs green, but my SB repeled him long enough. Green's homeworld was completely undefended, and so i took that out, but could not take the world as culture prevented it. Green had apparently won the red vs green battles and then withdrew to fight me, so red was busy trying to take back those worlds. By now, I had a huge momentum, and a vast fleet. I took one more green world (and this one was a real battle: SB, ships, missle batteries, hangars and all but I battleballed through it all) and he was defeated. Red was desperately trying to get worlds(green had taken out everything but his homeworld) and so had taken a couple worlds and not built defenses. This allowed me, now finished with green, to pin down his fleet, defeat it, and win the match.
This was alot of fun, because I saw that they hated each other more than me and was able to use that to my advantage. I had alot of lucky breaks, but most of it came down to timing. Obviously, if i had waited to attack green, red would have been defeated and i would have faced green with a solar system of resources. As it stood, red and I both took resources away from green, crippling his economy at the exact moment he needed to replenish his forces. If I had attacked earlier, green and red's fleets would have been stronger. Green might have chased me off his planet or maybe not, but clearly red would have been in a much stronger late game position. Also, if I had not seen that green and red were in a battle at that moment, I would not have known it was safe to attack.