Well in the first game we where mostly confused, we sort of played the mechanic trying to understand the rules and how it all ties together. I can't say we actually enjoyed it, I mean we thought it was interesting, in particular the battle mechanic but all of us were pretty much just playing the rules. The second game went with more understanding of the rules (less looking stuff up) but we still just played the mechanic.
It started with about our 3rd game when players started discussing things and applying more table talk. For example the Jol-Nar who gets to look at the top influence card realized that people caught on to the fact that wherever he deployed was the likely spot influence would appear so he took the oppertunity to force a big deployment into a random location away from all the influence and naturally everyone went for it, only to find out it was a trick, no influence actually appeared their. The light kind of came on when we all realized.. ya.. thats what its really about. Its not the mechanic that makes it great but how players take advantage of the sort of poker face elements and table talk the mechanic supports.
Now are games are full of politics and diplomacy with all sorts or bluffs, counter bluffs and pulling the rug from under people. Every action anyone takes gets immediatly scrutinized, sometimes people intentionally mislead each other, sometimes people try to point out possible strategies of an enemy. Other times for example the Jol-Nar will intentionally reveal what strategy cards we are bidding on so that at a key moment he can lie about it. The same with the Sol, they might warn of a the coming bombardment, or might lie about it depending what serves them better. Each time someone does again its scrutinized.. accusations go flying all over the place. Every race seems to have something to add to that aspect of the game and as such the games sort of hostile diplomacy and ugly politics come out. Betrayels have become common place, but we have found as long as everyone is going for a victory the game is awsome. Usually its only a problem when players come to the table unucustomed to this type of play style and take things personally that it falls apart. Aka you betrayed me now I will spend the rest of the game making sure YOU DON'T win. That actually kind of ruins it as two people in a grudge match does nothing but strengthens everyone else, but people catch on quickly so it usually only takes a game or two for a new player joining the group to get into the spirit of things.
Anywho it wasn't until we realized how far you can take the diplomatic and political aspects of the game that the mechanic started to make sense and the game kind of blew us away with its intricate and well designed subtlties.