I'm a brand new player to Twilight Imperium. I played one game against myself and then two in my local game group. Given the game's reputation we were surprised how we could finish the game within four hours. It was a lot of fun, too.
The objective system is surprising. I won the game while another player completely dominated the board militarily, and we discovered that when those Victory 2 objectives start flipping the game can end very rapidly. It seems strange the objectives, especially the Victory 2 objectives, are so easy to complete.
We've never played with more than three people; it's hard to get that many to meet at one time. I can tell I'm going to want to play a lot more of this game to learn how to play it well, more than I can expect to get, so I'm hoping someone releases a Vassal module soon so I can play remotely with others.
In any case, great game! I remember being memorized by the box of TI3 when I was a teenager and it's great to now be able to play TI4.