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. Probably my favorite of all time. Almost no luck involved, every game plays different, relatively simple, but incredibly complex in terms of strategy. It all involves around planning what your opponents do and adapting.
As much as I like Settlers of Catan, and Ticket to Ride, they are really simple games compared to a lot of the other really good board games out there.
Do have to give props for the people who said Battlestar Galactica and Race for the Galaxy. Race for the Galaxy is a lot like Puerto Rico, but more complex and more luck involved.
Battlestar Galactica is a game anyone who enjoys werewolf has to check out. Everyone is dealt out a card at the beginning of the game, and again at the half way point. These cards either label you as good or bad, and the bad ones try to secretly hurt the good characters anyway they can. This has caused some heated arguments with me and my friends over what reads people have.
Also for other fun complex games, check out Power Grid and Agricola.