Played Inca Empire on shabbat with Abe and Sara. I took it to a decisive victory: 122 to 121 to 120. The trouble is that I've played the game two times before, but these were their first plays.
The game is divided into a few phases that start with everyone getting workers and end with everyone scoring their board positions. In between, you alternate between a) playing cards that affect two players in the game (either you and an opponent, or two opponents; which you choose depends on whether the card is beneficial or harmful) and then b) placing two roads followed by an action: build a garrison, build a city, build a temple, build a terrace, conquer a territory, place another road, or pass. Each item gives some greater points one time only to the person who built it and some lesser points at the end of each phase to all players connected to it. Conquering territories and building terraces increase your worker income.
The phases get longer as the game goes on, which means played cards accumulate. The cards give you bonuses, or make things more or less expensive, etc. At the end of each phase, all cards are cleared away.
My having played before didn't prevent me from forgetting most of the rules and making some rule mistakes that I only corrected as the game progressed. For instance, only about two thirds of the way into the game did I realize that we each get two free roads each turn, not one. As sometimes happens with misplayed rules, I kind of liked the misplay. When we started playing with two roads each, we all connected to just about everything nearly immediately, which was kind of anti-climactic. On the other hand, the reason that we could all connect to everything all of a sudden was that the first cities and garrisons were all built close to the starting positions, so it's probably a wash.
We all enjoyed the game. It's probably a bit dry for some. There's a theme in there, but it's hard to remember.