There are four mini-expansions in the set, but we played them all. And to be honest, I don't think that was a bad thing at all. Dave, who brought the game and suggested it, claims to want to run a game with all 20 mini-expansions in play at once, although I personally think he should be careful what he wishes for. Four was plenty.
The first expansion is the Caravan. This is a series of cards you can buy to generate extra currency every turn, costing 8/4/2 of a single coinage for having 4/5/6 different building types in your garden. The cards have a single type of coinage (orange, blue, yellow, green) running as a track up the card, with "branches" to the other three types to the sides. Each level you move a marker up the card (one total bump per turn per player regardless how many you've bought) and it either increases the base coinage value by one to a max of 5, or else you can take one of the branches to the side. You can also choose not to advance any at all, trying for exact amounts to allow extra actions.
The second expansion is The Art of the Moors. Perhaps my favorite micro-expansion, this one rewards you for collecting multiple tiles in a given value rather than color. When you get two or more tiles that have value 6 or higher, you get a hexagonal tile that you place along a framing "wall" piece (that look like small versions of the frames for Settlers). Each "dial" (as I'll call them) has a range of values and qualifying garden tiles associated with each vertex of the hexagon. For example, the 6 dial has values 0-1-2-3-4-5 (I think, I never got this dial), and a requirement of 2 tiles for the first three, then 3, then 4. Different tiles have different values, most with big jumps at the top range.
When you get two garden tiles in the appropriate configuration in your play area (including the reserve!), you place the dial against a wall with the 0 value against the wall. You then take a small black cube and put it on the highest number you can turn the dial to based on how many garden tiles you have of that value, usually one or two spaces higher on the dial. As you add tiles of that value, you move up the cube and can turn it to 11 if you get enough. That's one better than 10, btw. As an action, you may rotate every dial you have that can be increased, and the points shown are added to your score in each round.
The third expansion is The Power of the Sultan. This is a set of special cards and a die, with the cards added into the deck in a gradual fashion, as with the scoring cards. When one of these cards comes up, the die is rolled to determine which of the six building types the card affects. You can buy these cards for seven of the stated currency, and it gives you the chance to steal a garden tile of the rolled color immediately after it has been placed on the purchase mat, starting with the player to the left of the person whose turn just ended (when you place the tiles). If you buy a card and don't like the color of tile it lets you steal, you can reroll and choose either the color rolled, or the one on the other side of the die (on a regular die, this would be combos of 1/6, 2/5, 3/4, for example).
The fourth expansion is The New Valuecards (wow, that's thematic). This one is simple - it simply mixes up the valuations of the different colors of tiles over the course of the game, so blue is no longer necessarily the cheapest. Our game was such that brown, purple, and white were the most valuable, while green was the least. My least favorite of the expansions, but that's not to say it doesn't change the game up a bit.
So why were these expansions such a good idea? It mostly has to do with the basic flaw of Alhambra - in the base game, you have limited choices. If you can't buy a card, you are more or less stuck taking money cards, and if none of those appeal to you, then you can always redecorate by shifting tiles to and from your reserve. However, that's about it, and there's a certain amount of cycles in the game where you really have no good choices of what to do, completely based on luck of the draw, both in cards and tiles.
With the first three expansions, the options open up. First of all, you have two new things to spend money on, the Caravan cards and the Sultan cards. Know you want to be able to steal a tile when it shows up? Spend seven on a Sultan card. Once the game has gotten underway and you have five or six different types of buildings, then the Caravan cards are particularly useful as you can augment your income over time without having to draw cards.
The caravan cards also encourage you to diversify early to make them cheaper and more attractive, which means that you have more "good" choices from the tile draft. The Art dials (also called Culture in the translation) do the same, encouraging you to pick numbers that match a set as well as colors. Frankly, knowing that I needed to bump those up from time to time drove me to choose that function rather than drawing cards as I wasn't sure a scoring round was coming up or not. They were a big part of my points, scoring (by themselves) 23 points in the second and third scoring rounds, and Dave pulled off 29 points at the end (enough to give him the win over me, as I was never able to draw more tiles of those numbers).
The end result is two more things you can buy, one more thing you can do as an action, and increased diversification of tile choices during the game. Not to mention increased tension. While I'm unlikely to pull this out for non-gamer friends with this expansion (as Greg said about playing with his wife), but it turns Alhambra into a gamer's game with a rich decision set. You are still, at the core, at the mercy of the tile and card draws, but because more tiles are desirable and you have potentially three things you can spend money on, that luck is mitigated to a certain extent.
We played with three people, and that seemed to be a very good number. I think four would be worthwhile as well, but it's still Alhambra, and six people would be painful to watch. However, those Sultan cards would be snapped up immediately, as the ability to snag tiles fresh from the bag would be worth it's weight in real estate.
If you are a Gamer (tm), like Alhambra but wish it had more tactical options, and your play group often finds you in groups of three or four, this is a big winner. Something I'll be adding to my collection very soon, and Alhambra will see a lot more play time on my table. Thanks to Dave for introducing me to the expansion!