Ascension: Storm of The Souls (ASOTS) is a deck-building game, akin to Thunderstone and Dominion. Players build a custom deck with in-game currencies like the aforementioned games, but ASOTS is simpler, and looks and feels more like the original source of inspiration, Magic: The Gathering. Another major difference is that ASOTS has more randomness in deck-building.
In both Dominion and Thunderstone, the card market is randomized in fixed sets, allowing players to see all the cards available for deck-building. In ASOTS, only six cards are available for purchase and the rest are revealed as cards are bought. Thus, one cannot fully plan card mix strategies, rather one must acquire cards tactically, carefully watching the card purchases of other players.
Having played all three sets -- Ascension: Chronicle of the Godslayer, Ascension: Return of the Fallen, and Ascension: Storm of Souls -- on the iPad app by Playdek, the latest set, ASOTS is the best. In Ascension: Chronicle of the Godslayer, the cards that allow you to optimize your deck by trashing cards are low in frequency; but they are overly numerous in Ascension: Return of the Fallen; and perfectly tuned in ASOTS. Furthermore, in the previous Ascension games, I would count my currencies and buy (or defeat) the most expensive card I can afford -- an obvious choice. ASOTS has cards that create combos which make them more valuable than the face value to different players. These combo cards makes card-buying more interesting while at same time creating asymmetrical card values between players.
The game follows the typical Eurogame formula of using money to build a "money engine" to generate more money, then buying victory points with that money. There are two currencies in Ascension: Runes and Power. Runes are a currency for buying cards that give more money, while Power buys (defeats) monster cards that usually earn one time Honor (victory points) and are then discarded. Therefore the game revolves around cashflow management of short-term and long-term gains.
The iPad app by Playdek offers all three sets and the limited promo cards. The AI is tough but the real fun is playing your friends over asynchronous network play. You make your turn and the system will alert the other player to make their move. This way you can play leisurely, making moves at your convenience. Because of the good AI, great UI, and asynchronous network play, Ascension is my most played iPad app by a large margin.