A significant issue in game balancing is understanding the game itself. For simple games end-to-end optimization approaches can help explore the game's design space, but for more complex games it is necessary to isolate and explore its parts. Hearthstone, Blizzard's popular two-player turn-taking adversarial card game, has two distinct game-playing challenges: choosing when and how to play cards, and selecting which cards a player can access during the game (deckbuilding). Focusing on deckbuilding, four experiments are conducted to computationally explore the design of Hearthstone. They address the difficulty of constructing good decks, the specificity and generality of decks, and the transitivity of decks. Results suggest it is possible to find decks with an Evolution Strategy (ES) that convincingly beat other decks available in the game, but that they also exhibit some generality (i.e. they perform well against unknown decks). Interestingly, a second ES experiment is performed where decks are evolved against opponents playing the originally evolved decks. Since the originally evolved decks beat the starter decks, and the twice evolved decks beat the originally evolved decks, some degree of transitivity of the deck space is shown. While only a preliminary study with restrictive conditions, this paper paves the way for future work computationally identifying properties of cards important for different gameplay strategies and helping players build decks to fit their personal playstyles without the need for in-depth domain knowledge.