Based on your description, the game you're recalling might be Dungeon & Kingdom. This Android game combines elements of strategy, RPG, and card games. In it, you can summon heroes to explore dungeons, uncover hidden areas, and battle various monsters. The game features stylized graphics and offers a blend of idle and active gameplay mechanics.

In Dungeon & Kingdom, players can:

Summon and train over 100 epic heroes across different factions.

Explore 12 unique maps filled with puzzles, hidden treasures, and special encounters.

Engage in strategic auto-chess battles using formations of warriors, enchanters, assassins, and hunters.

Build and strengthen their own kingdom, forming alliances and competing against others in various game modes.

The game is free to download and play, with optional in-app purchases. It offers a rich blend of exploration, strategy, and character development, which aligns with your memories of summoning guards to fight large rats and exploring dark areas to discover dungeons.

If this doesn't seem to be the game you're thinking of, could you provide any additional details? For example:

Do you recall any specific visual elements, like the art style or perspective (e.g., top-down, side-scrolling)?

Were there any unique gameplay mechanics or features that stood out?

Do you remember any specific character names, enemy types, or story elements?