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Shattered Pixel Dungeon an improved version of the roguelike game Pixel Dungeon, rebuilt from the ground up with various improvements to the balance. Like its predecessor, it is available for free.
SpecsUpdate
Pros
Pro Has a reasonable amount of strategical depth where the player can easily plan out their next move
The top-down, turn-based nature of the game gives the opportunity to plan out a complex series of moves. This way there is no time constraint, and the player can leisurely strategize what they would like to do next.
Pro Challenging and fun gameplay that lends itself well to repeat plays
SPD's gameplay is intuitive, allowing for it to be easy to get into. What is great though is that it's also very challenging, quickly making the experience both rewarding and addictive. Just one more game is a thought many will have before actually turning off their device.
Pro Tons of replayability thanks to the randomly generated levels
In true roguelike fashion, levels are randomly generated each time a new game is started. On top of this mechanic, Shattered Pixel Dungeon goes one step further by randomizing effects of all items as well, so it's impossible to tell if a dropped item will have a positive or a negative effect based on its sprite representation.