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Games that challenge the player with critical thinking to solve levels. 

Games where you discover new locations by traveling around in the game's environment

Set in a fictional universe, often (but not always) with fantastic or supernatural elements, alternate worlds, magic and monsters.

A turn-based game mechanic is the opposite of a real-time game mechanic. In a Turn-By-Turn mechanic (synonym), each player has to wait for the other to have played, so that they can play, and so on. This way, each player has the time to think about their strategy. TBT games rely less on action than real-time games.