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A set of rules that govern an in-game experience. Game design is an effort to come up with game mechanics that allow for players to have a fun and engaging experience.
4
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How to create a mathematical mechanism in order for a game to be balanced?
There are countless factors to consider. Question is too broad IMO :)
It's all relative too... dmg is only relative to hp, etc. Damage over time (eg damage per second) is likely a good place to start …