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Does playing games that require wifi on an iPhone 4S while its charging reduce its battery life ?

I play a game called eternity warriors 2 while my iPhone is charging . Does its battery life reduce ? Because I got it to 100% then played the game and it only lasted like 2 hours before it got to 10% normally it takes. 2 hr and a Half to get there . Is the battery getting damaged or does my I phone run out faster because of the game ? Also does letting it get to 10% then getting it to like 50% then using it damage its battery ? Thanks in advance