The Karate Kid was a game published by LJN for the NES. It is loosely based on The Karate Kid, Part II.
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The setup feels similar to 1985's Kung Fu, except that all of the parts integral to making a brawler or fighting game aren't present here: The controls are clunky, the hit detection is awful, the levels are poorly designed, and the enemies are annoying and there are projectiles being thrown at you off-screen constantly.