Beating Him At His Own Game

( doing the thing that the other person does well, but doing it better and winning ... )

"Beating him at his own game" is when you beat a person in a competition by doing better than him at the thing that he does very well. Example: "She was the star of our school's tennis team, and I still beat her." Reply: "You beat her at her own game." Another example: "I can't believe you beat me at chess!" Reply: "I beat you at your own game."

Winning in a competition by doing what the other person does well but doing it even better is "beating him at his own game". Example: "We know that these guys score a lot of goals. But today we are going to score more goals, and beat them at their own game." Another example: "I finally beat you at pool." Reply: "You beat me at my own game."