to make sb try very hard, using all their skill and effort, in order to beat you in a game or competition
GIVE SB A (GOOD) RUN FOR THEIR MONEY
Meaning of GIVE SB A (GOOD) RUN FOR THEIR MONEY in English
Oxford Advanced Learner's English Dictionary. Оксфордский английский словарь для изучающик язык на продвинутом уровне. 2005