The idiom "give someone a run for their money" means to give someone a tough competition or challenge. It is used when someone is competing against another person, and they are doing so well that the other person has to work hard to win.
For example, if two athletes are competing in a race, and one of them is expected to win easily, but the other athlete performs unexpectedly well and makes the race very close, then we can say that the second athlete gave the first athlete a run for their money.
Similarly, if two companies are competing for a contract, and one of them is considered the favorite, but the other company presents a very strong proposal and makes it difficult for the favorite to win, then we can say that the second company gave the first company a run for their money.
Overall, this idiom is used to describe a situation where someone is unexpectedly good at something and gives a tough competition to the other person or team.
• The world-renowned author is widely considered a literary genius, but I believe my latest novel can give him a run for his money in terms of critical acclaim and commercial success.
• The reigning champion is confident he will win the race, but I plan to give him a run for his money by training harder than ever before.
• The company's top salesperson thinks he's unbeatable, but I believe I can give him a run for his money with my persuasive skills.
• My brother is an excellent cook, but I think I can give him a run for his money with my lasagna.
• The debate team captain is known for her convincing arguments, but I am confident I can give her a run for her money with my research and preparation.
• I may be new to this game, but I can give you a run for your money.