To 'play into someone's hands' means to do something that benefits someone else unintentionally. When you 'play into someone's hands' you do something which gives someone else an advantage or gives them power.

1. Tom completely played into my hands when he reacted that way to my question. Now Claire can see his true colours.
2. He made a bad move during the chess games and played right into his opponents' hands.

1. My boss has made me work every weekend this month, but if I get mad at him then I will just be playing into his hands because he is looking for an excuse to fire me. 
2. Changing strategies at this stage will just mean playing into our competitors' hands.

1. The executive was convinced that the company's plans to downsize their operations would play directly into the hands of their rivals. She encouraged a different approach to dealing with their financial problems.