play (right) into the hands of (one)
To unwittingly do exactly what someone wants or needs in order for their plans or schemes to succeed. Don't waste your time investigating her husband! You're playing into the hands of the real killer! These violent, hate-filled demonstrations are playing right into the hands of the groups we're protesting against.
play into the hands of
Act so as to give an advantage to an opponent, as in The senator played right into the hands of her opponents when she backed that unpopular amendment to the tax bill . [c. 1700]