The phrase often implies helping someone by mistake, not realizing the benefit you're providing to them. Ignoring the bully might play into his hands, making him think he can continue.
Pro Tip 2/3
Idiom Uses
It's an idiom used mainly in strategic or competitive situations, not in everyday activities. Refusing to compromise could play into the hands of those who want the talks to fail.
Pro Tip 3/3
Figurative Expression
Understand that it's a figurative expression and doesn't involve physical hands or playing games. By underestimating their skills, we might play into our rivals' hands.