for what it's worth

Because of the disappearance of the old antimooners and the insouciance/incompetence of the new ones, I have little faith that I will receive a clear, satisfactory answer, but I'm going to fire the simple question anyway.

"I could do nothing but admire her as she delivered this barefaced lie. Nothing for me to do but accept the lie and then play it for all I was worth."

What's the meaning of "for all I was worth." also, "for what it is worth..."

It means he will gamble all his material worth to prove that she is a liar.

It does not necessarily mean that he wants to prove that she is a liar. It sounds more like he will go along with the lie because it could benefit him in some way, and he intends to maximize that benefit.