I have to disagree with you there. Play this one out and see what happens. But in general, there's nothing worse than allowing yourself to be played and strung along, especially if you know what's happening.
You actually get more from cutting your losses and walking away from a girl who is playing you. It reinforces your confidence, you know that one girl isn't everything and your time is better spent with women who want to be with you. Then when the next one comes along it gets easier to establish your own frame immediately and not get drawn into hers.
Good luck in any case.