Abstract: The Ping-Pong Lemma is a well known statement in geometric group theory which lets us prove a group Γ is free by finding subsets of a space X which Γ acts on that meet certain conditions. I will be discussing a recent generalization of the ping pong lemma in the context of group actions on projective space. Using this result I will describe an algorithm which can calculate explicit bounds on the size of the kernel of a representation of certain finitely generated groups into SL(2, R).