We continue our discussion of perfect and scattered subsets in the generalized Cantor space. We focus this week on generalizing the games played on subsets of 2^{\omega} considered previously to the 2^{\kappa} context, and introduce alternate notions of \kappa-perfect and \kappa-scattered. We show that \kappa-closed forcings can’t add branches to \kappa-scattered subsets of 2^{\kappa} if \kappa isn’t a strong limit, which has as an immediate corollary the well-known lemma of Silver which says that \kappa-closed forcings can’t add branches to \kappa-trees (again for \kappa not a strong limit).