A space X is said to have the star-C-I-Hurewicz (SCIH) property if for each sequence (Un : n ∈ N) of open covers of X there is a sequence (Kn : n ∈ N) of countably compact subsets of X such that for each x ∈ X, {n ∈ N : x < St(Kn,Un)} ∈ I, where I is a proper admissible ideal of N. We investigate the relationships among the SCIH and related properties. We study the topological properties of the SCIH property. This paper generalizes several results of [21, 24] to the larger class of spaces having the SCIH property. The star-C-I-Hurewicz game is introduced. It is shown that, in a paracompact Hausdorff space X, if TWO has a winning strategy in the SCIH game on X, then TWO has a winning strategy in the I-Hurewicz game on X