In the Constructor-Blocker game, two players, Constructor and Blocker,
alternatively claim unclaimed edges of the complete graph Kn. For given
graphs F and H, Constructor can only claim edges that leave her graph
F-free, while Blocker has no restrictions. Constructor's goal is to build as
many copies of H as she can, while Blocker attempts to stop this. The game
ends once there are no more edges that Constructor can claim. The score
g(n,H,F) of the game is the number of copies of H in Constructor's graph at
the end of the game, when both players play optimally and Constructor plays
first. In this paper, we extend results of Patk\'os, Stojakovi\'c and Vizer on
g(n,H,F) to many pairs of H and F: We determine g(n,H,F) when
H=Kr and χ(F)>r, also when both H and F are odd cycles, using
Szemer\'edi's Regularity Lemma. We also obtain bounds of g(n,H,F) when
H=K3 and F=K2,2.Comment: 16 page