We consider a system with genuine elements (GEs) and false targets (FTs) that cannot be distinguished by the attacker. To enhance the attack efficiency, the attacker uses a double attack strategy in which it tries first to eliminate with minimal effort as many false targets as possible in the first attack and then distributes its entire remaining resources among all surviving targets in the second attack. The model for evaluating the system vulnerability in the double attack is suggested for a single genuine element, and multiple genuine elements are configured in parallel or in a series. It is assumed that the attacker strikes a subset of the targets in the first attack, choosing the optimal number of targets in this subset. The defender can optimize its resource distribution among deploying FTs, protecting GEs and, in the case of a parallel system, deploying redundant GEs. Various examples of optimal attack and defense strategies analysis are demonstrated. The defense strategy is analyzed based on a two-period minmax game.