Effectiveness analysis is critical for making optimal network dynamic defense (NDD) strategies. Firstly

the attack success probability formula is derived by constructing the random sampling model from the perspective of vulnerability mutation

which can depict the influence caused by the mutation space

the mutation period and the number of vulnerabilities on the process of network attack. Then

two limit theorems of attack success probability are given and proved in single and multiple vulnerabilities cases respectively

and the calculating methods of optimal mutation space are given according to the two theorems. The simulation results show that the NDD's effectiveness improves with the mutation period reducing and the number of vulnerability attacked successively on a single attack path growing

meanwhile

although enlarging the mutation space is beneficial to improving the NDD's effectiveness in the beginning

the attack success probability would converge with the persistent enlargement of mutation space

which limits the continuous improvement of NDD's effectiveness.