We present a new fully adaptive computational model for attack trees that allows attackers to repeat atomic attacks if they fail and to play on if they are caught and have to pay penalties. The new model allows safer conclusions about the security of real-life systems and is somewhat (computationally) easier to analyze. We show that in the new model optimal strategies always exist and finding the optimal strategy is (just) an np-complete problem. We also present methods to compute adversarial utility estimation and utility upper bound approximated estimation using a bottom-up approach.