The free energy functional has recently been proposed as a variational\nprinciple for bounded rational decision-making, since it instantiates a natural\ntrade-off between utility gains and information processing costs that can be\naxiomatically derived. Here we apply the free energy principle to general\ndecision trees that include both adversarial and stochastic environments. We\nderive generalized sequential optimality equations that not only include the\nBellman optimality equations as a limit case, but also lead to well-known\ndecision-rules such as Expectimax, Minimax and Expectiminimax. We show how\nthese decision-rules can be derived from a single free energy principle that\nassigns a resource parameter to each node in the decision tree. These resource\nparameters express a concrete computational cost that can be measured as the\namount of samples that are needed from the distribution that belongs to each\nnode. The free energy principle therefore provides the normative basis for\ngeneralized optimality equations that account for both adversarial and\nstochastic environments.\n