We present the semantics of two variants of Probabilistic Propositional DynamicLogic (PPDL). Stochastic Differential Dynamic Logic is a logic for reasoning about hybrid systems with continuous state space that may evolve in contin- uous time according to stochastic differential equations, or in discrete time ac- cording to probabilistic or Angelic nondeterminism. Stochastic Game Logic can be seen as extending PPDL with Demonic nondeterminism, or Game Logic with probabilistic nondeterminism. For both logics, we develop sound reasoning principals over the presented semantics.