  Probabilistic game structures combine both nondeterminism and stochasticity,
where players repeatedly take actions simultaneously to move to the next state
of the concurrent game. Probabilistic alternating simulation is an important
tool to compare the behaviour of different probabilistic game structures. In
this paper, we present a sound and complete modal characterisation of this
simulation relation by proposing a new logic based on probabilistic
distributions. The logic enables a player to enforce a property in the next
state or distribution. Its extension with fixpoints, which also characterises
the simulation relation, can express a lot of interesting properties in
practical applications.
