  The stochastic interpretation of Parikh's game logic should not follow the
usual pattern of Kripke models, which in turn are based on the Kleisli
morphisms for the Giry monad, rather, a specific and more general approach to
probabilistic nondeterminism is required. We outline this approach together
with its probabilistic and measure theoretic basis, introducing in a leisurely
pace the Giry monad and their Kleisli morphisms together with important
techniques for manipulating them. Proof establishing specific techniques are
given, and pointers to the extant literature are provided. After working
through this tutorial, the reader should find it easier to follow the original
literature in this and related areas, and it should be possible for her or him
to appreciate measure theoretic arguments for original work in the areas of
Markov transition systems, and stochastic effectivity functions.
