  In this paper, we construct solvable ice models (six-vertex models) with
stochastic weights and U-turn right boundary, which we term ``stochastic
symplectic ice''. The models consist of alternating rows of two types of
vertices. The probabilistic interpretation of the models leads to novel
interacting particle systems where particles alternately jump to the right and
then to the left. Two colored versions of the models and related stochastic
dynamics are also introduced. Using the Yang-Baxter equations, we establish
functional equations and recursive relations for the partition functions of
these models. In particular, the recursive relations satisfied by the partition
function of one of the colored models are closely related to Demazure-Lusztig
operators of type C.
