  We show that applying any deterministic B-series method of order $p_d$ with a
random step size to single integrand SDEs gives a numerical method converging
in the mean-square and weak sense with order $\lfloor p_d/2\rfloor$.As an
application, we derive high order energy-preserving methods for stochastic
Poisson systems as well as further geometric numerical schemes for this wide
class of Stratonovich SDEs.
