  We provide a probabilistic representation of the solutions of ordinary
differential equations (ODEs) by random generation of Butcher trees. This
approach complements and simplifies a recent probabilistic representation of
ODE solutions, by removing the need to generate random branching times. The
random sampling of trees allows one to improve numerical accuracy by Monte
Carlo iterations whereas the finite order truncation of Butcher series can have
higher time complexity, as shown in examples.
