  We give examples of data-generating models under which Breiman's random
forest may be extremely slow to converge to the optimal predictor or even fail
to be consistent. The evidence provided for these properties is based on mostly
intuitive arguments, similar to those used earlier with simpler examples, and
on numerical experiments. Although one can always choose models under which
random forests perform very badly, we show that simple methods based on
statistics of `variable use' and `variable importance' can often be used to
construct a much better predictor based on a `many-armed' random forest
obtained by forcing initial splits on variables which the default version of
the algorithm tends to ignore.
