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.