  In this work we study randomised reduction strategies,a notion already known
in the context of abstract reduction systems, for the $\lambda$-calculus. We
develop a simple framework that allows us to prove a randomised strategy to be
positive almost-surely normalising. Then we propose a simple example of
randomised strategy for the $\lambda$-calculus that has such a property and we
show why it is non-trivial with respect to classical deterministic strategies
such as leftmost-outermost or rightmost-innermost. We conclude studying this
strategy for two sub-$\lambda$-calculi, namely those where duplication and
erasure are syntactically forbidden, showing some non-trivial properties.
