  Fix some $n \in \mathbb{N}$ and let $X_1, X_2,\dots, X_n$ be independent
random variables drawn from the uniform distribution on $[0,1]$. A decision
maker is shown the variables sequentially and, after each observation, must
decide whether or not to keep the current one, with payoff the overall rank of
the selected observation. Decisions are final: no recall is allowed, no regret
is tolerated. The objective is to act in such a way as to minimise the expected
payoff. In this note we give the explicit solution to this problem, known as
Robbins' problem of optimal stopping, when $n=4$.
