The deterministic space complexity of approximating the length of the longest increasing subsequence of
a stream of $N$ integers is known to be $\widetilde{\Theta}(\sqrt N)$. However, the randomized
complexity is wide open. We show that the technique used in earlier work to establish the $\Omega(\sqrt
N)$ deterministic lower bound fails strongly under randomization: specifically, we show that the
communication problems on which the lower bound is based have very efficient randomized protocols.
The purpose of this note is to guide and alert future researchers working on this very interesting problem.