Optimality conjecture for the Oldest random strategy in the Robin Hood game

Let $RH(r,s,A)$ be a Robin Hood game with resource functions $r,s$ and index set $A$. A random strategy is independent of the index set $A$ if its choices do not depend on $A$. Oldest random strategy optimality conjecture. The strategy $\mathsf{Oldest}_{\mathit{RND}}$ is the best random strategy among the strategies that are independent of $A$. The source presents this as one of its principal open problems; no resolution is given.