Improving the RHC-strategy

It is well known that the RHC-strategy is inadmissible. For example, Rao-Blackwellization yields a strategy which has uniformly smaller risk than the RHC-strategy. The complicated form of the Blackwellized RHC-strategy as well as its inadmissibility is a disadvantage of this strategy. We propose a new strategy which has also uniformly smaller risk than the RHC-strategy. Some optimality results are derived.