Eliezer: glad you followed up on Robin's suggestion to do this. The examples in my earlier post on "Useful Bias", then involve resorting to systematic error to deal with problems arising out of processes with unsystematic errors. Similarly, the examples other commenters gave, such as alcoholics foreswearing all drinks or persons setting their watches five minutes early, would also be cases of using sytematic error to avoid problems caused by unsystematic errors.