Woźniakowski [@Traub1988] on Information Based Complexity [@Nemirovsky1992; @Woniakowski2009], the branch of computational complexity that studies the complexity of approximating continuous mathematical operations with discrete and finite ones up a to specified level of accuracy. Indeed the concept that numerical implementation requires computation with partial information and limited resources emerges naturally from Information Based Complexity, where it is also augmented by concepts of contaminated and priced information associated with, for example, truncation errors and the cost of numerical operations. In this framework, the performance of an algorithm operating on incomplete information can be analysed in the usual worst case setting or the average case (randomized) setting [@Ritter2000; @Novak2010] with respect to the missing information. Although the measure of probability (on the solution space) employed in the average case setting may be arbitrary, as observed by Packel [@Packel1987], if that measure is chosen carefully (as the solution of a game theoretic problem) then the average case setting can be interpreted as lifting a (worst case) min max problem (where saddle points of pure strategies do not, in general, exist) to a min max problem over mixed (randomized) strategies (where saddle points do exist [@VNeumann28; @VonNeumann:1944]). As exposed by Diaconis [@Diaconis:1988] (see also 