from that of Player II) and Player II must solve a min max optimization problem over $\pi_{I}$ and $\pi_{II}$ to identify an optimal prior distribution for the Bayesian estimator (a careful choice of the prior also appears to be important due to the possible high sensitivity of posterior distributions [@OSS:2013; @OwhadiScovel:2013; @owhadiBayesiansirev2013]). Although solving the min max problem over $\pi_{I}$ and $\pi_{II}$ may be one way of determining the strategy of Player II, it will not be the method employed here. We will instead analyze the error of Player II’s approximation as a function of Player II’s prior and the source term $g$ picked by Player I. Furthermore, to preserve the linearity of the calculations we will restrict Player II’s decision space (the set of possible priors $\pi_{II}$) to Gaussian priors on the source term $g$. Since the resulting analysis is independent of the structure of and solely depends on its linearity we will first perform this investigation, in Section \[sec:problem\], in the algebraic framework of linear systems of equations, identify Player II’s optimal mixed strategy and show that it is characterized by deterministic optimal recovery and accuracy properties. The mixed strategy identified in Section \[sec:problem\] will then be applied 