We define and exercise the expected value of computation as a fundamental component of reflection about alternative inference strategies. We present a portion of Protos research focused on the interlacing of reflection and action under scarce resources, and discuss how the techniques have been applied in a high-stakes medical domain. The work centers on endowing a computational agent with the ability to harness incomplete characterizations of problem-solving performance to control the amount of effort applied to a problem or subproblem, before taking action in the world or turning to another problem. We explore the use of the techniques in controlling decision-theoretic inference itself, and pose the approach as a model of rationality under scarce resources.