Two duellists will shoot at each other in turns obeying a given ordering. How should we arrange the ordering to make the duel as fair as possible when the only information we have is that the duellists are equally bad with no memory?

This problem of Konyagin is the special case of a class of approximation problems in which we seek approximations of power series with bounded coefficients by power series with two distinct coefficients as the argument approaches 1 (or some other singular points). In this talk we will present near-optimal solutions to this generalized problem using infinite order sigma-delta quantization and outline a more general perspective via discrepancy theory.