Sequential sampling problems arise in stochastic simulation and many other applications. Sampling is used to infer the unknown performance of several alternatives before one alternative is selected as best.This paper presents new economically motivated fully sequential sampling procedures to solve such problems, called Economics of Selection Procedures (ESP). The optimal procedure is derived for comparing a known standard with one alternative whose unknown reward is inferred with sampling. That result motivates heuristics when multiple alternatives have unknown rewards.The resulting procedures are more effective in numerical experiments than any previously proposed procedure of which we are aware, and are easily implemented. The key driver of the improvement is the use of dynamic programming to model sequential sampling as an option to learn before selecting an alternative.It accounts for the expected benefit of adaptive stopping policies for sampling, rather than of one-stage policies, as is common in the literature.