Some recent developments in finite population sampling methods are applicable to oil and gas resource assessment. The objective of these methods is to provide an estimate of the empirical frequency function of magnitudes of undiscovered deposits in a petroleum play when the only observable data are deposit magnitudes in the order of discovery (observation). Our theme is the conceptual similarity of the well-known Arps and Roberts (1958) model for magnitudes of discoveries as a function of exploratory wells drilled to a finite population sampling scheme called "successive sampling" by statisticans. There are two types of approximately unbiased estimators for parameters of successively sampled finite populations: Gordon's (1983) moment matching estimator and Andreatta and K ufman's (1983) anchored estimator. Both are similar in functional form to Arps and Roberts original estimator for the number of deposits of a given magnitude ultimately discoverable in a play, but arise from different assumptions about the nature of the sampling scheme. Using Western Gulf Miocene-Pliocene data and North Sea data, some estimates of empirical field size distributions generated by the three above-mentioned estimators are presented. When applied to Western Gulf Miocene-Pliocene data, the moment-matching estimator appears sensitive to how the sample is split. The anchored estimator replicates Smith and Ward's (1981) maximum likelihood estimates reasonably well.