The size distribution of oil and gas fields within an arbitrary petroleum basin is approximated by the truncated Pareto distribution. We propose definite expressions for assessing the number and total resources of fields having any preset limits of field sizes and describe the application of simulational mathematical modeling for assessing the resource structure of a petroleum basin. The exploration filter model, which is a formal expression of oil and gas exploration strategy, is proposed. A definite expression for the filter operating in a given basin can be obtained from the history of oil and gas discoveries in that basin. The proposed concept can be used to predict the sequence of oil and gas fields of various sizes that are likely to be discovered in the basin during further exploration.