Risk analysis of an oil or gas prospect requires a probability distribution with two components, a dry-hole probability plus a distribution of oil or gas volumes if there is a discovery. While these components should be estimated objectively, risk analysis as currently practiced is mostly guesswork. Geologists assign outcome probabilities without appropriate procedures or data for objective estimation. Valid estimates require frequency data on regional exploratory drilling-success ratios, frequency distributions of oil and gas field volumes, and systematic tabulations of geological variables on a prospect-by-prospect basis. Discriminant functions can be used to analyze relationships between geological variables and hydrocarbons, leading to outcome probabilities conditional on discriminant scores. These probabilities can be incorporated in risk-analysis tables to yield risk-weighted financial forecasts. Computers are required for all procedures. Prior to drilling a petroleum prospect, the likelihood of good outcomes must be weighed against the bad to obtain a risked financial estimate that combines all possibilities. Some oil operators simply contrast the value of discovery that is expected, versus the cost of a dry hole. A cashflow projection yields an estimate of the revenue that will be received if a discovery is made. This assumes an initial producing rate and an ultimate cumulative production for the operator's net revenue interest, and an oil price. When the stream of revenue is discounted and costs for the lease, the completed well, and operating expenses and taxes are subtracted, the net present value is obtained. If the hole is dry, its cost is readily estimated. Only two monetary estimates coupled with an intuitive guess about the likelihood of a producer versus a dry hole form the basis for a decision. A great deal of oil has been found by both independent operators and major oil companies using such simple decision systems. Oil companies generally use more advanced methods at present. Many require their geologists to supply probability estimates for a spectrum of outcomes for each individual prospect, ranging from the probability of a dry hole through the probability of a small discovery, a medium-sized discovery, and various magnitudes of large discoveries.