Probability: Reserves Estimation, Monte Carlo Risk Analysis, and P90/P50/P10 Confidence Levels
Probability is a numerical measure of the likelihood that a specific event will occur, expressed on a scale from 0, meaning the event is impossible, to 1, meaning the event is certain, or equivalently as a percentage from 0 to 100 percent. In the oil and gas industry the concept reaches well beyond abstract mathematics, because nearly every capital decision rests on incomplete subsurface information, and probability is the language operators use to quantify that uncertainty. When a geologist assigns a 35 percent chance of geological success to an exploration prospect, or a reservoir engineer reports that reserves have a 90 percent probability of being met or exceeded, each is converting judgment about porosity, permeability, trap integrity, and fluid contacts into a single defensible figure. The formal framework in Western Canada is the Canadian Oil and Gas Evaluation Handbook, known as COGEH, which aligns with the Society of Petroleum Engineers Petroleum Resources Management System, or PRMS, and defines reserves categories in probabilistic terms: proved reserves correspond to a P90 confidence level, proved plus probable to P50, and proved plus probable plus possible to P10. Those percentiles come directly from probability theory applied to a distribution of possible outcomes. Probability also drives Monte Carlo simulation, where thousands of randomized samples of net pay, drainage area, recovery factor, and formation volume factor are combined to produce a full distribution of recoverable volumes rather than a single deterministic number. In the Montney and Duvernay plays, where a single horizontal well can cost 8 to 12 million CAD, understanding the probability that a well will reach payout separates a disciplined drilling program from a series of expensive dry holes. Probability underpins decline curve uncertainty, chance of commercial success, drilling hazard assessment, and the expected monetary value calculations that rank competing capital projects. It is the connective tissue between raw geoscience data and the financial models that the AER, investors, and lenders rely on when they evaluate a Western Canadian producer.
Key Takeaways
- Zero-to-One Confidence Scale: Probability is always bounded between 0 and 1, and the complement rule means the chance of an event plus the chance of its non-occurrence must sum to 1. A prospect with a 30 percent chance of success carries a 70 percent chance of failure, which is why explorers drill portfolios rather than single wells and expect a fraction of them to fail even when every prospect is technically sound.
- P90, P50, P10 Reserves Thresholds: Under COGEH and PRMS, proved reserves sit at P90, giving at least a 90 percent probability that recovered volumes equal or exceed the estimate. Probable is the incremental volume between P50 and P90, and possible is the increment between P10 and P50. The 1P, 2P, and 3P groupings map to these percentiles and drive every AER and securities reserves disclosure in Canada.
- Monte Carlo Distributions: Rather than multiplying single best-guess inputs, probabilistic evaluation samples each variable from its own distribution across thousands of iterations, producing a cumulative curve from which P90, P50, and P10 are read directly. This captures the reality that a Montney well's recoverable gas depends on many uncertain factors interacting, not one deterministic answer.
- Chance of Geological Success: Exploration probability multiplies the independent chances of source, reservoir, trap, seal, and timing all being present. Because these are multiplied, a prospect needing five factors each at 70 percent yields only a 17 percent combined chance, explaining why frontier exploration in the Deep Basin or offshore Flemish Pass carries such steep odds.
- Expected Monetary Value: Probability weights outcomes in EMV calculations, where the value of success times its probability is offset by the cost of failure times its probability. A positive EMV justifies drilling; a negative one does not. This single figure lets a WCSB operator rank a low-risk Cardium infill against a high-reward Duvernay exploration test on a common financial footing.
Probabilistic Reserves Categories Under COGEH and PRMS
Canadian reserves reporting under National Instrument 51-101 requires evaluators to classify volumes by certainty, and probability provides the dividing lines. When an independent qualified reserves evaluator such as GLJ or McDaniel builds a probabilistic model for a Tourmaline or ARC Resources property, they generate a cumulative distribution of estimated ultimate recovery. Proved reserves are read at the P90 point, meaning a 90 percent chance the true volume is at least that large; probable adds the volume down to P50; possible extends to P10. A Montney gas well might carry 4.2 Bcf proved at P90, 6.1 Bcf as 2P at P50, and 8.4 Bcf as 3P at P10, roughly 119, 173, and 238 e3m3 respectively. Lenders discount toward the conservative P90 figure when sizing a reserves-based loan.
Monte Carlo Simulation in Play Evaluation
Monte Carlo simulation turns geological uncertainty into a quantified range. An evaluator assigns a distribution to each input, for example net pay following a lognormal curve from 15 to 45 metres, porosity from 4 to 8 percent, and recovery factor from 20 to 35 percent, then draws random combinations across ten thousand or more iterations. Each iteration produces one possible recovery figure, and the assembled results form a smooth probability distribution. Reading P90, P50, and P10 from that curve gives the proved, probable, and possible reserves without relying on a single optimistic or pessimistic guess. For a Clearwater heavy oil play, this method exposes how sensitive economics are to recovery factor, guiding whether an operator commits to a full multi-well pad or drills a single delineation well first.
Fast Facts
The mathematical technique now called Monte Carlo simulation was named after the Monaco casino district by physicists Stanislaw Ulam and John von Neumann while working on nuclear weapons at Los Alamos in the 1940s, because the method relied on repeated random sampling much like a roulette wheel. The petroleum industry adopted it for reserves estimation in the 1960s and 1970s, and today a single probabilistic reserves run for a large WCSB asset may execute more than one hundred thousand iterations in seconds on a laptop.
Related Terms
Probability is inseparable from reserves, since the P90, P50, and P10 categories are defined entirely by probabilistic confidence. It powers Monte Carlo simulation, the sampling engine that converts uncertain inputs into a distribution of outcomes. It shapes estimated ultimate recovery, which is reported as a range rather than a point value, and it feeds decline curve analysis, where uncertainty bands around forecast production are themselves probabilistic statements about future rates.
Real-World WCSB Scenario: Ranking a Duvernay Exploration Test
A mid-cap operator near Fox Creek is weighing a Duvernay condensate exploration well against a lower-risk Montney infill. The Duvernay test costs 11 million CAD, carries a 40 percent chance of commercial success, and would be worth 34 million CAD if it works. The engineering team runs the expected monetary value: 0.40 times 34 million minus 0.60 times 11 million yields a positive EMV near 7 million CAD. The Montney infill costs 8 million CAD with an 85 percent success chance but only 14 million CAD upside, giving an EMV near 4.7 million CAD.
Despite the Duvernay's higher failure risk, its superior EMV and the strategic value of proving new acreage tips the capital committee toward drilling it, with the Montney infill sequenced as the fallback if the exploration test disappoints. Probability, not gut feel, framed the decision and let both options compete on identical financial terms.