jats:pThis paper is concerned with optimal strategies for drilling in an oil exploration model. An exploration area contains jats:italicn</jats:italic>jats:sub1</jats:sub> large and jats:italicn</jats:italic>jats:sub2</jats:sub> small oilfields, where jats:italicn</jats:italic>jats:sub1</jats:sub> and jats:italicn</jats:italic>jats:sub2</jats:sub> are unknown, and represented by a two‐dimensional prior distribution jats:boldπ</jats:bold>. A single exploration well discovers at most one oilfield, and the discovery process is governed by some probabilistic law. Drilling a single well costs jats:italicc</jats:italic>, and the values of a large and small oilfield are jats:italicv</jats:italic>jats:sub1</jats:sub> and jats:italicv</jats:italic>jats:sub2</jats:sub> respectively, jats:italicv</jats:italic>jats:sub1</jats:sub> > jats:italicv</jats:italic>jats:sub2</jats:sub> > jats:italicc</jats:italic> > 0. At each time jats:italict</jats:italic> = 1, 2, …, the operator is faced with the option of stopping drilling and retiring with no reward, or continuing drilling. In the event of drilling, the operator has to choose the number jats:italick</jats:italic>, 0 ≤ jats:italick</jats:italic> ≤ jats:italicm</jats:italic> (jats:italicm</jats:italic> fixed), of wells to be drilled. Rewards are additive and discounted geometrically. Based on the entire history of the process and potentially on future prospects, the operator seeks the optimal strategy for drilling that maximizes the total expected return over the infinite horizon. We show that when jats:boldπ</jats:bold>≻jats:boldπ</jats:bold>jats:sup′</jats:sup> in monotone likelihood ratio, then the optimal expected return under prior jats:boldπ</jats:bold> is greater than or equal to the optimal expected return under jats:boldπ</jats:bold>jats:sup′</jats:sup>. Finally, special cases where explicit calculations can be done are presented.</jats:p>