This paper was motivated by the problem of developing an optimal strategy for exploring a large oil and gas field in the North Sea. The problem resembles a classical multi-armed bandit problem, but probabilistic dependence plays a key role: outcomes at drilled sites reveal information about neighboring targets. Good exploration strategies will take advantage of this information as it is revealed. We develop heuristic policies for sequential exploration problems and complement these heuristics with upper bounds on the performance of an optimal policy. We begin by grouping the targets into clusters of manageable size. The heuristics are derived from a model that treats these clusters as independent. The upper bounds are given by assuming each cluster has perfect information about the results from all other clusters. The analysis relies heavily on results for bandit superprocesses, a generalization of the classical multi-armed bandit problem. We evaluate the heuristics and bounds using Monte Carlo simulation and, in our problem, we find that the heuristic policies are nearly optimal. (Joint work with Jim Smith, Duke University).