We analyze the properties of searches devoted to finding planetary transits by observing simple stellar systems, such as globular clusters, open clusters, and the Galactic bulge. We develop the analytic tools necessary to predict the number of planets that a survey will detect as a function of the parameters of the system, the observational setup, site properties, and planet properties. We find that the detection probability is generally maximized for I-band observations. The signal-to-noise

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... io of a planetary transit is weakly dependent on the mass of the primary for sources with flux above the sky background, and falls very sharply for sources below sky. Therefore the number of detectable planets is roughly proportional to the number of stars with fluxes above sky (and not necessarily the number of sources with photometric error less a given threshold). In order to maximize the number of detections, experiments should be tailored such that stars near sky are above the detection threshold. Once this requirement is met, the number of detected planets is relatively weakly dependent on the detection threshold, diameter of the telescope, exposure time, seeing, age of the system, and planet radius. The number of detected planets is a strongly decreasing function of the distance to the system, implying that the nearest, richest clusters may prove to be optimal targets.