The Large Synoptic Survey Telescope (LSST) will survey the southern sky from 2022--2032 with unprecedented detail. Since the observing strategy can lead to artifacts in the data, we investigate the effects of telescope-pointing offsets (called dithers) on the $r$-band coadded 5$sigma$ depth yielded after the 10-year survey. We analyze this survey depth for several geometric patterns of dithers (e.g., random, hexagonal lattice, spiral) with amplitude as large as the radius of the LSST field-of-view, implemented on different timescales (per season, per night, per visit). Our results illustrate that per night and per visit dither assignments are more effective than per season. Also, we find that some dither geometries (e.g., hexagonal lattice) are particularly sensitive to the timescale on which the dithers are implemented, while others like random dithers perform well on all timescales. We then model the propagation of depth variations to artificial fluctuations in galaxy counts, which are a systematic for large-scale structure studies. We calculate the bias in galaxy counts caused by the observing strategy, accounting for photometric calibration uncertainties, dust extinction, and magnitude cuts; uncertainties in this bias limit our ability to account for structure induced by the observing strategy. We find that after 10 years of the LSST survey, the best dither strategies lead to uncertainties in this bias smaller than the minimum statistical floor for a galaxy catalog as deep as $r$$<$27.5. A few of these strategies bring the uncertainties close to the statistical floor for $r$$<$25.7 after only one year of survey.
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