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Many sightings of the Ivory-billed Woodpecker (Campephilus principalis) have been reported during the past several decades, but nobody has managed to obtain the clear photo that is regarded as the standard form of evidence for documenting birds. Despite reports of sightings by teams of ornithologists working independently in Arkansas and Florida, doubts cast on the persistence of this iconic species have impeded the establishment of a meaningful conservation program. An analysis of the expected waiting time for obtaining a photo provides insights into why the policy of insisting upon ideal evidence has failed for this species. Concepts in statistics and probability are used to analyze video footage that was obtained during encounters with birds that were identified in the field as Ivory-billed Woodpeckers. One of the videos shows a series of events that are consistent with that species and are believed to be inconsistent with every other species of the region. Another video shows a large bird in flight with the distinctive wing motion of a large woodpecker. Only two large woodpeckers occur in the region, and the flap rate is about ten standard deviations greater than the mean flap rate of the Pileated Woodpecker (Dryocopus pileatus). Supplemental materials for this article are available online. [ABSTRACT FROM AUTHOR]