The thylacine (Thylacinus cynocephalus), one of Australia's most characteristic megafauna, was the largest marsupial carnivore until hunting, and potentially disease, drove it to extinction in 1936. Though thylacines were restricted to Tasmania for two millennia prior to their extinction, recent "plausible" sightings on the Cape York Peninsula in northern Queensland have emerged, leading some to speculate the species may persist, undetected. Here we show that the continued survival of the thylacine is entirely implausible based on most current mathematical theories of extinction. We present a dataset including physical evidence, expert-validated sightings, and unconfirmed sightings leading up to the present day, and use a range of extinction models, focusing on a Bayesian approach that incorporates all three types of data by modelling valid and invalid sightings as independent processes, to evaluate the likelihood of the thylacine's persistence. Although the last captive individual died in September 1936, our analyses suggest the most likely extinction date would be 1940; other extinction models estimated the thylacine's extinction date between 1936 and 1943, and even the most optimistic scenario suggests the species did not persist beyond 1956. The search for the thylacine, much like similar efforts to "rediscover" other recently extinct charismatic taxa, is likely to be fruitless, especially given that persistence on Tasmania would have been no guarantee the species could reappear in regions that had been unoccupied for millennia. The search for the thylacine may become a rallying point for conservation and wildlife biology, and could indirectly help fund and support critical research in understudied areas like Cape York. However, our results suggest that attempts to rediscover the thylacine will likely be unsuccessful. This article is protected by copyright. All rights reserved.