The thylacine, or Tasmanian tiger, was one of Australia's most characteristic megafauna, and was the largest marsupial carnivore until hunting, and potentially disease, drove them to extinction in 1936. Current knowledge suggests the thylacine became extinct on mainland Australia two millennia prior to its eradication on Tasmania, but recent “plausible” sightings on the Cape York Peninsula have emerged, leading some to speculate the species may have escaped extinction mostly undetected. Here we show that sighting evidence indicates the continued survival of the thylacine would be entirely implausible based on current mathematical theories of extinction. We present a sightings dataset including physical evidence, expert-validated sightings, and unconfirmed sightings leading up to the present day, and use a Bayesian framework that takes all three types of data into account, by modelling them as independent processes, to evaluate the likelihood of the thylacine's persistence. Although the last captive thylacine died in 1936, our model suggests the most likely extinction date would be 1940, or at the latest the 1950s. We validated this result by analysing our dataset with other frequently used extinction estimator methods, all of which confirm that the thylacine's extinction likely fell within the interval of 1936-1943. Even the most optimistic scenario suggests the species did not persist beyond the 1960s. The search for the thylacine, much like similar efforts to “rediscover” the Ivory-Billed Woodpecker and other recently extinct charismatic species, 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 centuries. The search for the Tasmanian tiger may become a rallying point for conservation and wildlife biology in the coming years, 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.