hope against hope

Likely a paraphrase of the first few words of Romans 4:18.^[1]

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hope against hope (third-person singular simple present hopes against hope, present participle hoping against hope, simple past and past participle hoped against hope)

1. (idiomatic) To continue to hope, even when what is hoped for seems unlikely or impossible.
   • 1913, Edgar Rice Burroughs, The Return of Tarzan, New York: Ballantine Books, published 1963, page 206:

     Would he be in time to rescue? He hoped against hope. At least he could be revenged, and in his wrath it seemed to him that he was equal to the task of wiping out the entire population of that terrible city.