From Longman Dictionary of Contemporary Englishthe luck of the drawthe luck of the drawCHANCE/BY CHANCEthe result of chance rather than something you can control → luck
Examples from the Corpus
the luck of the draw• It was by the luck of the draw that I got a corner office.• United are getting the luck of the draws, but still need a lucky win.• As always, jury duty is the luck of the draw.• It depends on the luck of the draw. 