against all odds
In spite of seeming very unlikely, as in Against all odds we had a snowstorm in early May, or Against all odds the slower team won. This transfer of a betting term to general usage occurred about 1900.
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Examples from the Web for against all odds
And talk about an against-all-odds romance: for years it seemed as though nothing could keep Hunter and Edwards apart.What You Can Learn From John Edwards and Rielle Hunter|Michelle Cottle|June 27, 2012|DAILY BEAST