against all the odds

(achieve sth) against all (the) odds (achieve sth despite the fact that you were not likely to succeed; despite very low probability; in a most unlikely way) — несмотря на все препятствия; вопреки тому, что все было против кого-л./чего-л.; несмотря на то, что все складывается неблагоприятно; несмотря на то, что обстоятельства против кого-л.
against all odds

Example 1: Terry came from a poor, deprived background and yet got a place at University against all the odds.

Example 2: Nobody had given him a chance but he won the race against all the odds. (SS)

Example 3: Against all odds, she managed to win the trophy. (thefreedictionary.com)

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