The phrase ‘Against all odds’ means despite very low probability; in a most unlikely way.
Example of use: “She managed to win the trophy against all odds.”
Odds literally means the likelihood of success, given a specific set of numbers. The origin of the idiom “against all odds” can be traced to the origin of the word odd, which was first used in a wagering sense by none other than the great William Shakespeare in his 1597 work Henry IV. The pluralization of odd to odds did not happen until the 19th century, so it’s likely that this idiom was coined after the use of the word “odds” instead of “odd” came into common use. Who said it first? No one really knows.