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buck the odds ("Buck the odds" means to proceed with your intentions against (buck) a high probability (odds) of defeat, and (in a fairly common usage but not at all necessarily) to succeed, to win.
 usingenglish.com fa158) | |||
| go to the limit (Andrey Truhachev); roll the dice (Ballistic); push it past the red line (Alex_Odeychuk) | |||
| bet one's bottom dollar on something; bet one's last dollar on something; put one's shirt on; put one's shirt upon | |||