It often implies an attempt at foreseeing success in things like investments, sports, or contests. Everyone thought she was just lucky, but she has a knack for picking winners in start-up companies.
Pro Tip 2/3
Not Literal
'Picking a winner' is frequently used metaphorically and doesn't always involve an actual choice. With his recent promotions, it looks like he's picked a winner of a career path.
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Gambling Connotations
This phrase can associate with gambling, where choosing the winning person or thing is literal. She went to the derby and picked a winner, doubling her money!