“I love him,” said Chris Dercon, director of the Tate Modern in London. “Most people want to collect like their neighbors. He wants to collect things he doesn’t know yet. He’s not afraid to make a mistake.”

In the brief time before the fair ends on Sunday, Mr. Wilson wants to visit as many of the 258 dealers registered as possible. He and his wife, Laura Lee Brown, an artist and a part of Kentucky’s aristocracy — her grandfather was the founder of what is now Brown-Forman, the maker of Jack Daniels and Southern Comfort — were among an estimated 50,000 visitors perusing Art Basel’s $3 billion worth of art, a mix of works by Modern and contemporary masters, along with pieces by emerging stars. The couple also want to take in the dozens of satellite fairs, museum exhibitions and private open houses that are spread throughout downtown and northern Miami. (By Friday afternoon, the two had bought more than 25 pieces.)

The pair’s taste and shopping techniques could not be more different. Ms. Brown is slow and deliberate. Mr. Wilson, thin and lanky, races along the aisles in his black Prada sneakers like a kid with only one day at Disneyland and a determination to try every ride.

“I like things that are provoking, that people have trouble talking about,” Mr. Wilson said. So he and his wife have a rule: “We don’t say no to each other.”

The couple’s interest in art came together in 2006 when they created 21c, a combination museum and hotel in downtown Louisville, their hometown. It is filled with selections from their 1,600-piece collection by living artists. Mr. Wilson generally negotiates with dealers for a museum discount.