Growing up an Andretti in Nazareth, Pa., is tough. As the son and grandson of racing legends Michael and Mario, Marco Andretti was taunted by envious blue-collar classmates.

“They’d say ‘you’re rich, you’re rich, you’re rich,’” said Mr. Andretti on a recent Friday, seated by the pool of the 12,226-square foot mansion where he grew up. “I was like, ‘No, my dad’s well off, but that’s not my money.’ I want to work for my money. I’m still not there. I still have a lot of work to do.”

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