A teenager, then known as William Martin Joel, lived on a half-acre plot in the working-class suburb of Hicksville — his family so limited that they didn’t own a TV. He took a tiring minimum wage job dredging oysters.

The dredge crisscrossed the waters of Long Island Sound, including a bay that curves like a comma and faces some of the most expensive real estate in the United States. From the boat, he could see a stately brick mansion.

“Rich bastards,” he thought to himself. “I’ll never live in a house like that.”

Several decades and dozens of Top 40 hits later, Billy Joel — the oysterman turned piano man — bought that very mansion on Centre Island in 2002.

Mr. Joel, 75, has told that story many times, right down to throwing in the vulgarity, maybe because it’s so unbelievable: “The word that applies is ‘absurd.’ I grew up in a quarter-acre lot house in Hicksville. And I would ride my bicycle up here and take a bike ride and look at all the rich people and cuss them out,” he says.