Venue: Flushing Meadows, New York Dates: 29 August-11 September
Coverage: Daily radio commentaries across BBC Sounds and the BBC Sport website and app, with selected live text commentaries and match reports on the website and app

Still loaded with endorphins and adrenalin, Danielle Collins went along with the premise.

“I came from nothing, and when you come from nothing you have nothing to lose.”

It was an irresistible soundbite. The Louis Armstrong Stadium crowd gobbled it up, hollering their approval. Collins – the daughter of a gardener and a grade-school teacher – was their adopted underdog, snarl sharpened by adversity.

The theory is a well-worn one. Mean streets breed a winning streak. Boxing great Marvin Hagler summed it up in words. “It’s hard to get up at 6am when you’re wearing silk pyjamas,” he said.

The Williams sisters’ journey from Compton to champions bore it out in gold.

But Jessica Pegula is different.

The American number one, who takes on Petra Kvitova in the last 16 on Monday (17:00 BST), is from the other side of the tracks.

Pegula is the daughter of Terry Pegula, an oil and gas magnate who, according to Forbes, is worth $6.7bn (£5.82bn).

It’s wealth beyond wealth. But, Pegula says, it guarantees little on the court.

“I have never wanted people to think I was given things,” she told BBC Sport.

“I think I have definitely earned my stripes in the tennis world.

“There are people on the outside who maybe don’t understand, who make assumptions.”

The buy-in to the Tour game is undeniably high. Annual travel and coaching costs can hit six figures at the top end.

Pegula’s family, who bought NFL team the Buffalo Bills in 2014, said they would support the teenager with the costs as she turned professional. Five years later, though, they wondered if their investment was worth it. For her, as much as them.

Pegula’s promise had been spiked by injuries. A knee operation in 2014 was followed by a leg injury and then keyhole hip surgery in the early part of 2017. Every ranking rise seemed to precede a return to painful rehabilitation. The bright lights and big stages always seemed out of reach.

In October 2017, the comeback trail ran through the Van der Meer Shipyard Tennis Club. On Hilton Head, off the South Carolina coast, it mainly serves seniors who want a change from the resort’s golf courses and beaches.

Pegula went there, along the shell-studded boardwalks, in front of the salt-bleached wooden stands, for a low-level clay event.

She lost her first match. Her opponent was world 1,025 Petra Januskova. The scoreline was 6-2 6-4. The bottom line on her prize cheque was just $147.

The cost was never too much, of course. But Pegula’s mother Kim feared the pain and disappointment might be.

“I remember thinking, ‘Why would she want to keep doing this?'” Kim Pegula told ESPN of her daughter in an interview last year.

“There are other women whose families are relying on them through tennis but she doesn’t have that worry. She doesn’t have to do this and her life would be so much easier if she didn’t.”

Pegula had an out. Unlike others, she had options; a skincare range she has founded, a charity she works with. She could walk away into another career, put on the silk pyjamas and prove the old theory right.

“There was definitely a point where I was 23 or 24, where I kept getting injured whenever I was getting close to the top 150 or top 100 and it would never quite happen,” she remembered.

“The last surgery I had was definitely a low. I wasn’t sure whether it would work out, whether it was worth it, whether I was good enough.”

Her family’s fortune would make it easy to quit and leave that last question unanswered. The story behind it made it less so.

Terry started work as a teenager. Like his own father, he drove trucks around the coal mines of Pennsylvania before starting his own mining business with a $7,500 loan.

Kim was adopted by an American family after being abandoned outside a Seoul police station by her biological parents in South Korea. She was planning to move to Alaska to work in a fish factory before she met her husband.

Neither had an easy start. Pegula decided she didn’t want one either.

“That is just the way I am wired; I don’t want to give in,” she said.

“And I love to play. Why would I give up the opportunity to do something great, something I love when lots of people don’t get the chance?

“Growing up, standards were always high to work hard and do well.

“My parents didn’t really come from a lot, so to see them make so much of themselves was really inspiring.

“It was about not taking anything for granted, working hard and you never know where you will end up.”

On Monday, it takes her to the biggest tennis stadium in the world – Arthur Ashe – for arguably the biggest match of her career.

She won’t make the same claims as Collins if she wins. But she won’t make any apologies either.

“My story is just different, but it is just me,” she concluded.