The sensational, spidery plot of the most gripping game of thrones in modern history is best captured by two images. The first is from Donald Trump's extravagant third wedding at his Mar-a-Lago estate in 2005: The junior senator from New York, glowing in gold silk, smiles up at the mogul with genuine delight as he says something that cracks up Hillary, Bill and Trump's bride, Melania. Donald and Hillary look "just like teenagers in love" in the flashbulb moment, as David Patrick Columbia, the editor of the website New York Social Diary, notes drily. The second, more sinister image is from the St Louis presidential debate last month: Trump looms behind Hillary like a horror-movie fiend as she makes a point, while three of Trump's guests in the front row, women who accused Bill of sexual assault, give her the stink eye. What a difference a decade makes: from a Babylonian celebration to a seething face-off.

We are in the final days of the first presidential contest between two New Yorkers in 72 years, since Thomas Dewey ran against Franklin D. Roosevelt. On election night, the party and the wake will both be held in Manhattan. Hillary will hold hers at the Javits Convention Centre, with its literal glass ceiling and, as The New York Times' campaign reporter Maggie Haberman noted, an air of trolling: Back in the late 1970s, Trump wanted to build the centre and slap the Trump name on it, but the city refused.

In this election, which could lead to the death of the Republican Party and the ideological makeover of the Democratic Party, the New York aspect has been largely overshadowed. The story of how Donald Trump and Hillary Clinton rose and reinvented themselves and embraced and brawled is the story of New York itself. It is a tale of power, influence, class and ambition that might have intrigued Edith Wharton, whose family once owned a grand home down the block from what is now Trump Tower.

START OF THE REINVENTION

The Clintons started their move to New York from Washington in 2000, so Hillary could pursue her bid for the US Senate. She had never lived in New York, but carpetbagging was no sin to cosmopolitan New Yorkers, who embraced Bobby Kennedy when he decamped from Massachusetts and suburban Washington in 1964, so she looked North to Daniel Patrick Moynihan's Senate seat.

Hillary knew she should not be seen as a Manhattan insider, so just as Bobby chose Long Island as his base, she chose Westchester. New York - and being a senator in the aftermath of Sept 11 - would change Hillary. "It toughened her up," says Senator Charles Schumer of New York. "She's harder-nosed about things. Life did that, but New York did, too."

Bill also needed a reinvention. After the impeachment, he was in bad odour. He had to abandon plans to rent lavish offices for their foundation in Carnegie Hall Tower for almost US$800,000 a year after critics pounced. The former president moved instead into offices in Harlem for US$210,000 a year. He was snubbed by four of the prestigious Westchester County golf clubs he reportedly tried to join. He started a campaign to improve his image, making speeches at colleges and enlisting former Cabinet members to talk up his legacy. Once Bill moved up in public estimation, he moved downtown with the foundation.

As the Clintons fashioned a new life in New York, Trump, too, was transforming himself - from a risk- taking developer facing bankruptcy to a low-risk licenser of his name for other people's projects, from a brazen builder to a reality-TV star on The Apprentice. He had come out of Queens, a pushy New York kid with family money but no social tools to climb the society ladder.

The New York society scene was set by the Rockefellers and the Astors with a tradition of civility, philanthropy and the arts at its heart. Even those who make money the rough way adopt this genteel facade. Michael Bloomberg is the quintessential emblem of this model and Trump is the quintessential raspberry to it. One top New York foundation official who requested anonymity - many people will only speak anonymously about the Trumps and the Clintons, because both clans are known to be vindictive - notes that "in the community of plutocrats and superachievers who come to New York, Donald Trump is seen as persona non grata. He's not a civic leader". When the tightfisted Trump hosts a charity event for veterans or a charity golf tournament, it is dismissed as something to polish the Trump brand.

Trump wants to belong, to get more legitimacy by elbowing his way into the power crowd, while the Clintons passed that threshold of belonging after two terms in the White House. A top media mogul dismisses all three as outsiders: "No one here thinks of the Clintons as New Yorkers, and Donald is a bridge-and-tunnel person. He's always been a poseur in New York."

KINDRED SPIRITS

Trump realised golf was his entree if he wanted to pal around with Bill Clinton, whom he considered a kindred spirit in some ways - a great man who attracted jealous haters. "Bill is kind of Trump with a dictionary," says one author who has written about New York real estate. Trump had his own country club with a golf course in Westchester, which he bought in the late 1990s. He closed the club in 1999 to redevelop it, reopening it as Trump National Golf Club in 2002. It was six miles (10km) from the Clintons' house, and Trump could play with him, ingratiating himself further by hanging photos of Bill on the wall.

Trump greased the wheels of his relationship with the former president and the senator, giving the Clinton Foundation a US$100,000 gift from his own foundation. According to Trump Revealed, by Michael Kranish and Marc Fisher, Trump donated to Hillary's Senate war chest six times between 2002 and 2009, for a total of US$4,700.

The friendship, on both sides, was a transaction. Trump's life in New York was all about promoting the brand and making money for the family business. It was the same for the Clintons. A former Clinton White House official puts it more bluntly: "This was a classic Clinton go-where-the-money-is move."

Trump wasn't on the dinner-party circuit. He lived in an alternate universe called Trumpworld, and his favourite way to spend the evening was ordering a steak or cheeseburger (well done) from Fresco by Scotto and watching a sports event on TV. "Trumpworld is a world he weaves for his own needs and desires, depending on what they are... and when they are," says Louise Sunshine, a former Trump Organisation vice-president, noting that Clintonworld is much broader and more global.

Though the Clintons might show up at some events and galas, they were never really around enough to become part of the society dinner- party circuit, either. When I asked Trump last summer to describe his relationship with the Clintons, he was neutral: "As a businessman, you have to get along with all politicians," he said. "I wouldn't say it was a close relationship."

Hillary presents the trip to Trump's wedding as a lark. "The dates worked," a friend says. But some of her aides expressed surprise that she was going to such a gaudy affair; they believed Hillary rearranged her schedule because she thought Trump was a more important donor than he was.

The senator and former president beamed in pictures, mingling with the starry crowd, which included Heidi Klum, Barbara Walters, Arnold Schwarzenegger, Usher, Don King, Simon Cowell and Katie Couric. Andre Leon Talley attended with Anna Wintour because the bride was going to be featured on the cover of Vogue, where he was then American editor at large. He had flown to Paris to shop with Melania for the dress - she chose a John Galliano for Dior strapless gown worth US$230,000 and a Vera Wang cocktail dress to change into later.

Trump was a reality-show star now, starting his third hit season of The Apprentice on NBC. Just as his taste in his apartment at Trump Tower was "like Louis XIV dropped acid", as Timothy O'Brien, author of TrumpNation, describes it, so was his third wedding straight-up Versailles. "This was a man building a ballroom for his trophy wife," Talley said. "It was Baroque, the way he loves it. The marble was flown in from Italy, and the ceiling was like a palace, all gold, painted by artisans flown in from France."

David Patrick Columbia, the society editor, asserts that the Clintons were another accoutrement: "Donald liked the fact that the Clintons were there because it was just another affirmation of who he had become in his life, a successful person. That's what matters to him."

WACKIER AND WACKIER

Perhaps the collision of Trump and the Clintons on the biggest stage of all was inevitable. But was it orchestrated? At the restaurant in Trump Tower last summer, I asked the mogul about that phone call he got from Bill Clinton in May 2015, when the businessman was making up his mind whether to run. The Washington Post quoted four Trump allies and one Clinton associate as saying Clinton encouraged Trump's efforts to play a larger role in the Republican Party.

Roger Stone, author of The Clintons' War On Women, and a long-time Trump confidant, claims that Bill urged Trump to get in the race and told him he thought he could get the nomination.

I tried to get to the bottom of this story that day at Trump Tower, but when you're dealing with Bill and Donald and truth, it's an elusive goal.

"Did Bill tell you that you should run?" I asked.

"He didn't say one way or the other," Trump replied.

To make the whole conspiracy wackier, when I began fact-checking this story, the Trump Tower version flipped, with Trumpsters saying the phone call entailed Bill trying to talk Donald out of running because the former president knew that Trump could beat Hillary.

This new version was met with mockery from Clintonistas. "Bill Clinton is not Frank Underwood," a former top aide says. "I guarantee you he did not call Trump with an uber-plan, where he was five moves down the chessboard. He has a theory: You've got to give a lot to get a lot. But he doesn't meddle like that, telling people to get in and get out. Trump shouldn't flatter himself that Bill gave a damn one way or the other. Trump was just another guy on the call list."

No matter how Trump got into the race, the way he has conducted it has made Bill burn. Trump escalated his attacks after the Billy Bush hot mic incident, dragging Bill's accusers back onto the stage. No one else would have said, as Trump did, that Hillary had "one of the great women-abusers of all time sitting in her house, waiting for her to come home for dinner". Trump also eagerly pounced to lash the Clintons to a new twist in the FBI e-mail investigation, involving Anthony Weiner, the estranged husband of Hillary's closest aide, Huma Abedin, and his sexts to a 15-year-old North Carolina girl.

New York elites have gone from flabbergasted that Trump got this far to debating how the Trump family and a top Trump strategist, Jared Kushner, Ivanka's husband and the publisher of The New York Observer, will be received if they have to slink back into town. Some people say the attitude towards the Trump children will be more lenient; others think the Trump brand is irrevocably damaged and that the whole family will be pariahs.

"I can tell you, in my crowd, they would rather not do anything associated with Trump," says one advertising and marketing big shot.

"People are nauseated by what he's doing."

Cindy Adams, the New York Post columnist, disagrees: "He'll go back to being the most famous face on this planet. No, his brand won't be hurt. Trump will be Trump. Everybody will still want to meet him."

At the annual Al Smith dinner last month at the Waldorf Astoria, a white-tie charity fete put on by the Catholic Archdiocese of New York that brings together high society and media and features humorous speeches by politicians, Trump was greeted warmly enough after he was introduced by Al Smith IV. "A kid from Queens with a big heart and a big mouth is without question a New York institution," Smith said.

But when Trump began to make harsher cracks about Hillary towards the end, out of sync with the tone of the event, he was repeatedly booed. Afterwards, he fled quickly without talking to anyone. As Trump returned to the seclusion of his Fifth Avenue Xanadu, he was playing a scene of megalomania and mortification straight out of one of his favourite movies, Citizen Kane, about the fall of a brash New York mogul who flew high, gave politics a shot and then had a steep fall after a sex imbroglio.

"Citizen Kane was really about the accumulation," Trump once said. "At the end of accumulation, you see what happens, and it is not necessarily all positive." Hillary, meanwhile, was spotted nearly 20 minutes after he left, still laughing and mingling with the crowd.

• Adapted from an article that originally appeared in The New York Times Magazine.