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Cameron, left, and Tyler Winklevoss leave the 9th Circuit Court of Appeals after a hearing on a settlement dispute with Facebook's Mark Zuckerberg in San Francisco, Calif., on Jan. 11, 2011.STEPHEN LAM/Reuters

The Winklevoss twins are not the first to imagine that Bitcoin is an idea so revolutionary it deserves the moniker Web 3.0. But when Tyler and Cameron muse on the virtual currency, it means something more: victory.

The story of how Mark Zuckerberg, a Harvard contemporary, emerged as king of Web 2.0 – to the brothers' fury – was told in the 2010 movie The Social Network, which dramatized their legal claim that Mr. Zuckerberg stole the idea for Facebook from them.

Perhaps only a move into the third Internet era, confining Mr. Zuckerberg's victory to the past, will help them put their grievance behind them. This week, the brothers launched the Winklevoss Bitcoin Trust – an exchange-traded product that is sponsored by their company, Math-Based Asset Services. In the event it is approved by regulators and accepted by an exchange, it will invest directly in Bitcoins, tracking their dollar price.

Investors in the fund would expose themselves to an exceptionally odd asset. Bitcoin was created by an unknown computer scientist, and its principle purpose is to allow anonymous online money transfers outside the banking system. The price of Bitcoins – based on little more than the hope the system will become a substantial means of exchange – has been yo-yoing. It was below $7 (U.S.) a year ago and reached $266 in April before dropping below $80. It has been called "a modern tulip mania but without the pretty flowers."

To its adherents, Bitcoin's advantages mean it could disintermediate banks. To the authorities, it looks like a medium for money laundering. The discovery that the Winklevoss brothers hold 1 per cent of the currency will do little to help establish its seriousness as a force in finance. To describe the Winklevoss Bitcoin Trust as "long-odds" is an understatement. But they have hired good lawyers to begin the regulatory steeplechase.

Cameron and Tyler were born moments apart in the summer of 1981, but their parents have never revealed who is older. Their father, a business school professor turned entrepreneur, had by then already grown rich from an accounting software venture. But, stressing their self-made credentials, the twins like to say they built their first startup at 16, when they founded a rowing club at their elite all-boys prep school in Greenwich, Conn. The twins revealed to Vanity Fair that their older sister, Amanda, died of a drug overdose in 2002 aged 23.

Their physiques made them ideally suited to rowing, and their sibling bond meant they came as a coxless pair. Their hard physical training helped win them places at Harvard and on the U.S. rowing team. They competed, coming sixth, in the men's pairs in the 2008 Beijing Olympics. Oxford university took them in for an MBA; they were in the losing crew in the 2010 Boat Race.

That year, writers of The Social Network popularized a sneering, Latinate nickname for the duo – the Winklevii – which has stuck. It speaks to a perception that their privilege and natural gifts have given them a sense of entitlement. Divya Narendra, a friend and fellow litigant against Facebook, says this aggravates them above all.

"They are enterprising guys, and not lazy about success," he says. "They are not sitting around waiting for stuff to happen to them, but actively building their own careers. They leverage what they have been given, but they certainly build on top of it."

Yet the perception of entitled arrogance has stuck. The reason, of course, is how Mr. Narendra and the Winklevosses reacted when the precocious web developer they engaged to build their student dating site in 2003 suddenly launched an alternative called TheFacebook.

Larry Summers, then president of Harvard, ignored their request that Mr. Zuckerberg be kicked out of the university. Several years later, Mr. Summers recalled: "One of the things you learn as a college president is that if an undergraduate is wearing a tie and jacket on Thursday afternoon at 3 o'clock, there are two possibilities. One is that they're looking for a job and have an interview; the other is that they are an asshole. This was the latter case."

Unhappy with their first settlement with Mr. Zuckerberg – a $65-million cash and shares deal that, during Mr. Zuckerberg's stewardship of Facebook, swelled to be worth several times that – the pair sued to reopen negotiations, claiming they had been duped about the company's true value. Facebook and Mr. Zuckerberg have always denied wronging the brothers in the first place – and finally won the legal battle to prevent the settlement being torn up in 2011.

This is the baggage the twins must overcome in their hoped-for career in angel investing: that their millions come not from building a company but from suing someone who did. The pair have set up the headquarters of Winklevoss Capital, their investment vehicle, in the Flatiron District, a Manhattan start-up neighbourhood. Tyler has one corner office and Cameron another. But co-workers say they are more often found together in the conference room that links the two. They claim complementary skills: Cameron is left-handed and more creative; Tyler is right-handed and more analytical. At Math-Based Asset Services, Tyler is the chief financial officer to Cameron's chief executive.

More than a year after retiring from rowing and setting up Winklevoss Capital, the brothers remain outsiders on the New York tech scene. Before Bitcoin, they made only two investments: in Mr. Narendra's new venture, SumZero; and an e-commerce company run by two women that a childhood friend happened to sit next to on a bus to a wedding. Bitcoin is their biggest bet, and their reputations as investors would probably not survive its failure. Either way, it offers a chance for them to be known for something other than their rowing or their fight with Mr. Zuckerberg. Something new – perhaps Winklevii 3.0.

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