Co-founding Microsoft ultimately made Paul Allen, who has died of non-Hodgkin’s lymphoma aged 65, one of the world’s richest men. But while he could buy anything he wanted – yachts, famous paintings, sports clubs – he lived with the threat of recurring cancer. His illness – initially diagnosed as Hodgkin’s lymphoma – was first treated with radiation therapy and a bone marrow transplant in 1982, and caused him to leave Microsoft the following year. He said: “It makes you that much more focused on realising your dreams and hopes, because all of our times on this planet are limited.”

Allen will mainly be remembered for his association with Bill Gates, which started at Lakeside, a private school in Seattle. In 1968 the school’s mothers’ association funded the purchase of a Teletype ASR-33 text terminal to a remote General Electric GE-635 mainframe, and a small group of boys became fanatical users. As Allen wrote in his memoir Idea Man (2011): “I had discovered my calling. I was a programmer.”

Allen soon teamed up with a younger kid, the freckle-faced, hyperactive Gates, with Allen acting as the older brother, applying logic to some of his wilder ideas. That was not enough to stop an early business venture in Traf-O-Data, their attempt to process data from road traffic counters. However, this had a significant benefit: it prompted Allen to write a program that enabled a mainframe to emulate an Intel microprocessor.

Allen left Lakeside to study at Washington State University (1971-74) and a couple of years later Gates went to Harvard. That might have been the end of it. But somehow, when Allen was 21, Gates persuaded him to switch coasts and take a programming job at Honeywell in Boston. It was there that Allen famously brandished a copy of the January 1975 issue of Popular Electronics magazine, which had a cover story on the $397 MITS Altair 8800 build-your-own microcomputer kit. Allen was convinced this marked the birth of a new personal computer industry, and that they needed to get involved before it was too late.

As it happened, the Altair 8800 did nothing useful, and MITS desperately needed a language so that owners could write programs to run on it. Gates and Allen decided to create a small (4K) version of Basic for it, even though they did not own one. Allen adapted his Intel chip emulator to run on Harvard’s mainframe, and they wrote their Basic with the help of another student, Monte Davidoff.

Allen flew to Albuquerque in New Mexico to demonstrate the Basic to MITS and, seemingly miraculously, it worked. Allen ended up working for MITS, and then had to persuade Gates to take leave of absence from Harvard and move to Albuquerque.

It was there that Gates and Allen founded Micro-Soft (initially hyphenated) in 1975, with Gates, the chief executive, owning 60% of the company. They planned to sell their Basic to other emerging microcomputer companies, making Microsoft’s program the de facto standard.

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Microsoft moved to Seattle in 1979, and got its big break when IBM, the most powerful computer company of the age, wanted Microsoft Basic for its IBM PC, launched in 1981. Microsoft also ended up supplying its most popular operating system, MS-DOS, which put it on the road to riches.

At the time, of course, Microsoft was still a small private company. In 1982, its annual sales were only $24.5m, compared with IBM’s $34.4bn. It was not worth much. However, Allen’s massive wealth and a lifetime of indulgence ultimately derived from a single argument with his co-founder. Since he was being treated for cancer, Allen did not want the stress of dealing with Gates any longer, so he decided to leave.

Gates wanted to buy his stake for $5 a share, and Allen wanted at least $10. As Allen said in Idea Man: “If he’d been willing to offer something close to my asking price, I would have sold way too soon.” He kept his stake.

Microsoft went public at $21 per share in 1986, and after the success of Windows and Office in the 1990s increased in value by almost 24,000%. At today’s share price, Allen’s holding would have been worth $300bn, compared to the estimated $26bn fortune he left.

Microsoft shares provided a river of cash that enabled Allen to indulge in an astonishing range of investments, foundations and philanthropic donations. These ranged from funding an elephant census in Africa and fighting Ebola to founding several museums and backing space ventures such as Burt Rutan’s SpaceShipOne project and his own Mojave Aerospace Ventures.

Allen’s home town of Seattle was a major beneficiary. His most visible memorial is the Museum of Pop Culture (MoPOP), aka the Jimmy Hendrix museum, in an extraordinary building designed by Frank Gehry to look like a smashed guitar. Allen also founded the Flying Heritage Collection, to house his lovingly-restored second world war aircraft, and a Living Computer Museum, for his vintage computers.

Allen already owned the Portland Trail Blazers basketball team and became a local hero by buying the Seattle Seahawks to stop the American football franchise from moving to California.

Under Allen, the Seahawks won Super Bowl XLVIII (2014) in devastating style. He also part-owned the Seattle Sounders, a Major League Soccer team, and built the team a new stadium.

Obviously, Allen bought some of the world’s biggest yachts, including the 414-foot (126m) Octopus. This had two helicopters, a submarine, a swimming pool, a basketball court, and a full-size recording studio where the guitar-playing Allen could channel his love of Hendrix. He enjoyed jamming with pop stars and even released a couple of CDs. Everywhere at Once by Paul Allen and the Underthinkers featured Chrissie Hynde, of the Pretenders, and Joe Walsh, of the Eagles.

Born in Seattle, Paul was the son of Kenneth Sam Allen, a librarian at the University of Washington, and Faye Allen (nee Gardner), a school teacher. He ran his Vulcan holding company with his sister Jody (Jo Lynn) Allen, and she survives him.

• Paul Gardner Allen, computer programmer and businessman, born 21 January 1953; died 15 October 2018