Liu Yiqian and his family can now fly free all over the world after he used his credit card, which earns points, to buy a $170m painting

A Chinese billionaire will never have to pay for a plane ticket again, after he accrued a staggering number of air miles using his American Express card to buy a $170m painting.

Liu Yiqian Liu was the winning bidder for Amedeo Modigliani’s Reclining Nude at a Christie’s auction house earlier in November.

Modigliani's Reclining Nude fetches second-highest ever art auction price Read more

A high-profile collector of Chinese antiquities and art, Liu has used his Amex in the past at auctions. In 2014 he reportedly put a $36m tea cup from the Ming Dynasty on his credit card. He and his wife said they also plan on using their card to pay for the Modigliani, according to news reports after the sale.

American Express would not confirm Liu Yiqian’s Modigliani purchase, or say if it would be the biggest ever on their cards, citing privacy reasons. But it can be done.

“In theory, it’s possible to put a ($170m purchase) on an American Express card,” said spokeswoman Elizabeth Crosta. “It is based on our relationship with that individual card member and these decisions are made on a case-by-case basis, based on our knowledge of their spending patterns.”

Liu has an American Express centurion card, also known as the Amex “black card”, an invitation-only card that is given to Amex’s biggest spending clients. The card has no official credit limit – and it earns points, just like most of the cards non-billionaires carry around.

Facebook Twitter Pinterest Crowds admire Amedeo Modigliani’s Nu couche. Photograph: Timothy A. Clary/AFP/Getty Images

Each Amex card issued in each country accrues points differently. But using a baseline of one point per dollar, what American Express uses for its US platinum and centurion cards, Liu would earn 170,400,000 membership reward points for his painting purchase, which doesn’t include tax or the fees Christie’s charges. He has probably earned tens of millions of points for his earlier fine art buys, like the expensive tea cup.

Liu and his wife, in an interview with the New York Times, said they planned to use the points to allow their family to travel for the rest of their lives.

That shouldn’t be a problem, according to Zach Honig, the editor-in-chief of the travel rewards site ThePointsGuy.com. “He’s probably reached that goal with that single painting,” Honig said.

Honig estimated that if Liu converted his membership rewards points into one of a number of airline frequent flyer programs, he and his family could travel anywhere, in style. He could fly 3,000 times between the US and Europe in the ultra-deluxe first class suites offered by Singapore Airlines (estimated cost: $17,800 round trip), if he converted points to Singapore’s program.

Lui, who is worth $1.4bn according to Forbes, probably didn’t use his Amex for the points. China allows its citizens to transfer no more than $50,000 out of the country in any year, and using his card could help him get around this limit because he’s just paying back American Express or the bank in China that issues his card.

One potential loser here could be Christie’s. Every time an American Express card holder uses the card, Amex charges the merchant a fee. That fee is usually 2% to 3%, depending on the merchant. For a $170m painting, millions of dollars could flow to Amex instead of Christie’s – enough, presumably, for Amex to pay for the Liu family’s future flights, and then some.