EVERY New Year, cruise lines brace themselves for “wave season”—the first three months of the year, in which nearly a third of all holidays at sea are booked. They will do well to improve on their 2015 results. On December 18th Carnival, the world’s largest operator, with more than 40% of a global market worth nearly $40 billion a year, announced a record $2.1 billion in full-year earnings, 40% up on 2014, thanks to buoyant demand and cheap fuel oil. Along with Royal Caribbean Cruises (RCL) and Norwegian Cruise Line (NCL), the trio now control around 80% of the industry.

Amid worries that demand for cruises may be peaking in some rich countries, the big three are now piling into the biggest potential market of all, China. Although Carnival based its first ship—the Costa Allegra—at a mainland Chinese port back in 2006, only in the past year have the big three got serious about moving capacity there from America and Europe.

In 2016 Carnival plans to increase the number of its ships in China from four to six. In October it announced the launch of a joint venture with a Chinese shipbuilder and China Investment Corporation, a sovereign-wealth fund, to establish the first new cruise brand aimed at the domestic Chinese market. RCL, which had three ships based in China in 2014, now has four and will add a fifth in the next few months. NCL, which has hitherto stayed away, plans to enter the Chinese market in 2017.

Carnival and RCL no longer send elderly cast-off hulks from America and Europe to China. Now they send their newest and best, such as RCL’s Quantum of the Seas, a megaship that can carry 4,180 holidaymakers, which has been based in Shanghai since June 2015.

Such are Carnival’s hopes for the Chinese market that it recently moved its chief operations officer, Alan Buckelew, to Shanghai to oversee the firm’s expansion there. The number of Chinese households earning over $35,000 a year—the figure the industry sees as the point at which foreign travel takes off—has increased from 6m to more than 27m over the past decade, according to Oxford Economics, a consulting firm. The number of mainland holidaymakers going on cruises—a comparatively fuss-free way of travelling abroad for the first time—has been growing by around 80% a year, and is expected to keep doing so despite China’s slowing growth rate. The government wants to promote the cruise-lines business together with the building of the ships it uses, as part of a rebalancing of the economy towards consumption in its latest five-year plan.

The Chinese market is also very profitable. This is partly because higher daily rates can be charged for the short, four-to-six-night cruises that are more popular in China, but also because the Chinese spend far more onboard. They are less interested than Americans or Britons in boozing and spa treatments, but keener on gambling, and really go to town in the onboard shops, buying such things as foreign-made appliances. One recent shopping craze on Carnival’s Chinese ships was for Japanese rice cookers, Mr Buckelew says.

If China’s economic slowdown intensifies, or if consumer interest in cruises turns out to be a fad, the operators risk being left with excess capacity and having their margins squeezed. Even so, betting on the rise of the Chinese holidaymaker looks more attractive than sticking to the main Western markets.

In Europe bookings have been hit by recent terrorist attacks in France and north Africa, according to Greg Badishkanian, a cruise-line analyst at Citigroup, a bank. And in Britain cruise-passenger numbers have been falling since 2013 because newly retired people, staple customers, have less disposable income than the previous generation of pensioners, who are now too old to travel. The future plans of the big three operators suggest they have concluded that the American market is saturated and has poor growth prospects. In 2017 there could be the first fall on record in North American cruise-ship capacity, according to Robin Farley, an analyst at UBS, another bank. For the moment, the decision by the big three to sail for China is a choice. But it could become a necessity.