In Vila Mimosa, they were expecting a blowout.

This neighbourhood, with its whimsical name and filth-encrusted cobbled streets, is the one synonymous with the sale of sex in the city with the unrivaled global reputation for licentiousness.

In the days before the World Cup began in mid-June, the staff of the brothels that line the main street of Vila Mimosa put up green-and-yellow bunting, flags of European nations and signs that said "Welcome!" in a half-dozen languages. They took on extra staff, and the women started to make mental lists of what they would do with the windfall from the mass influx of foreign tourists.

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And? Nothing. "It's dead around here," sighed Monique da Cruz, sipping a Coke and staring at the quiet street a few days ago. "It's not even worth it for us, coming to work." She said she was making the equivalent of $300 a week instead of the usual $600 to $700. The only foreigners looking to buy sex were Argentines who, with their devalued currency, found Rio prices too high; they tried, but failed, to haggle.

Men spent their money on soccer tickets, Ms. da Cruz speculated, or got drunk with their friends instead, and the promised boom in business turned out to be one more myth about sex in Brazil.

Brazil has had a reputation for debauchery since the first Portuguese explorers arrived and sent titillated letters full of descriptions of naked and shameless indigenous people. It became, eventually, a part of the national identity – some nonspecific quality of sexiness that all Brazilians, but women in particular, are said to possess, brewed from the tropical climate, the mesmerizing natural beauty, and stereotypes about race and the mixing of it.

The tourism industry has not shied away from using the image to market Brazil, and women here often seem to relish it even as they strain against the restrictions it imposes. It makes for a country where gender identity is rigid and restrictive. Where the sale of sex is legal. Where sexual morality is muddled – women wear only pasties to dance in the Carnaval parade, but it is entirely unacceptable to be topless at the beach.

"I do think foreigners think we're easier to 'get,' " said N.B. Vasconcelos, 28, a lawyer in Rio. "They think that because of Carnaval, bikinis and the tiny clothes we wear." That's what women are supposed to be like here, added Ms. Vasconcelos. "But then men say, 'There are no good women any more, there are no women you can marry,' " because the sexy image women feel compelled to present is also considered tainted.

The sociologist Marlene Teixeira Rodrigues, an expert on gender and prostitution at the University of Brasilia, calls it the "daily hell" of Brazilian women. "You're thought of as accessible – women in all social classes, races, and generations, in every way," she said.

Prof. Teixeira Rodrigues said people, both foreign and local, have a fascination with the range of skin tones in Brazil, and the sexual mixing it implies, both historical (between European masters and African slaves) and current. It may no longer be socially acceptable to voice these ideas over dinner but they haven't really changed, she said: the darker a skin tone is, the more sexually available, skilled and interested a person is assumed to be.

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"On the one hand, women live with sexual harassment every day. On the other, they have to live up to expectations. There is a demand for us to be hypersexual, for a performance that fits that idea … especially if you're mixed race and even more if you're black. At the same time, since our culture is also conservative, there is also the possibility you will be discriminated against for having that desire."

When 675,000 tourists, most of them men, descended on the country for the World Cup, it seemed that "sex with a Brazilian" was on the top of their to-do list. It was an implicit message in much of the marketing around the Cup. The sportswear company Adidas, for example, launched a line of World Cup T-shirts that had slogans like "Looking to Score" and a soccer ball made to look like a woman's buttocks in a thong. The company was forced to withdraw them after complaints.

It was all both exhilarating and uncomfortable for women, who found their sidewalks and cafés full of men looking for company and expecting the women to be receptive. (Some young women embraced it, using apps such as Tinder to manage their encounters with foreigners.) And, in anticipation of a rush of World Cup clients, the sex workers' professional association in the state of Minas Gerais even offered its 4,000 members free English classes, and high-end brothel owners in Sao Paulo reportedly brought in tutors for a range of European languages.

But however keen visitors were to explore their stereotypes of Brazilians, far fewer men than expected seemed prepared to pay for the pleasure.

Before the Cup, there were dark predictions from anti-trafficking organizations that tens of thousands of people, including children, would be moved into and within Brazil to cater to sex tourists. It was enough of a concern for government that President Dilma Rousseff warned that Brazil welcomed visitors but was "ready to act against sexual tourism."

Those fears of mass trafficking were ridiculous, according to Thaddeus Blanchette, an anthropologist focused on sex work at the Federal University. "You have waiting lists to get taken on at the termas that are two years long," he said. "They called up their reserve list in anticipation of the Cup. They didn't need to traffic anyone in here."

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Buying and selling sex is legal in Brazil. Profiting on someone else's sale, by pimping or running a brothel for example, is not. But establishments, from the "houses" in Vila Mimosa to the high-end brothels, called termas, of Copacabana, operate freely, paying off police and putting up with occasionally being ostentatiously shut down. (It was from the most legendary of these, Centaurus, that Justin Bieber was photographed leaving last year, "disguised" in a branded sheet.)

But why did the brothel business drop? Jacqueline, a sometimes-bar-manager in Vila Mimosa who uses only one name, speculated that the Cup inflated prices and the cost of living in Rio so dramatically that men couldn't afford their usual purchases.

Prof. Blanchette is a member of a group of academics affiliated with the federal university who study sex work, called the Prostitution Observatory. The team closely monitored sexual commerce in five Brazilian World Cup host cities. While police have yet to release any information about sexual exploitation cases they may have investigated during the event, the Observatory collated the government's own figures to show that from 2004-2007 fewer than 1 per cent of cases of sexual exploitation reported involved a foreigner and that the vast majority of cases of sexually abused children involved an adult known to them, suggesting that the high-profile focus on trafficking was misdirected.

"Men don't go to brothels to dominate women; they go to [act out their] perform masculinity," he said. "And if you're already there in the stadium drinking loads of beer, cheering with all your friends, you don't need to go to a brothel." Many tourists paid the $75 admission fee for the higher-end establishments "for the experience" and taking the brothel selfie, but not paying the additional $200 to have sex with a woman upstairs, he added.

The Observatory also found that during the World Cup many sex workers had left the brothels and Vila Mimosa and headed for the beachfront in Copacabana, the focus of the foreign tourist festivities, where they sought clients with hotel rooms.

Ms. da Cruz, who at 44 has been in the business for 21 years, says she would have done the same. "But I'd have to know English, Spanish or Italian to be able to work there."

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For Ms. da Cruz, the stereotype of Brazilian women is just one more demand of her job. "It's a lot of pressure – men who come here with the idea that Brazilian women are hotter, they're better in bed. I have to pretend I'm [having an orgasm] for them, they expect that."