The lure this time is "RewardVille," a show of appreciation aimed at getting players even more absorbed in their online farms, cities, crime rings and poker games. The program unveiled a week ago doles out game points and credits that can be used to buy more virtual goodies on Zynga’s existing games.

It’s the latest attempt to deepen people’s attachment to Zynga’s strangely addictive world at a time attention spans are becoming more fickle. Several entertainment options now bombard people on an array of digital devices.

Zynga’s success in capturing people’s free time so far has been remarkable — and profitable, according to the privately held company’s executives.

Its games are simple, but getting ahead requires time and dedication. In "CityVille," for example, players start with a simple plot of land, roads and buildings. They can add businesses, farms and landmarks through lots of faithful dragging and clicking of the mouse. They can invite friends to play and send them virtual gifts.

All games are free to play, but players can pay real money — a few coins or dollars at a time — to buy special items or reach a higher level of play more quickly.

Since CEO Mark Pincus launched the San Francisco startup in 2007, Zynga has attracted about 250 million game players — most of whom connect on Facebook’s even larger Web hangout. Zynga’s audience is somewhere between the population of the U.S. and Indonesia, the world’s third and fourth most populous countries.

Zynga has grown so fast that it already has 1,500 employees and is moving into larger headquarters, which can accommodate several hundred more workers.

Zynga started a tradition in 2009 — ages ago in Internet time — where employees would wear red shirts for every day that "FarmVille" added another million users. There were some weeks where people would run out of red shirts, said Cadir Lee, Zynga’s chief technology officer. More recently, "CityVille" demonstrated Zynga’s drawing power by attracting 100 million players in the first seven weeks after its December introduction.

"That’s the fastest-growing media property in the history of the planet," said social media analyst Lou Kerner of Wedbush Morgan.

Prospective investors are clamoring for a piece of Zynga in an initial public offering of stock that could come within the next year.

Marc Andreessen, who helped trigger an Internet boom in the mid-1990s after co-founding Web browser pioneer Netscape Communications, already bought a stake for his venture capital firm. He said he foresees Zynga becoming "one of the primary Internet franchises of the next 10, 20, 30 years."

Zynga makes most of its money through the sale of virtual items in its games, with the rest from advertising and partnerships with companies such as Netflix or Vistaprint on special offers.

In an example of how quickly the company can drum up money, Zynga recently raised $1 million in 36 hours for Save The Children’s Japan charity. The donations for earthquake victims came through special virtual items that Zynga created for the cause. That number has since grown to $1.5 million.

Kerner estimates Zynga’s revenue will approach $850 million this year, up from $529 million last year. As for recent investments that have valued the company as high as $10 billion, Kerner believes Zynga will be worth a lot more than that if it maintains its torrid growth pace. Zynga recently closed on $500 million of financing on that valuation.

But Zynga has its skeptics.

Ian Bogost, a game designer and Georgia Tech professor who studies video games, likened its games to fast food — mass-produced fare with little nutritional value. He even created a parody, "Cow Clicker," where the sole object is to click on virtual cows. Zynga’s games, he said, are not as much about how well you can play or how much fun you have, but about how much effort or money you put in it.

"I don’t want to celebrate them just because they have a lot of users and make a lot of money," Bogost said. He added that the company has been "very, very brazen about their business process. It turns your relationships into these resources that form the backbone of their business."

And Facebook users have often complained that Zynga’s games are unimaginative and unwelcome intrusions into online banter and content sharing. Facebook last year changed the way it notifies users about games so that people who don’t play a particular game won’t continually get updates when friends send gifts of pigs or plum trees.

Nonetheless, just as McDonald’s has thrived by churning out tasty burgers and fries for decades, Zynga is quickly building a lucrative franchise with a menu of frivolous distractions. BTIG Research analyst Rich Greenfield believes media conglomerates such as Walt Disney Corp. and Time Warner Inc. should be worried because Zynga’s lightning-fast ascent threatens to take people’s attention away from TV sets, movies and other sources of entertainment.

"Media has been fragmenting, and Zynga seems to be doing the exact opposite," he said. It "is growing at a staggering rate and reaching eyeballs that none of these companies are doing."

Disney responded to the threat last year by buying Zynga rival Playdom for $563 million.

The new program to reward loyalty is logical for Zynga, Greenfield said, because it probably will encourage people to spend even more time playing games.

Zynga is already devouring a lot of leisure time — and perhaps even diverting some players from their jobs or families. In this way, it’s no different than TV or more traditional video games played on the Wii or the Xbox, or even knitting or crossword puzzles.

FarmVille’s manicured plots, quirky animals, fairy cottages and quaint duck ponds provide Kim Lindell of Hampton, Conn., with a way to escape from stress. As a social worker, her job involves working with people in tough circumstances, dealing with substance abuse and homelessness. "I can leave all that behind" for a couple hours a day, Lindell said.

After getting up at 4 a.m., Lindell, 43, signs on to Facebook and, like 50 million other "FarmVille" players, dutifully tends her virtual farm. She said she spends about as much money on the game in a month as it would cost to go out to dinner at a restaurant a couple of times.

Many players, including 60-year-old Lucille Skibinski, don’t pay anything at all. Skibinski, who is on disability and spends much of her time at home, said avoiding the temptation to buy something is part of the challenge.

"I like taking nothing and making something out of it," said Skibinski, from Caseyville, Ill., who recently reached the highest possible level, 100, on "FarmVille." "Anybody can buy levels if they’ve got money. I, on the other hand, got mine with no money but with a lot of skill and work."

Despite its successes, Zynga isn’t in a rush to go public, partly because it already is sitting on a stockpile of cash. It doesn’t need more investors — or their scrutiny — as long as it can keep churning out new games on its own terms and count on its next "Ville" to be just as addictive.