Social games maker Zynga, the developer behind smash hits like FarmVille and CityVille, has raised a total of $845 million in its four years of operation, according to its S-1 filing with the Securities and Exchange commission on Friday.

The social gaming company has not been entirely explicit about how much money it has raised. The new filing indicates that Zynga was able to raise the funding across only three official rounds, the latest of which — a $490 million third round — was completed in February. Other companies have raised as much money as Zynga, but have done so over more rounds of funding.

It’s also surprising that Zynga, one of the largest Web 2.0 companies, has not needed to raise more money than it has. Group-buying site Groupon raised more than Zynga’s total amount of funding in a single round that it completed in January. Facebook has also raised an enormous amount of funding, including a $1.5 billion round in January.

Zynga filed for an initial public offering on Friday. It’s the most profitable Web 2.0 company to file for an IPO this year after making $90 million in 2010. The company made a net profit of $11.8 million in the first quarter this year, compared to $6.4 million in the first quarter of last year. The company has nearly $1 billion in cash — meaning it’s done quite well and has not burned through a lot of its funding as quickly as other companies.

By comparison, Groupon has gone through its cash like water. The company finished raising nearly $1 billion in January, but only had around $208 million in cash at the end of March.

Zynga has since become a Facebook distribution powerhouse like no other game company. That makes it a lot easier for Zynga to generate revenue, since a percentage of users usually pays for items in otherwise free games. The company has delivered hit after hit to Facebook.

Zynga’s latest social game, Empires and Allies, is another hit for the company. It attracted more players than Farmville, its first breakout hit, in just 25 days. Empires and Allies is gaining new users at a rate of a million a day and 8 million a week now, according to AppData.

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