Candy Crush isn’t just a crazily addictive time-waster: It’s also a really, really big business. Now the company behind it wants to go public.

King Digital Entertainment, the Irish publisher behind Candy Crush and several other big mobile games, has filed its initial IPO papers with the SEC, and says it wants to trade on the NYSE under the KING ticker. The initial appeal for investors will be obvious: This is a huge, fast-growing company. And the risk is obvious as well: It’s a huge, fast-growing company based around a single game.

A quick scan of some eye-popping numbers: Last year King generated profits of $568 million on revenue of $1.88 billion. That’s up from a loss of $1.3 million on revenue of $64 million in 2011. (An earlier version of this story incorrectly reported that King made a profit in 2011.)

Almost all of that growth comes from one game: King launched Candy Crush in the summer of 2012, and the game now generates 78 percent of its revenue. The game has a staggering 93 million people playing it every day.

The question is what happens to King if and when people get tired of Candy Crush — the same question that dogs every big mobile/social games company, from Zynga to Rovio, the Angry Birds people.

And there is already a warning sign in King’s filing: Even though revenue skyrocketed last year, it declined from $621 million in the third quarter to $602 million in the fourth quarter. King said “the decline was driven by a decrease in Candy Crush Saga gross bookings,” even though it is making a concerted effort to diversify into other games like Pet Rescue Saga, Farm Heroes Saga, Papa Pear Saga and Bubble Witch Saga.

Like every other big game company, King gives away its product, and makes the majority of its money from a minority of its users who buy virtual power-ups that help them get a leg up in the game. King says 4 percent of its users — about 12 million people — are regular buyers, who are spending an average of $17.32 a month.

And like just nearly every other big game company, King’s business is dependent on your phone — 70 percent of its revenue comes from mobile users — and a handful of big distributors: Almost all of its money comes from people who got the game from Facebook, or the app stores run by Apple, Google and Amazon.

If for some reason King decides not to go forward with its offering — two days ago, the Telegraph announced that the company’s IPO plans were “on hold” — it is throwing off enough cash to make plenty of money for its existing investors.

In the last few months the company has made more than $500 million in dividend payments — including a $217 million payout this month — to its board of directors, its top executives and major investors. Private equity fund Apax owns 48.2 percent of King; Index Ventures owns another 8.3 percent.