Coinstar — previously best-known for its coin-counting machines — has transformed the 17-year-old Redbox DVD-rental business into a major player in the home-entertainment business.

Like a kid playing one of the skill-crane machines it used to own, Coinstar has reached out and plucked a big prize from a jumble of stuffed footballs and Teletubby dolls.

That prize, the Redbox DVD-rental business, has transformed the 17-year-old company — previously best-known for its coin-counting machines — into a major player in the home-entertainment business.

“I’ve said they should change their name to ‘Redstar,’ ” jokes John Kraft, an analyst who follows Coinstar for D.A. Davidson in suburban Portland.

Redbox didn’t seem all that promising when it was developed eight years ago by McDonald’s. Coinstar, which already had experience convincing supermarkets and other mass-market retailers to put odd-looking machines in their stores, bought into Redbox in 2005; it gradually expanded its stake and took sole ownership last year.

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As of the end of 2009 there were 22,400 Redbox kiosks installed across the country, renting DVDs for $1 a night. The convenience and price have proved a hit with customers: Coinstar took in $773.5 million last year, comprising two-thirds of the company’s total revenue.

Along with rent-by-mail company Netflix, Redbox has decimated the traditional video-rental business. Hollywood Video’s parent company is shutting down; Blockbuster, which introduced its own kiosks late last year, is struggling to avoid bankruptcy.

The big movie studios initially took a dim view of Redbox, largely because they weren’t getting a cut of the rental fees but also because it seemed a low-end operation.

“It wasn’t long ago that these guys were sending people out to Walmart or Costco, buying as many DVDs as they could and hand-stuffing them into the machines,” Davidson’s Kraft said.

But recent deals with Sony Pictures and Warner Home Video indicate that Hollywood is learning how to live with the new box on the block.