Wired has the backstory on Rovio, the creator of the Angry Birds empire. The company was near bankruptcy in early 2009:

One afternoon in late March, in their offices overlooking a courtyard in downtown Helsinki, Jaakko Iisalo, a games designer who had been at Rovio since 2006, showed them a screenshot. He had pitched hundreds in the two months before. This one showed a cartoon flock of round birds, trudging along the ground, moving towards a pile of colourful blocks. They looked cross. "People saw this picture and it was just magical," says [Niklas Hed, who co-runs the company]. Eight months and thousands of changes later, after nearly abandoning the project, Niklas watched his mother burn a Christmas turkey, distracted by playing the finished game. "She doesn't play any games. I realised: this is it."

Alexis chimes in:

I've long thought casual games are like pop songs. Everyone knows roughly what they're supposed to sound like, but getting everything just right is stupendously unlikely. Since nearly every single casual game or pop song won't be a hit, the key skill seems to be the right ear (or fingers) to feel when something isn't good, but great. Or maybe you just have to get lucky.

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