The studio risk is that the creative output of the individuals is the value you're investing in. Very few studios produce quality content in a machine like fashion, though there are exceptions (EA maybe? Lucas Arts in it's prime?).
Zynga might be another example of a VC funded "gaming" company.
OMGPOP: http://techcrunch.com/2012/03/21/omgpop-iminlikewithyou-ycom...
Game of War, Machine Zone: http://blog.ycombinator.com/machine-zone-yc-w08-debuts-game-...
A Thinking Ape
[0] http://techcrunch.com/2012/03/27/freemium-game-dev-addmired-...
In 2008 they raised 7 million in VC funding from Benchmark Capital and FirstMark Capital.
Here's the press release: http://www.riotgames.com/sites/default/files/uploads/080710_...
There have been some recent IPO successes (Zygna, King). (And king.com is starting to look like a one hit wonder with Candy Crush Saga.)
If Notch had solicited VC before he was a hit, the VCs probably would have just laughed him out of their office.
If I am not mistaken, he mentioned that they were backed by YC and a couple other high-profile investor in the valley.
[edit] Yeah, I meant in the last year.
Would highly recommend you have a finished game + some revenue before you hit up institutional investors. In the mean time, find angels who respect you. Believe you are an engineer, so people won't often doubt your ability to produce.
(I'm a YC partner)