6770m most likely (if I remember right, that's the base GPU choice for 2011 27" iMacs, with the option to upgrade to 6970m.)
While not the best GPU, it should be able to handle most games fine if you turn down the settings.
If I'm not wrong, 6770m is based on desktop 6670, which is a rebrand of 5670. (6970m is based on desktop 6870.)
I had a desktop 5670 and it ran Crysis at medium settings reasonably decent (say 30fps ish at 1080p), to give you an idea of its performance, but with 27" iMac's native resolution of 2560x1440 you'll have to turn down the settings a bit further, depending on the game.
Another option would be to run the game in a smaller window, thus reducing the resolution, yes?
I guess what I was wondering also is if things like turning Time Machine off would help a lot, disabling Dropbox, etc. Not sure that those would result in bigger gains.
I've run Battlefield 3 via Bootcamp and it works OKAY...on greatly reduced settings.
This is going sound crazy is 512mb of graphics still enough to play lastest games like sim city and bio shock infinity or is it time I buy a new iMac with 2gb of video ram.
This is going sound crazy is 512mb of graphics still enough to play lastest games like sim city and bio shock infinity or is it time I buy a new iMac with 2gb of video ram.