How do save files work with iCloud?

So I downloaded a few games for the iPad. Some of them like Ghost Tricks and 'World ends with you' are quite large and take up a lot of space. (Both are currently on sale btw and particularly the former with all chapters IAP unlock for 99 cents a no brainer)

I was wondering what happens with the save files when I eventually delete them and later decide to reinstall? I take it the save files on iCloud will also get deleted when I delete the app? Is there some way to preserve the same state without jailbreaking?

Edit: I forgot, sometimes when I delete a game it asks if I want to remove the game from game center? So what is it that gets saved to game center? If I say don't remove and later reinstall, Ill get the save states back?