You can patent software in the US, but (rightfully!) not in Europe.
Also, there's very little point patenting an entire game, it's too broad, e.g. if you patent a whole game, I'd only have to change a few things to release a very similar but technically non infringing game. You have to be able to write a document which explains, in excrutiating detail, exactly what part/concept the patent covers, and why, and in which circumstances, that part/concept is original.
Instead, you'd generally patent all of the small aspects of the game, so that I couldn't release anything which incorporated those small aspects (without getting prior agreement from you). E.g. you might patent the concept of a "button which when clicked on invokes an action in a program", so that I couldn't use that construct anywhere without your permission.
But, with something like that (and probably most things that you, or even those who actually go so far as to file these things) consider patenting, there's very usually something(s) you've got the idea from, e.g. some prior art. Technically the existance of such prior art should invalidate any subsequent patent application, but there are occasions where they do get granted regardless (with enough jargon & legalese you can make just about anything sound original).
It's quite disgusting, IMHO, since a company can get away with taking legal ownership, and sole licensing rights, of some technique that they never originally developed in the first place, meaning no-one else can use that technique, even though that company relied on the technique already existing! (That said, I don't mind so much when a company actually DOES develop the thing it patents, and when that thing is not some blatently obvious combination of simple existing things)
You get copyright for "free", in terms of effort. Anything you've done is copyright of you unless you state otherwise. Protecting your copyright is another matter entirely..
