Game rules are specifically excluded from copyright - they can't be protected.
Specific implementations of algorithms can be patented, but this doesn't really allow you to protect game ideas.
Design-patents allow you to protect the look of a product, such as the shape of a coke bottle or the UI layout of Tetris...
Patents are also horribly expensive, need to be written by expert lawyers (again horribly expensive) and if anyone violates your patents, you'll need to wage legal war against them (sue) which is again, horribly expensive.
No one bothers with that stuff in the games industry. The extent to which your ideas can be protected is not worth the cost of that protection.
As for trying to sell it, nobody buys ideas. Most people wont even let you pitch an idea to buy as (1) It's a waste of their time and (2) it opens them up to legal liability - if they're already working on a similar idea, you'll complain that they've stolen it from you.
The real value is in the implementation of ideas, not the idea itself. Ideas are only a starting point of a very long an expensive journey. Game designers do not just write down an idea and then go home for a year while it's created for them. Game designer is a full-time job for the entire duration of a project - constantly guiding the development team and refining the idea as implementation of it exposes rough edges that could not have been predicted at the start. Companies don't buy ideas, or hire idea-people, they hire designers.
The exception is is you have an idea and lots of money. In that case you can hire a studio of designers and developers and give them your idea...
If you don't have money, you could take the idea to investors first, to convince them to give you the money... But you will need way more than an idea - you'll need an entire business plan and enough business acumen to put a realistic value on your company (which has nothing but a valueless idea and no ability to execute it,a very risky investment).
You can try and do the kickstarter thing, but it's the same deal - just an idea and no ability to execute does not inspire confidence... Plus you'd have to disclose the idea.
Alternatively if you want to extract some value from it, you can just go ahead and start refining the idea further in public (on forums, blogs, etc). In the unlikely event that someone steals your idea, at least you'll be known as the inventor / first person to publish the idea,which, if it actually is revolutionary, is a great thing for a future career as a designer.
Chances are that no one will steal it though as everyone has way more ideas already than they have the time/money to create 
