The first thing I suggest doing, even if you are broke, is to spend about $100 dollars and file a provisional patent application with as much disclosure as you can generate. Describe the game, the rules, variations, design, potential gameplay, and so forth. A provisional patent application will allow you up to one year to figure out what, if anything, you want to do as far as patent protection. During this time you can say you have a patent pending, if you wish.
Public disclosure will start a one year grace period to file something with the patent office, barring some experimental use. So be careful with whom and how you share/test your game.
Now, to the hard part. It's hard to deal with this kind of subject matter in the abstract. Certain parts of a game can be protected by patent, copyright, and trademark law, and it's difficult to say without seeing the game or at least some details. Even if you are broke, if you wish to protect your rights, spend the money for an hour or two of an attorney's time and show them the game. Tell them what you want and they can give you some plans and projected costs for how to get it. Best of luck!
Games can be patentable, and board games are often trademarkable, and some parts of them, such as the rules and the "pictorial matter appearing on the gameboard or container" can be registered for copyright as well. Without you consulting an IP lawyer who can review what you've got, it's difficult to guess what legal protections you can use for your particular game.
If you're broke, it's hard to imagine that you'll be able to get study participants to play your game and give you feedback, so it seems you'll have to be prepared to invest some money in developing, protecting, and marketing your game. Whether your game is worth any investment of more of your time and some money, or whether you're wasting your time are things only a qualified IP lawyer can help you decide.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
The good news is that the United States legal system is most hospitable of any country towards protecting rights in a newly created game. No other country, not even Monaco (home of a famous casino) grants patents for new casino games, but the U.S. does. The name and logo associated with the game can also be protected as a trademark, which may be registered at the U.S. Patent and Trademark Office. And the instructions and the graphics on the board and packaging could be protected by copyright, and registered with the U.S. Copyright Office.
I have helped clients patent a number of games. If you visit our website http://elman.com and click on the button for Clients' Patents, you'll be able to see some examples.
Beware that the disclosure requirements for a provisional patent application are filled with potential pitfalls. So it would be wise to consult a patent attorney for advice rather than trying to file a provisional patent application first.
I agree with the other answers that a provisional application may be a good first step. But please be aware that the provisional application must describe your invented game with sufficient detail to prove that you invented it, it must enable someone skilled in the game industry to build and use your game, and it must describe the best mode or way of building and using your game that you know of. A provisional application does not need to have claims that claim in legal terms, the boundaries of the invention, but ultimately the provisional appllication will be judged according to how well the support claims that are ultimately written in a subsequent full utility application. So it is good for the provisional application to be thorough and to have good illustrations as well.
The provisonal application expires in one year, unless a untility application is filed. Ultimately, patent protection costs money. And it is advisable to have a patent attorney spend a little time helping you with the legal advice and with any provisional application.
The above is not legal advice, but only general principles. As stated, I think you need to see a patent or intellectual property attorney to get advice regarding the best way to protect your rights.
You wrote: I'm broke.
Response: There are no ways of which I'm aware that, for free, you can use to protect the various intellectual property rights in your board game. So if your goal is to protect the rights you've created by inventing your game then, yes, you are clearly wasting your time.
You should, therefore, buy the book How to License Your Million Dollar Idea by Harvey Reese [see http://j.mp/cpsN0a -- a used copy costs about $13].
You should also buy Patent It Yourself by David Pressman and focus on the provisional patent application section [see http://j.mp/aXywze -- a used copy costs about $36].