Patent searching is not an easy thing. You can start on the USPTO's website (USPTO.gov), but patents are very complex. Remember also that there are strict rules for what is patentable.
If you're looking to patent something you need to talk to an IP attorney, and it can be extremely expensive.
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You can use Google.com/patents for an informal search, but it will be very difficult to understand what is covered until you get advice from a patent attorney. Games are a unique type of intellectual property, covered in a variety of ways. Keep the game and rules a secret until you talk with an IP attorney about your options.
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Its possible to get patent protection for a unique board game but unlikely for a card game. You can search google patents, the USPTO, or hire an attorney to do the search for you. There are other ways of protecting your card game. The more likely way to protect your ideas is through copyright and/or trademark. Either way, keep your idea private and consult with an intellectual property attorney.
Odds are, you won't be able to patent your card game. Most family-made card games (e.g. not made by a professional game designer) are simply going to be rehashes of games that have been played for centuries and not patentable subject material; even when there are sufficient differences to make the matter patentable, there are many pitfalls regarding time limits to prosecuting a patent that you must adhere to. Also, pursuing a patent is generally expensive and runs in the thousands of dollars for patents that go through "perfectly" (without any issues from the USPTO examiners) -- a patent for a card game is almost certainly going to face some issues in the construction of the patent's claims. Sorry to be so negative, but there are only so many rules one can make with a card game, and the subject matter requirements for patentability require both novelty (i.e. what you are doing is new) and non-obviousness (that your changes would not be obvious to someone of ordinary skill in the art). My experience with game design is that card games (a major exception being collectible card games/LCGs like Magic the Gathering or Netrunner, but that doesn't sound like what you're doing) generally fail to meet one or both of these requirements. I hate to be blunt, but you cannot hope to succeed on this if you do not hire a patent attorney to represent you, and are willing to pay a significant amount of money to pursue it, and still it would be a very long shot. Best of luck.
I focus my practice on (video) gaming industry, casino gambling, and complex internet law issues, electronic free speech, entertainment law, copyright and trademark law, and computer fraud. I primarily represent game developers and founders of emergent internet technologies. The author is a Maryland attorney; however no answer given on Avvo is intended as legal advice or intended to create an attorney-client relationship.