If you have been playing dominoes with your family since you were in kindergarten, then you are a good candidate to write a dominoes computer player algorithm. If you just learned the rules to chess yesterday, don't even attempt to write the program. Leave it to someone who knows what they are doing. Sometimes you can find documentation for computer player algorithms. Books have been written about chess, checkers, and bridge strategies.
Clubs exist for Scrabble and backgammon.
Sometimes graduate students write papers on these subjects. It may take a little digging, but for classic problems you can often get a head start by looking at algorithms developed by others. Ideally, you want to write your computer player algorithm in such a way that the computer goes through the same thought processes as a human player. To do this, you need to start with a human player, and watch how he plays. Ideally, the human player should be yourself.