Air Hockey 
Playing the Air Hockey table game in a dream is symbolic of your good old childhood experiences or memories.
Alternatively, it means an ongoing debate or disagreement with someone you know very well. If this has been going on back and forth for quite some time, now is the good time to be the bigger person and resolve it.
Checkerboard
To dream of a checkerboard implies that your character consists of many different and perhaps, complicated levels or attributes. You are a very complex and interesting person.