Not all games have American Sign Language (ASL) signs. For example, you fingerspell cards, video, chess, and checkers. All board and card games are fingerspelled. Mimic throwing dice for gambling and dealing cards for any card games. After you do this, fingerspell specifically what game you mean. Some indoor games do have signs, though, and you can find many of them in this table.
If your Deaf friends have a local sign for a game, just use that sign instead.
Here are some sentences to get you ready for game night:
English: Who wants to play poker?
Sign: P-O-K-E-R — WANTS — WHO Q
English: Deal the cards.
Sign: DEAL CARDS
English: He likes playing chess.
Sign: C-H-E-S-S — HE LIKES
English: Do you gamble?
Sign: GAMBLE YOU Q