Answer: Checkers

The game of Checkers is the only board game that has specific provisions for tobacco consumption during play. Per the official rules of the American Checker Federation for the play of Standard American Checkers, smoking is a perfectly acceptable part of the game play experience:

14. Players shall be allowed to smoke during the conduct of the game, but care must be exercised not to blow smoke across the board, lest it annoy an opponent. If the player is thus annoyed he may object to his opponent smoking, in which case neither player shall be allowed to smoke.

Smoking is in, but blowing smoke rings to distract your opponent is definitely out.