In Islam, it is not permissible to play backgammon because it involves the use of dice which are haram and emphatically forbidden. For more, see the detailed answer.

Those who engage in bodybuilding uncover their `awrah when practicing this sport, which is undoubtedly haram. The `awrah of a man extends from the navel to the knee, and it is not permissible for him to uncover it in front of anyone other than his wife. If the aim is relaxation and maintaining good health, then sport is permissible. If it involves something haram, such as missing prayers, uncovering any part of the `awrah or mixing with women and so on, then it is haram.