Backgammon according to the normal movement rules. The first player to bear off all fifteen of his/her own checkers wins the game. If the opponent has not yet borne off any checkers when the game ends, the winner scores a "gammon", which counts for double stakes. If the opponent has not yet borne off any checkers and has some on the bar or in the winner's home board, the winner scores a "backgammon", which counts for triple stakes. To speed up match play and to provide an added dimension for strategy, a doubling cube is usually used. The doubling cube is
Backgammon the emperor had for his given position. Zeno, who was white, had a stack of seven checkers, three stacks of two checkers and two "blots", checkers that stand alone on a point and are therefore in danger of being put outside the board by an incoming opponent checker. Zeno threw the three dice with which the game was played and obtained 2, 5 and 6. As in backgammon, Zeno could not move to a space occupied by two opponent (black) pieces. The white and black checkers were so distributed on the points that the only way to use all of