Of social games played by the topers we mention, besides the complicated kottabos, the games played on a board or with dice. Homer already mentions a game of the former class, and names Palamedes as its inventor; of the exact nature of this game we know little or nothing. Neither are we informed of the details of another kind of petteia played with five little stones on a board divided by five lines.
The so-called "game of cities" seems to have resembled our chess or draughts. The board was divided into five parts. Each player tried to checkmate the other by the skillful use of his men. Games of hazard with dice and astragaloi were most likely greater favorites with the topers than the intellectual ones hitherto described. The number of dice was at first three, afterwards two; the figures on the parallel sides being 1 and 6, 2 and 5, 3 and 4. In order to prevent cheating, they were cast from conical beakers, the interior of which was formed into different steps. Each cast had its name, sixty-four of which have been transmitted to us by the grammarians. The luckiest cast, each of the dice showing the figure 6, was called Aphrodite; the unluckiest, the three dice showing the figure 1, had the names of "dog" or "wine" applied to it.
Another game of a similar nature was played with the so-called astragaloi, dice of a lengthy shape made of the knuckles of animals. Two of the surfaces were flat, the third being raised, and the fourth indented slightly. The last-mentioned side was marked 1, and had, amongst many other names, that of "dog;" the opposite surface, marked 6. The Latin names of the two other sides marked 3 and 4 were _suppus_ and _planus_ respectively. The figures 2 and 5 were wanting on the astragaloi, the narrow end-surfaces not being counted. The number of astragaloi used was always four, being the same as in the game of dice. Here also the luckiest cast was called Aphrodite, with which at the same time the honor of king-of-the-feast was connected.
Young girls liked to play at a game with five astragaloi, or little stones, which were thrown into the air and caught on the upper surface of the hand. This game is still in use in many countries. We possess many antique representations of these various games.