Tali is the Latin name for Knucklebones, which were called Astragaloi or Astragals by the Greeks. The Ancient Greeks originally made the pieces from the knucklebones of sheep or goats, like the ones shown below, but the Romans would also make them from brass, silver, gold, ivory, marble, wood, bone, bronze, glass, terracotta, and precious gems. When tossed, the tali would each fall on one of four sides and the most common form of the game resembled modern dice.

 

At the left is shown the backside of a bronze mirror inscribed with an image of Venus playing Tali with Pan. This mirror dates from 350 BC and comes from Greece, where Venus was know as Aphrodite. In 350 BC players in both Greece and Rome likely still played with astragali, but more and more they changed to using dice.

There were variations on scoring. Numerical values did not have precedence over a Venus, the Vultures, or a Senio. Numerical values for the other possibilities would represent a simple variation.    

In place of numerical values, the concept of pairs of numbers could take precedence, as it does in modern cards. Other rules could be agreed upon at the start of the game, in much the same way as is done at the beginning of a poker hand.

Obviously the odds of any side coming up were not equal. Perhaps the "chian" throw (narrow convex) and the "coan" throw (narrow concave) tended to come up more frequently.
 

The astragali shown on the left is made from onyx. The astragali on the right side is made from rock crystal. These are part of the Townley collection in the British Museum.

The large astragali at right is made from agate, and comes from the Hamilton collection. The smaller astragali is made from glass and is said to be from Leucas, Arcanania. These are both from the British Museum.

The two astragali above left are made from glass. The third astragali is made from lead and comes from Camirus, Rhodes. The large astragali at the right is made from bronze, from the Hamilton collection. These are from the British Museum.

It has been suggested by one modern source that the side facing down was the one counted, but this is most improbable. Given that three or four astragali were thrown, some deduction would be required to figure out what sides were facing down, since it would never be obvious. This wouldn't be much fun, of course, and for someone to pick up the astragali and verify the throw could lead to mortal violence if gambling were involved. In any event if the bottom side were counted then the top side would simply come to represent that value on sight, negating the idea of counting the bottom side. Like the later dice that replaced them, the tali were surely counted based on the side that came up, not down.

Based on the scant descriptions of the scoring in Tali, it would appear that only Venus, Senio, Vultures, and Dogs were scored, and that all other results were simply ignored and replayed. That is, the only throws that counted were Venus, Senio, Vultures. Any other result and the tali would be throw again by the next player, presumably. The pot, if any, would remain until a winner was decided. Also, if a Senio was thrown by two or more players, it would be a draw and the next round would presumably begin again with the pot remaining. Scoring rules are provided below for the simple version without Senio scoring.