From the developer, Moshe Callen:
Petteia, although it meant "a board game", was often used as the name of a particular game (more precisely called Poleis) played in antiquity by the Greeks, in all likelihood from as far west as Spain to as far east as India. Other peoples played the game too, whether they learned the game from the Greeks or in some other way. The Romans were among those who also played the game, although I'm inclined to the view they learned it from the Greeks in southern Italy — the area known as Magna Graecia. The Japanese still play a couple of different versions of the game to this day.
My description of the rules arises from my historical research into the game. Just as Linnaeus' observation of Tablut in play allows us to fill in the gaps in the rules for other Traditional Games: Tafl games, so the Japanese games allow us to fill in the gaps of the ancient Greek and Roman versions of the game. Even among the Greeks or among the Romans, rules varied because "house rules" were the only rules in the sense that rules were neither written down nor standardized. We have allusions to the rules and descriptions of the game, enough to have a pretty good overall picture of the game. Yet no one ever to our knowledge completely described the rules of the game in detail.
My response to this fact was to choose a board and pieces unearthed most often at archaeological finds. Since a few different versions of the rules seem to be attested, I've tried to present each of these. All of them have been play-tested. I present them as historical reconstructions, but I am confident of their historicity.
We also know that later games, like the Traditional Games: Tafl games evolved from this game. So, I've also included a couple of games which are not historically attested except in the sense that we know the end-points of the evolutionary process. Logically something very like them probably existed, and in that sense they are also historical re-constructions, but I do not claim they are based on documentary evidence. To that extent, these last games are speculative. The others, the versions of Petteia, are not.
12 Sept 2013. I (Moshe Callen) am adding this for clarity.
In Greek, the proper name of the game was Poleis, but it was also called Pessoi (literally "game pieces") and Petteia (literally "a board game [using pessoi]"). I have chosen to follow the modern usage which nearly universally calls the game Petteia to avoid confusion.
The rules as written deliberately reflect the many varieties of ways in which the game was played by ancient peoples. Thus, one can play a version of the games with or without a die (d4 like the animal's knucklebone which would have been used)the former for gambling or divination and the latter as a game of skill. In those games where the object is to capture the greater number of pieces, one can play to the bitter end or until more than half a player's pieces are taken, as agreed beforehand by the players. These and similar details and variations are in the rules.
The games included are termed as follows but would to the ancients likely have been simply petteia or matrunculi:
1. [b]simple petteia[/b]: One row of pieces each without a leader played to capture more pieces
2. [b]double petteia[/b]: Two rows of pieces each without a leader played to capture more pieces
3. [b]simple latrunculi[/b]: One row of pieces each with a leader played to capture more pieces
4. [b]double latrunculi[/b]: Two rows of pieces each with a leader played to capture more pieces
The above games are well attested.
5. [b]simple capture the leader[/b]: One row of pieces each with a leader played to capture the leader piece
6. [b]double capture the leader[/b]: Two rows of pieces each with a leader played to capture the leader piece
These above two games are debated but strongly believed to have been played.
7. [b]simple passing of the leader[/b]: One row of pieces each with a leader played to get the leader piece to the other side of the board
8. [b]double passing of the leader[/b]: Two rows of pieces each with a leader played to get the leader piece to the other side of the board
9. [b]proto-tafl[/b]: Two rows of pieces each without a leader against one row of pieces each with a leader played respectively to capture the leader or to get the leader to the other side of the board
These three above games are not specifically attested but fit with the widely held hypothesis that the tafl games developed from petteia.