Traditional - Greece

This game is played on a 8x8 or 12x8 square board, with the following setup:

MOVE - Stones slide orthogonally any number of empty cells (like Chess Rooks).
CAPTURE - A stone is captured when it is surrounded on two orthogonal sides (custodian capture).
Multiple captures can be made with the same move, since the stone may help surround enemy stones on different directions.
A stone can be played inside two enemy stones without being captured.
The outside edges cannot be used to capture stones.
GOAL - Wins the player who captures all enemy stones, or stalemates the opponent.

These seems to be the reconstructed rules for City (a.k.a. Petteia which is a Greek word for board/piece game). But this rule set is prone to a drawish strategy. It is very hard for a player to gain advantage unless a serious mistake is made. First, a cornered stone cannot be captured, so it seems that edges should be used for capturing purposes. Second, something must be done to prevent situations like the one presented on the second diagram.

There is also the suggestion that stones would not slide, but just move to adjacent empty cells. Myron Samsin suggests that there is a connection between City soldiers and chess pawns. Perhaps (I say) this stone movement is even more restricted (only forward?). That would bring some solutions to the apparent problem of this game.

An example

On this position, Black has won, since White cannot move any stone.

A solid structure

Black can create this structure without resistance. Now, the stone at g1 can move to cell [1] and back, forcing a draw.

From S. Reynolds: Petteia is referred to many times in Greek literature. In ‘The Republic’ Plato compares Socrates victims to “bad Petteia players, who are finally cornered and made unable to move by clever ones.” In the same works Plato quite clearly tells us that Petteia involves long training if skill is to be achieved. Aristotle, tutor to Alexander The Great, wrote “a citizen without a state may be compared to an isolated piece in a game of Petteia”. It seems quite likely that these ‘petteia’ games spread from ancient Athens to Persia, Asia Minor and India with the armies of Alexander The Great around 330 BC.

The game is very similar to the Egypt game Siga (or Seega). After the Greek cultural influence over Ancient Rome also had its echoes on Latrunculi. Other related games can be found here. I found on the net also these names of related games: Tau, Pente Grammai, Nard, Shantarad, Fitchneal, Tawlbyund, and Alea Evangeli, most of which I do not know...

Some people defend that Chaturanga was combined with City. The result was a game close to modern Chess. The dice were eliminated, and the emphasis of the game shifted from chance to strategy. On Chess - An Illustrated History (1990) it is said "It is essentially to Averbakh that I owe the theory of the meeting of Greek Petteia with Indian dice games along Alexander's route of Hellenic colonization, producing the earliest form of chess."

Check also this webpage about the game. There is a ZRF to play City/Petteia with Zillions.