It appears that the basic setup, being the most balanced, is the best way to play. This then is the presumption of all of the following comments.

Babylon and then Egypt have the best economics.

Babylon's special ability allows it to expand influence very quickly. It tends to receive the best trade hand each turn, i.e. the one with the most cards and the most uniqueness within it. It can also acquire a fair number of taxes, a popular item, which when given up in trade, readily permits acquisition of 9 different items. Once this is achieved, the Temple of Artemis can be purchased which gives automatic acquisition of a seventh item, making further achievement of 9 different items even easier.

Egypt pursues victory in a different way. As a result of the many city sites in its sphere, it can use cities and temples to acquire many tax cards rather quickly. Its special ability enhances this by allowing it to convert one trade item to yet another tax card. These cities and temples also tend to make it the Political director, allowing it to purchase before others when items are scarce or react to others when war build up is possible.

The key to preventing gains by these two powers is in the hands of the Commerce director, usually held by Carthage since its geography tends to dictate that it has the most caravans and markets. With careful choices of the number of cards traded, Carthage should work to force Egypt to break up its large collection of tax cards and to prevent Babylon from collecting too many different types of items. He can use his commodity draft to enhance this, either by choosing the card that one of these empires wants or by refusing to choose from either of them in the hopes that no other opponent will either, preventing them from grabbing anything valuable.

When all of the above is happening, players next need to worry about Rome which appears to have a pronounced advantage in its one-third off legions and fortresses. This discount is even better than it looks since so often one is left with two odd cards which in most other empires are simply worthlessly discarded. Countering this empire is the job of the Greeks who, being the nearest overland neighbor, are in the most danger. Mastery of the sea derived from one-third off cost fleets which get +1 in naval combat is their tool to do it. By this means they can invade at will whichever part of the Rome is weakest and keep it somewhat neutralized.

In fact the Greeks should act as a general enforcer around the board, positioning their fleets so as to be able to strike at any lightly defended region belonging to any player who outdistances the pack.

On land, Egypt ought to build a few legions and a couple of fleets both as defense and to keep Babylon on their toes, striking when necessary.

For their part, Carthage should build forts and then legions to threaten Egypt with the same thoughts in mind. Despite its considerable power as Commerce director this side appears to have the least chance of winning, depending as it does on others neutralizing one another. But if everyone is on top of their defense, its extra strong legions may eventually provide a long-winded path to a win.

By the way, a consequence of these particulars is that when players have varying experience levels with the game, the least experienced should play Babylon, then Egypt, then Rome while the Greeks and Carthage should be left for those who know the game best.

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