having played this variant i entirely disagree.
Egypt is connected to presia, greece and cartage. persia is connected to greece, egypt, and by going over the top of greece(which may annoy the greek player, unless he's helping) to rome.
Greece is connected to everyone except carthage.
Cartage is connected to Rome and Egypt.... i really need a diagram for this. But it's not entirely a circle, with the greece-egypt strong connection, and the persia - rome weak connection the circle is broken (and that's ignoring the seas which may be so full of fleets that convoys to pretty much anywhere are posible, and also ignoring Carthage - Greece sea lanes, but i've never seen them used so i'm less convinced of that conection.)
2 vs 2 vs 1 is possible, with that one shifting.
In a 2 vs 3 senario, Rome and carthage can form the equivalent of the juggernaut and roll over the three eastern powers if they are squabling amongst themselves, but at some point when the 3 (greece, egypt and persia) are recuded to two or one, rome and carthage are likely to turn on each other....
The two power alliance is probably more stable, but breaks down when they are on the way to a solo...
my 2 cent.
Advice for egypt. Hold the line against both persia and carthage.
Leptis is always fun, and Jerusalme are always bones of contention.
Crete and cyprus re also worth diploming over...