Hayasdan may be poor, but it is not that bad.
The trick is to safe money --> build army. It does not have to be big, it just needs to be good enough for one mission. Pick FM and conquer a city. Then disband 90% of that army (you can keep highly depleted units, as retraining may be less expensive in the long run). Rinse and repeat.
Caucasian Spearmen and Caucasian Archers are extremely useful, despite their low costs. The Caucasus can be conquered without too much cavalry.
This works extremely well for the Eleutheroi Caucasian cities. My preferred order is Ani-Kamah, Trapezous / Kotais, Mtshketa, Kabalaka, Phraaspa.
Despite your economy being poor, in the first few years you simply don't need much garrisons. Building a port in Kotais and getting some traderights with Pontus, and the Western Hellenic factions also improves the situation a lot. Build roads. Build markets, and build basic farms. Armavir is a bit special as it needs population boosts as well.
By the time you have taken Phraaspa, you are guaranteed to run into some Seleukid aggression. By that time your economy should be on track. Use your spy network to get an early warning when they are invading. Build up defences in that city (90% of the time it will Armavir anyway), and move the second army from Phraaspa to Ekbatana. Once you conquer and enslave Ekbatana, your cities with FMs will get nice population boosts.
And another big defensive bonus for the Hai is that cities are further apart than in Asia Minor. Use your spies and watchtowers. I think Hayasdan are overall the easier faction.
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