Naval battles in EB are handled via auto-resolve. Auto-resolve gets more difficult the higher the campaign difficulty level is.
On Medium campaign difficulty, you can usually win with a 1.5 to 1 numerical advantage in ships over the enemy (assuming equal experience).
On Hard campaign difficulty, you need at least 2 to 1 numerical advantage in ships over the enemy to win. Or an equal number of ships one tier bigger than those of the enemy (e.g. they have Pentekonteroi, you have Triereis).
On Very Hard campaign difficulty, you need at least 3 to 1 numerical advantage in ships over the enemy to win. Or an equal number of ships two tiers bigger than those of the enemy (e.g. they have Pentekonteroi, you have Quadrireme).
This is another reason I play Medium campaign difficulty.
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