This is just a collection of formulas for easy reference. It's highly recommended that you read the corresponding article to understand conditions or criteria when the formula may deviate.
Espionage and Magic
0.8 ^ (2 / ((Your Ratio / Defender Ratio) * 1.4) ^ 2))
0.8 ^ (2 / ((Your Ratio / Defender Ratio) * 1.2) ^1.2))
If target is less than 55% the size of the attacker:
0.75 * ( 0.304 * ((Target Size/Attacker Size) ^ 2) - 0.227 * Target Size/Attacker Size + 0.048) * Attacker Size)
If target is greater than or equal to 55% but less than 75% the size of the attacker:
0.75 * (0.154 * ((Target Size/Attacker Size)^2) - 0.069 * Target Size/Attacker Size) * Attacker Size)
For 75% and up:
0.75 * (0.129 * ((Target Size/Attacker Size)^2) - 0.048 * Target Size/Attacker Size) * Attacker Size)
The amount of acres gained by the attacker is twice the amount conquered.
Land Conquered * 1
Prestige is gained and lost using two different formulas.
20 + (Target's Prestige * Land Ratio / 12)
- Cannot exceed 10% of your current prestige.
- Prestige cannot exceed your land size when prestige is added.
- May be reduced for additional invasions on already invaded target within 24 hours.
Prestige * 0.05
Prestige Bonus to OP
OP bonus is multiplicative, meaning it is added to OP bonuses like any other bonus.
Bonus + Prestige / 10000
Prestige Bonus to Population and Food
Bonus * (1 + Prestige / 10000)
The cost of rezoning is determined by the following formula.
(Land - 250) * 0.6 + 250