Formulas

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.

Construction

Construction costs platinum and lumber.

Platinum Cost

850+([Total Land]-250)*1.53

Lumber Cost

88+([Total Land]-250)*0.35

Espionage and Magic

There are two formulas which determine the chance of success for espionage ops and offensive magic spells.

Info Ops

0.8 ^ (2 / ((Your Ratio / Defender Ratio) * 1.4) ^ 2))

Black Ops

0.8 ^ (2 / ((Your Ratio / Defender Ratio) * 1.2) ^1.2))

Land Gains

Land conquered by attacker (and lost by target) during invasion is calculated according to this formula.

If target is less than 55% the size of the attacker:

0.80 * ( 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:

0.80 * (0.154 * ((Target Size/Attacker Size)^2) - 0.069 * Target Size/Attacker Size) * Attacker Size)

For 75% and up:

0.80 * (0.129 * ((Target Size/Attacker Size)^2) - 0.048 * Target Size/Attacker Size) * Attacker Size)

Land Generation

The amount of acres gained by the attacker is twice the amount conquered.

Land Conquered * 2

Prestige

Prestige is gained and lost using two different formulas.

Prestige Gain

60 * Land Ratio

Only generated on successful invasions where Land Ratio > 75%.
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] [is this still applicable?].

Prestige Loss

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

Population and food production bonus from prestige is multiplicative.

Bonus * (1 + Prestige / 10000)

Rezone

The cost of rezoning is determined by the following formula.

(Land - 250) * 0.6 + 250