# 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.

## Contents

## Construction[edit]

Construction costs platinum and lumber.

### Platinum Cost[edit]

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

### Lumber Cost[edit]

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

## Espionage and Magic[edit]

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

### Info Ops[edit]

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

### Black Ops[edit]

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

## Land Gains[edit]

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:

`0.75 * ( 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)`

### Land Generation[edit]

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

`Land Conquered * 1`

## Prestige[edit]

Prestige is gained and lost using two different formulas.

### Prestige Gain[edit]

`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 Loss[edit]

`Prestige * 0.05`

### Prestige Bonus to OP[edit]

OP bonus is multiplicative, meaning it is added to OP bonuses like any other bonus.

`Bonus + Prestige / 10000`

### Prestige Bonus to Population and Food[edit]

Population and food production bonus from prestige is *multiplicative*.

`Bonus * (1 + Prestige / 10000)`

## Rezone[edit]

The cost of rezoning is determined by the following formula.

`(Land - 250) * 0.6 + 250`