Formulas - Revision history

ODWikiBot: Regenerate formulas from Round 50 source

2026-07-01T22:11:59Z

Regenerate formulas from Round 50 source

← Older revision		Revision as of 22:11, 1 July 2026
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	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~~.		This page lists commonly referenced source-backed formulas. Most formulas are affected by race, spell, tech, wonder, hero, and other modifiers after the base value is calculated.

	== ~~Construction~~ ==		== Exploration ==

	~~[[Construction]] costs [[~~platinum~~]] and [[lumber]].~~		The platinum cost per explored acre is based on current land before exploring:

	~~=== Platinum Cost ===~~		<code>0.6 * Land^1.299 + LowLandAdjustment</code>

	~~<code>850+([Total~~ Land~~]-250)*1.53</code>~~		If Land is below 1520:

	=~~== Lumber Cost ===~~		<code>LowLandAdjustment = -0.001 * Land^2 + 1.91 * Land - 593</code>

	~~<code>88+([Total Land]~~-~~250)*0~~.~~35</code>~~		At 1520 land and above, LowLandAdjustment is 0. The final per-acre platinum cost is rounded after exploration-cost modifiers are applied.

	~~== Espionage and Magic ==~~		The draftee cost per explored acre is:

	~~There are two formulas which determine the chance of success for [[espionage]] [[ops]] and offensive [[magic]] [[spells]].~~		<code>floor(Land / 150) + 3</code>

	=== ~~Info Ops~~ ===		== Construction ==

	~~<code>0.8 ^ (2 / ((Your Ratio / Defender Ratio) * 1.4) ^ 2))</code>~~

	~~=== Black Ops ===~~		Base construction costs use explored and conquered acres:

	<code>~~0.8 ^ (2 / (~~(Your Ratio / Defender Ratio) * 1.~~2) ^1.2)~~)</code>		<code>Platinum = round(850 + ConqueredAcres + 1.25 * ExploredAcres)</code>

	=~~= Land Gains ==~~		<code>Lumber = round(87.5 + ConqueredAcres / 4.25 + 0.285 * ExploredAcres)</code>

	~~[[Land]] conquered by attacker (~~and ~~lost by target) during [[invasion]] is calculated according to this formula~~.		Construction-cost modifiers are applied after the base cost. Platinum construction cost cannot be reduced below 20% of base cost, and lumber construction cost cannot be reduced below 25% of base cost.

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

	<code>0.80 * ( 0.~~304 * ((Target Size/Attacker Size)^~~2~~) - 0.227~~ * ~~Target Size/Attacker Size + 0.048~~) * Attacker Size</code>		<code>Platinum = round(250 + 0.6 * ExploredAcres + 0.2 * ConqueredAcres)</code>

	~~If target is greater than or equal to 55% but less than 75%~~ the ~~size of the attacker:~~		Factory and other rezone-cost modifiers are applied after the base cost.

	~~<code>0.80 * (0.154 * (Target Size/Attacker Size) - 0.069 * Target Size/Attacker Size) * Attacker Size</code>~~		== Operations ==

	~~For 75% and up~~:		Information operation success chance is based on relative spy or wizard ratio:

	<code>0.80 * (0.~~129 * (Target Size/Attacker Size~~) ~~- 0~~.~~048 * Target Size/Attacker Size~~) * Attacker Size</code>		<code>Chance = 0.8 ^ (2 / ((RelativeRatio * 1.4) ^ 1.2)) + StrengthModifier</code>

	~~=== Land Generation ===~~		Theft and black-op success chance uses:

	~~The amount of acres gained by the attacker is twice the amount conquered~~.		<code>Chance = 0.7 ^ (2 / ((RelativeRatio * 1.3) ^ 1.2)) + StrengthModifier</code>

	~~<code>Land Conquered * 2<~~/~~code>~~		StrengthModifier is based on the attacker's current spy/wizard strength minus the target's current strength. Final chances are clamped by operation type.

	== ~~Prestige~~ ==		== Land Loss and Gains ==

	~~[[Prestige]]~~ is ~~gained~~ and ~~lost using two different formulas~~.		Successful invasions first calculate target land lost from attacker land, land ratio, and war status. The base land-loss multiplier is 0.75, with higher multipliers for unilateral and mutual war.

	~~=== Prestige Gain ===~~		If LandRatio is below 0.55:

	<code>60 * ~~Land Ratio~~ </code>		<code>Segment = 0.304 * LandRatio^2 - 0.227 * LandRatio + 0.048</code>

	* Only generated on successful invasions where Land Ratio > 75%.		If LandRatio is at least 0.55 and below 0.75:
	* Prestige cannot exceed your land size when prestige is added.

	=~~== Prestige Loss ===~~		<code>Segment = 0.154 * LandRatio - 0.069</code>

	<code>Prestige * 0.~~05</code>~~		At 0.75 LandRatio and above:

	=~~== Prestige Bonus to OP ===~~		<code>Segment = 0.129 * LandRatio - 0.048</code>

	~~[[OP]] bonus is multiplicative~~, ~~meaning it is added to OP bonuses like any other bonus~~.		<code>TargetLandLost = max(10, floor(Segment * 0.75 * AttackerLand * WarMultiplier))</code>

	~~<code>Bonus + Prestige / 10000</code>~~		The attacker gains the target land lost plus generated land equal to the target land lost.

	=== Prestige ~~Bonus to Population and Food~~ ===		== Prestige ==
	~~[[Population]] and [[food\|food production]] bonus from prestige is ''multiplicative''.~~

	~~<code>Bonus * (1 + Prestige / 10000)</code>~~

	~~== Rezone ==~~		Attacker prestige gain starts from the target's land ratio and land size:

	~~The cost of [[rezoning]] is determined by the following formula.~~		<code>Gain = min(LandRatio * 200 - 115, 70) + max(0, DefenderLand - 750) / 100</code>

	~~<code>(Land~~ - ~~250) * 0~~.~~6 + 250</code>~~		Prestige gain is then affected by morale and other prestige-gain modifiers. Defender prestige loss is 5% of defender prestige, capped by the attacker's prestige gain when applicable.

Oment at 14:54, 16 October 2021

2021-10-16T14:54:43Z

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	* Only generated on successful invasions where Land Ratio > 75%.		* 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.		* 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 Loss ===

202.146.25.38: /* Land Gains */

2021-10-16T09:48:20Z

Land Gains

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

	<code>0.80 * ( 0.304 * (Target Size/Attacker Size) - 0.227 * Target Size/Attacker Size + 0.048) * Attacker Size)</code>		<code>0.80 * ( 0.304 * ((Target Size/Attacker Size)^2) - 0.227 * Target Size/Attacker Size + 0.048) * Attacker Size</code>

	If target is greater than or equal to 55% but less than 75% the size of the attacker:		If target is greater than or equal to 55% but less than 75% the size of the attacker:

	<code>0.80 * (0.154 * ((Target Size/Attacker Size~~)^2~~) - 0.069 * Target Size/Attacker Size) * Attacker Size)</code>		<code>0.80 * (0.154 * (Target Size/Attacker Size) - 0.069 * Target Size/Attacker Size) * Attacker Size</code>

	For 75% and up:		For 75% and up:

	<code>0.80 * (0.129 * ((Target Size/Attacker Size~~)^2~~) - 0.048 * Target Size/Attacker Size) * Attacker Size)</code>		<code>0.80 * (0.129 * (Target Size/Attacker Size) - 0.048 * Target Size/Attacker Size) * Attacker Size</code>

	=== Land Generation ===		=== Land Generation ===

202.146.25.38: /* Land Gains */

2021-10-16T09:33:12Z

Land Gains

← Older revision		Revision as of 09:33, 16 October 2021
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	If target is less than 55% the size of the attacker:		If target is less than 55% the size of the attacker:

	<code>0.80 * ( 0.304 * ((Target Size/Attacker Size~~) ^ 2~~) - 0.227 * Target Size/Attacker Size + 0.048) * Attacker Size)</code>		<code>0.80 * ( 0.304 * (Target Size/Attacker Size) - 0.227 * Target Size/Attacker Size + 0.048) * Attacker Size)</code>

	If target is greater than or equal to 55% but less than 75% the size of the attacker:		If target is greater than or equal to 55% but less than 75% the size of the attacker:

Oment at 09:21, 16 October 2021

2021-10-16T09:21:39Z

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

	<code>Land Conquered * 1</code>		<code>Land Conquered * 2</code>

	== Prestige ==		== Prestige ==

202.146.25.38: /* Land Gains */

2021-10-16T09:19:46Z

Land Gains

← Older revision		Revision as of 09:19, 16 October 2021
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	If target is less than 55% the size of the attacker:		If target is less than 55% the size of the attacker:

	<code>0.75 * ( 0.304 * ((Target Size/Attacker Size) ^ 2) - 0.227 * Target Size/Attacker Size + 0.048) * Attacker Size)</code>		<code>0.80 * ( 0.304 * ((Target Size/Attacker Size) ^ 2) - 0.227 * Target Size/Attacker Size + 0.048) * Attacker Size)</code>

	If target is greater than or equal to 55% but less than 75% the size of the attacker:		If target is greater than or equal to 55% but less than 75% the size of the attacker:

	<code>0.75 * (0.154 * ((Target Size/Attacker Size)^2) - 0.069 * Target Size/Attacker Size) * Attacker Size)</code>		<code>0.80 * (0.154 * ((Target Size/Attacker Size)^2) - 0.069 * Target Size/Attacker Size) * Attacker Size)</code>

	For 75% and up:		For 75% and up:

	<code>0.75 * (0.129 * ((Target Size/Attacker Size)^2) - 0.048 * Target Size/Attacker Size) * Attacker Size)</code>		<code>0.80 * (0.129 * ((Target Size/Attacker Size)^2) - 0.048 * Target Size/Attacker Size) * Attacker Size)</code>

	=== Land Generation ===		=== Land Generation ===

202.146.25.38: /* Prestige Gain */

2021-10-16T09:19:20Z

Prestige Gain

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	<code>60 * Land Ratio </code>		<code>60 * Land Ratio </code>

	* Only on successful invasions where Land Ratio > 75%.		* Only generated on successful invasions where Land Ratio > 75%.
	* Cannot exceed 10% of your current prestige.		* Cannot exceed 10% of your current prestige.
	* Prestige cannot exceed your land size when prestige is added.		* Prestige cannot exceed your land size when prestige is added.

202.146.25.38: /* Prestige Gain */

2021-10-16T09:15:42Z

Prestige Gain

← Older revision		Revision as of 09:15, 16 October 2021
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	<code>60 * Land Ratio </code>		<code>60 * Land Ratio </code>

			* Only on successful invasions where Land Ratio > 75%.
	* Cannot exceed 10% of your current prestige.		* Cannot exceed 10% of your current prestige.
	* Prestige cannot exceed your land size when prestige is added.		* Prestige cannot exceed your land size when prestige is added.

202.146.25.38: /* Prestige Gain */

2021-10-16T09:14:41Z

Prestige Gain

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	=== Prestige Gain ===		=== Prestige Gain ===

	<code>~~20 + (Target's Prestige~~ * Land Ratio ~~/ 12)~~</code>		<code>60 * Land Ratio </code>

	* Cannot exceed 10% of your current prestige.		* Cannot exceed 10% of your current prestige.
	* Prestige cannot exceed your land size when prestige is added.		* Prestige cannot exceed your land size when prestige is added.
	* May be reduced for additional invasions on already invaded target within 24 hours.		* [May be reduced for additional invasions on already invaded target within 24 hours] [is this still applicable?].

	=== Prestige Loss ===		=== Prestige Loss ===

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2020-11-07T02:01:47Z

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