The Complete Civilization II Combat Guide v1.1

INTRODUCTION

This document contains all there is to know about how combat works in Civilization II, by Microprose. Although it claims to be complete, there are some issues that need resolution. An occasional update can be expected whenever significant changes need to be recorded. Included with all of the general topics is the formula for calculating the probability of a unit winning a combat.

While scenario makers push the limits of what is possible by altering the rules.txt, I have strayed only minimally from the default settings. This was to simplify and make general all the topics contained herein. Any alterations to how the game normally works continue to follow the rules explained in this document. However, you may create situations that extend beyond the descriptions provided. For example, applying the “can attack air unit” flag to a naval unit.

I welcome any input to this document. The mathematics has stood up to extensive, rigorous testing. Some multipliers are proven, others are not known. If you discover anything new, or find something described here to be misinformation, contact me with your discovery. My contact information is provided at the end of the document.

Version 1.1 updates and clarifies text regarding domains and details about the “Can attack air units” flag in rules.txt.

1. BASICS

Definition

Description

Damage

Effects on movement

Land units

Air units

Sea units

Domain 3 units

Airborne bombers defined

2. UNIT COMBAT FACTORS

Attack strength

Defense strength

Hit Points

Firepower

3. ADJUSTMENT FACTORS

Veteran status

Fortifying

Fortress

Terrain

City Walls

Coastal Fortress

SAM Batteries

Flags in rules.txt

Partisans

Shore Bombardment

SDI Defenses

Sneak Attack!

Barbarians

Nuclear attack

4. THE COMBAT FORMULA

Background

The formula

Discussion

5. ADDITIONAL CONSIDERATIONS

6. HEALING

Land units

Sea and Air units

Time

7. SHORT HINTS AND TIPS

8. FALSE STATEMENTS

9. CREDITS

List of discussion thread sources for this compilation

Contact information

1) BASICS

a) Definition: Combat occurs when a unit with an attack value greater than 0 attempts to enter a square occupied by a unit of another, non-allied, civilization.

b) A battle results in the destruction of one unit or the other. The primary defender is the unit with the greatest modified defense value at the moment of the attack. If the primary defender is destroyed, all other defenders (stacked) in the same square are also destroyed unless:

i) They occupy a city square, or

ii) The square has the fortress or airbase improvement built on it.

c) Units involved in combat usually sustain damage. Damage is shown in the unit’s strength bar by color and percentage.

i) Green: 2/3 to full strength,

ii) Yellow: 1/3 to 2/3 strength

iii) Red: less than 1/3 strength

d) Except for air units, damaged units have reduced movement points approximately proportional to the damage. However, land units will never have less than 1 movement point, and sea units will never have fewer than 2. The proportion of damage is rounded to the nearest integer, but never less than the minimum for that unit, using the following formula:

CMP = CHP/HP * MP + 0.2

Where

CMP = current movement points

CHP = current hit points

HP = maximum hit points (from rules.txt)

MP = maximum movement points (from rules.txt)

e) Land units (domain 0) can attack any other unit on a land square, except airborne bombers.

f) Air units (domain 1) Air units can attack any unit, except airborne bombers, on any terrain. Air units with the "Can attack air units" flag (fighters) can also attack other air units.

g) Sea units (domain 2) can attack any unit occupying any adjacent square, except for airborne bombers. Units with the "Submarine advantages/disadvantages" flag (submarines, thus) can only attack other sea units. When a sea unit attacks a land unit, it is called shore bombardment (3.j).

h) Special domain 3 units can attack any other unit, regardless of flags. Domain 3 units can in turn be attacked by any other unit. They ignore city walls, SAMs, and coastal fortresses.

i) Airborne bombers (any air unit with range > 1) can only be attacked by a unit with the “can attack air units” flag (fighter). This holds true regardless of what domain the attacking unit is.

2) UNIT COMBAT FACTORS

Units have four basic factors figured into the calculation of a combat result: attack strength, defense strength, hit points, and firepower.

a) Attack strength is the likelihood of inflicting damage when attacking an opponent. Units with an attack strength equal to zero cannot initiate combat.

b) Defense strength represents the ability of a unit to defend itself when attacked; It is the likelihood that damage will be inflicted on an attacking unit.

c) Hit points indicate how much damage a unit can withstand before it is destroyed. The true number of hit points is the hit point value x10. A 2hp unit thus has 20 hit points.

d) Firepower indicates how much damage a unit can inflict in one round of combat. A successful round reduces the opponent’s total hit points by the value of the unit’s firepower.

3) ADJUSTMENT FACTORS

Many factors affect the four basic Unit Combat Factors, depending upon the circumstance of the battle. All factors that apply are multiplied together, unless otherwise noted.

a) Veteran units receive a x1.5 bonus for both attack and defense strengths.

b) Fortified land units receive a x1.5 bonus for defense strength. This bonus is superceded by fortress improvement (3.c) and city walls (3.e). It can be used in combination with a SAM battery (3.f) or a coastal fortress (3.g).

Notes:

· This bonus applies only on the next turn, after the unit appears with the dirt entrenchment, not while in the process of fortifying.

· It has been suggested, but not tested, that city defenders in multiplayer games do gain the bonus immediately if given the order to fortify with the ‘f’ key, but not the menu.

· Air and naval units may fortify in a city or air base (or other land square), but do not gain the defensive bonus.

· Land units gain the bonus against an attack by any domain unit.

c) The fortified (3.b) bonus increases to x2 for a land unit occupying a fortress improvement, whether given the order to fortify or not. This improvement gives no bonus against an attack by an air unit. A city built on an existing fortress eliminates that fortress. If a city is built on a square where a fortress is in the process of being built, the fortress will have no effect.

d) Terrain increases defense strength of all units by:

i) x1.5 if on forest, jungle, or swamp

ii) x2 if on hills

iii) x3 if on mountains

iv) +0.5 if on a river, additively enhancing any other terrain bonus. For example, a hill square with a river gives a x2.5 bonus, a (2 + 0.5)% multiplier.

e) City walls triple the defense value of city defenders against attacks by land units only. This bonus can apply only to land units.

f) SAM batteries double the defense value of city defenders against attacks by air units. This bonus applies to any unit defending a city except a scrambling fighter, which receives a separate defense bonus. Combined with an SDI (3.l), the defense against missiles is quadrupled.

g) Coastal fortresses double the defense value of city defenders against attacks by naval units. This bonus applies to any unit defending a city.

h) Some flags in rules.txt can alter combat calculations as follows:

i) Negates city walls (howitzer): The city walls (3.e) defense bonus is negated.

ii) x2 on defense versus horse (pikemen): This is actually a limited bonus, x1.5 if the attacker is a land unit with move=2, hp=1, and fp=1.

iii) Can attack air units (fighter): The unit can attack air units with range > 1. This also affects other combat circumstances, as follows:

(1)     A fighter stationed in a city that is attacked by an air unit with range <> 1 scrambles, gaining a x4 defense bonus.

(2)     A fighter stationed in a city scrambles and gains a x2 defense bonus when attacked by another fighter.

(3)     Any helicopter attacked by a fighter suffers a x0.5 defense adjustment and has its firepower reduced to 1.

(4)     A fighter cannot benefit from a SAM (3.f) adjustment unless attacked by a missile. This applies to any domain unit with this flag.

Note: Scrambling applies only to air units with the fighter flag.

iv)  x2 on defense versus air (AEGIS): Any AEGIS sea unit gains a x3 bonus when attacked by an air unit, x5 if the attacker is a missile (a unit with the “destroyed after attacking” flag).

v) Can make amphibious assaults (marines): Can attack from the sea (a ship). This does not count as shore bombardment (3.j). The attacking marine does not ignore city walls (3.e).

i) Partisans (or any unit in the partisan slot of units.gif) gain an attack advantage against non-combat units (any with attack value = 0). The partisans’ attack value is increased eightfold (x8).

j) Shore bombardment. When a sea unit attacks a land unit, both units have their firepower reduced to 1.

k) Caught in port. A sea unit’s firepower is reduced to 1 when it is caught in port (or on a land square) by a land or air unit; The attacking air or land unit’s firepower is doubled.

l) SDI defenses thwart any nuclear attack (except those set by spies) within 3 squares of the city in which it is built. A SDI doubles the defense value of city defenders against attacks by missiles. Combined with a SAM Battery (3.f), the defense of a city’s primary defender against missiles is quadrupled.

m) Sneak attack! A sneak attack gives an advantage to the attacker. The value of this bonus is currently unresolved. Testing has not yet resulted in a multiplier.

n) Barbarians do not always attack and defend at normal unit strengths. Barbarian archers defend with a base value of 1, not the normal archer defense value of 2. Other barbarian units have normal defense values. All barbarian attack factors are affected by the difficulty level of game being played:

Chieftan        x0.25 the normal attack value

Warlord        x0.5

Prince        x0.75

King        x1

Emperor        x1.25

Deity        x1.50

o) Nuclear missiles have a special attack value of 99. Unless thwarted by a SDI, this sidesteps any combat result calculations. If a nuclear missile attacks a unit, a strike results. This kills all units within one square of the strike, causes pollution on land squares, and reduces the population of any city within the radius by half.

4) THE COMBAT FORMULA

First, some background. The manual provides a simplified combat formula to approximate the likely outcome of a combat. This formula states that the total modified attack and defense factors are combined; the chance of victory is approximately the ratio of the unit’s factor to the total. In other words,

U / (a + d), where:

U = the unit’s modified factor,

a = the attacker’s modified attack factor, and

d = the defender’s modified defense factor

This approximation has proven insufficient for many players. Much debate has led in a more detailed formula. First, an explanation of what it entails. For explanatory purposes, a combat is a single round, a battle the cumulative result of all combats.

The attacker and defender each own a portion of the total modified attack and defense values proportional to their value, as the simplified formula, above, expresses. For each combat, a winner is determined by this ratio. In simple terms, the higher modified value is more likely to win a combat. For each combat won, the opponent reduces its hit points by the winner’s firepower. This continues until one unit is reduced to zero hit points and is thus destroyed.

Heated discussion about the complex combat formula led to several ideas for a simpler formula being put forth. The one that most closely gives the results of the complex formula is:

Odds = (S + (S – W)) * Shp * Sfp / (W * Whp * Wfp)

where:

S = Stronger unit’s modified attack or defense value

W = Weaker unit’s modified attack or defense value

Shp = Stronger unit’s hit points

Sfp = Stronger unit’s firepower

Whp = Weaker unit’s hit points

Wfp = Weaker unit’s firepower

No playtesting results to test the accuracy of this formula have surfaced.

On to the real calculation…

Each unit gets a randomly generated number from 0 to its modified value minus one, multiplied by a constant. This constant has been best-guessed (based on play testing) to be 8. The unit with the higher random number wins the combat, ties going to the defender.

· If the defense value is equal to or greater than the attack value, the probability (p) of the attacker winning the combat round is

p = (A – 1) / 2D

· If the attack value is greater than the defense value,

p = 1 – ((D + 1) / 2A)

Where A = (a * 8) and D = (d * 8). The resulting p is the odds of the attacker winning the combat. This result can be used to determine which unit is likely to win the battle. To calculate the actual odds of the attacker winning the battle, p is plugged into the following equation:

P = SUMn(COMB(n-1,dh-1) * (p^dh) * (1-p)^(n-dh))

Where "n" is summed from dh to dh+ah-1.

ah = Attacker’s modified hit points

dh = Defender’s modified hit points

p = probability for attacker to win combat round

P = probability for attacker to win battle

Note: Modified hit points: An opponent’s total hit points are divided by the unit’s firepower. Thus an attacker with 2fp halves the defender’s total hit points.

Comments:

This formula accounts for damaged units, as the input is the unit’s current hit point total.

In layman’s terms, P is the sum of the probabilities of all the possible outcomes of the attacker winning. For example, the odds of the attacker winning ten straight combats, plus that of winning ten out of eleven, plus that of winning ten out of twelve, and so on, added together to produce a grand total. The maximum number of rounds is the attacker’s and defender’s total hit points minus one. Basically, until the winner is left with a single hit point after destroying the loser. The defender’s chance is (1 – winner’s probability).

For those unable to decipher the above mathematics,

· An advantage in hit points is slightly more beneficial that an advantage in firepower, other factors being equal. An increase in HP produces a greater range of values of n to be summed. Because FP is in the denominator of the fraction, its effect is less; Greater HP is all accounted for in the range, half of a greater FP is. The greater range of values means more COMBinations are calculated. COMB values increase at a greater rate than the final exponent ^(n-dh) reduces the total value in our equation.

· The more total hit points involved in the battle, the more likely the unit with the greater modified value, the stronger unit, in other words, will win.

· With an even attack to defense ratio, the higher the values, the better the odds for the attacker.

Units with 0 defense can occasionally win because it generates a number between 0 and 0 (0, thus), and the attacker can also end up with a 0. The tie goes to the defender, meaning he wins that combat round. A damaged unit, or one attacking at partial strength (after using part of its movement allowance), can on rare occasions end up on the short end of this possibility.

An Example

Veteran Artillery and Armor units attacking veteran Riflemen behind city walls. The formula stacked up to artillery, but was off slightly with the armor results. Marko Polo of Apolyton tested ten sets of ten attacks with each unit. Other tests to verify this formula, excepting one, have used a minimum of 234 attacks.

Artillery (10a, 1d, 20hp, 2fp) vs. Rifleman (5a, 4d, 20hp, 1fp): The formula predicts 82.5% victories, Marko Polo tests resulted in 79%.

Armor (10a, 5d, 30hp, 1fp) vs. Rifleman (5a, 4d, 20hp, 1fp): The formula predicts 45.8% victories, Marko Polo tests resulted in 44%.

Other tests of Cavalry vs. Armor, Fanatics vs. Musketeer, Fanatics vs. Alpine Troops, Warrior vs. Warrior, Catapult vs. Musketeer, and others all matched the formula closely.

5) ADDITIONAL CONSIDERATIONS

a) A city’s population is not reduced if the city has city walls and a defender loses a combat, or if the city was attacked from a sea square.

b) A sacked city will have its population reduced by one. A size one city will usually be destroyed if sacked. There is unresolved discussion about when size one cities are captured instead of destroyed. For discussion, see the thread City Razing Problem .

c) Air units attacking land units ignore city walls and fortresses.

d) Airbases provide no defense bonus.

6) WHEN THE DUST SETTLES…

After the battle, the victor is usually damaged. Units can heal as long as they are not given the order to move, even along railroad. They heal at varying rates, depending on their proximity to a friendly city or barracks. Settlers and Engineers, the only units incapable of fortifying, heal while working.

a) Land Units:

i) 100% of total hit points healed every turn in a city with barracks.

ii) 40% of total hit points healed every turn in a city without barracks.

iii) 30% of total hit points healed every turn near a city with barracks.

iv) 20% of total hit points healed every turn near a city without barracks.

v) 10% of total hit points healed every turn on any square that does not fit the above categories.

vi) A fortress (3.c) always adds an extra 10% to the normal rate for that particular square.

“Near a city” means no further than 3 squares from a city, i.e. a 7×7 square.

b) Sea and Air Units:

i) 20%/20% of total hit points healed every turn in a fortress or a city

ii) 10%/0% of total hit points healed every turn on any other square

iii) 100%/100% of total hit points healed every turn in a city with port facility/airport, respectively.

iv) Airbase and barracks have no effect.

v) Port facilities and airports affect only the city square.

c) Healing away from a city or fortress (by skipping that unit’s turn) occurs immediately, before the next unit is available for an order. Barracks healing occurs at the end of the player’s turn.

d) The rate of healing by “entering” an allied city has not been determined.

7) SHORT HINTS AND TIPS

As a general rule, the unit with the higher modified attack or defense strength will likely win the combat, ties favoring the defender.

Against 1hp defenders:

· Even strengths or a defensive advantage strongly favor the defender.

· Even a slight attack advantage means a much greater possibility of winning the battle.

Against 2hp and 3hp defenders:

· Even strengths slightly favor the defender.

· Defensive advantages again heavily favor the defender.

· Attack strength advantage strongly favors the attacker.

· A 2hp attacker needs at least a fourth again as much strength as the 3hp defender to have even slightly favorable odds.

· A 1hp attacker needs better than half again as much strength as the 2hp defender, and more than double the 3hp defender to gain slightly favorable odds.

Defenders in a city have the advantage of maximum defense and healing. Also, only a diplomat or spy can see what units reside in an enemy city.

Stacked defenders are immune to bribery unless adjacent to a city that is bribed.

8) LIES, LIES, LIES !!!

Much discussion has surrounded figuring out how combat works. In the process, some misinformation has been spread. This section addresses these incorrect ideas. The following statements about combat in CivilizationII are all FALSE. Where applicable, an outline reference number before the statement directs you to the section where the correct information can be found:

· The attack strength of the defender is figured into combat resolution.

· The defense strength of the attacker is figured into combat resolution.

· The terrain on which the attacking unit begins is figured into combat resolution.

· (1.d) Damaged units have movement points proportional to their damage.

· (3.b) The defensive bonus of fortifying a unit enhances the city wall or fortress bonus.

· (3.b) The defensive bonus of fortifying is immediate.

· (3.c) A unit must be fortified in a fortress to gain the defensive bonus.

· (3.d) The defensive bonus of rivered terrain is multiplied along with other adjustment factors.

· (3.e) City walls increase the defense strength of any unit.

· (3.h.ii) The pikeman bonus works against all land units with more than one movement point.

· (3.j) A ship caught in port has its defense strength reduced to 1.

· The combat formula in the manual is correct.

· (5.d) Marines attacking from a ship ignore city walls.

· Defenders attacked by marines on a ship gain the coastal fortress bonus.

· (6.b.iv) Air units gain a healing bonus in an air base.

9) CREDITS

The first linked thread, discussing the final formula, should be read if any clarification is needed about how it was found and what it means.

Eggman, Buenos, and Euclid provided the bulk of the math in this process. Special thanks to SlowThinker and others for extensive testing to verify suspicions and ideas!

The following discussion threads contributed to this topic:

The Civ2 Battle Equation Solution

Defense Multipliers

AI cheats on naval bombardment

The Pikeman’s defense

Modifiers for Attack/Defense

What is the difference between firepower and attack points?

Barbarians and level of play

Veteran units… (Healing)

Hit points and firepower

Fortification bonus within walls or fortress

Defensive terrain for air and water units

Fighter vs. SAM

Civfanatics combat odds discussion and testing

The Marquis de Sodaq can be contacted at sprout@bitstream.net