Combat System ?

[Tom|420]

Had a fight with my friend about the inner working of the combat system. I decided to ask so to end the fight. Please answer only if you know the real answer (not guess/opinion) or this will just add more players into our fight.

Let's use those units for the examples (numbers all different on purpose, just to avoid confusion):

K = 4.3 (Attack 4 Defense 3)
S = 1.2

Initiator: The one who starts the combat (that is, the one who's turn it is to play)


Theory 1: Each unit attacks at each round, one after the other

K is Initiator. K attacks with 4 againts 2, if succesful S looses a hit point. Then, S attacks with 1 againts 3, if succesful K looses a hit point. And we go to next round, until one gots no more hit points.

Theory 2: The whole combat is all based on the Initiator

K is Initiator. K attacks with 4 against 2, if succesful S looses a hit point. Then, S attacks with 2 against 4, if succesful S looses a hit point. Then go to next round.

OR (variation on the same theory)

K is Initiator. K attacks with 4 against 2, if succesful S looses a hit point, else K looses a hit point. Then go to next round.


So here are the two theories we fight over. I voted for Theory 1, he voted for the 2nd one. I wrote 2 variations over Thery 2, but I believe the result is the same (or pretty similar). I believe Theory 2 gives the Initiator a better chance of success (but I'm not sure, didn't do the math).

Which of the theories is the one used in the game? Again please only answer if you know the answer for sure, or at least say you are giving your opinion/guess.

Thanks in advance

 

[Grille]

It's like the "variaton" of theory2.

Initiator only uses its A-value, defender the D-value.

Lets say we have:
Unit1 - Attacker (aka initiator) with A=10, D=1
and Unit2 - Defender with A=150, D=1


For each round, there's a 10:1 chance that the defender loses a hitpoint (a random number generator 'rolls the dice' to figure the result). The fairly nice A-value of Unit2 and the bad D-value of Unit1 is not considered if Unit1 attacks Unit2.

 

[lbhhh]

Variation of theory 2. Just go to page 82 of your civ3 manual, it gives an example using a knight and a spearman and explains how it works.

"[...] the probability of either side winning is approximately the the ratio of each side's factor compared to the total. For example, if a knight (attack factor 4) attacks a spearman(defense factor 2) the total factors is 6 (4+2). The Knight has about 66% chance (4 out of 6) of winning each round."

So there you have it. This has been the combat system since civ1.

 

[anarres]

Well, the last 2 posters almost got it right.

Taking Grilles example:

Lets say we have:
Unit1 - Attacker (aka initiator) with A=10, D=1
and Unit2 - Defender with A=150, D=1

If Unit 1 attacks Unit 2 then each round of battle will take 1 HP from the defender with probability:

A/(A + D)

where A is the attack value and D is the modified defense value (taking in to account rivers, terrain, barbs, fortification, terrain improvements, cities, etc).

If the attack is successful the defender loses 1HP, otherwise the attacker loses 1HP.

So, if A=10 for Unit1 and D=1 for the defender (not exactly likely, but possible if the defender is on water ), the chance of the defender losing each round (1 HP) of battle is:

10/(10+1) = 10/11.

Obviously, this means for each round of battle the attacker has a 1/11 chance of losing 1 HP.

HTH!

 

[lbhhh]

Originally posted by anarres

where A is the attack value and D is the modified defense value (taking in to account rivers, terrain, barbs, fortification, terrain improvements, cities, etc).

Of course you have to take into account the defense modifiers
I was being lazy and just going for the quick answer, although it did answer the question.

 

[Tom|420]

Thanks to all. The fight is now over between my friend and I, and looks like I lost

What was the fight about was mainly wether only the Initiator attack score and Defender defense score were counting, or both attack and defense values of both, which was replied clearly.

Thanks again

 

[lbhhh]

Originally posted by Tom|420
Thanks to all. The fight is now over between my friend and I, and looks like I lost

What was the fight about was mainly wether only the Initiator attack score and Defender defense score were counting, or both attack and defense values of both, which was replied clearly.

Thanks again

Glad to help. Before getting in a fight next time ask on this site get the answer, then be sure to win Besides, the best way to win an argument with a fellow civ player is to beat him/her in a multiplayer game.

 

[ImperialHR]

Hi

I have a question regarding this combat formula...

Say I have a German Panzer (16/8/3), and attacking an infantry (6/10/1).

If I count NO def bonus, odds of my Panzer winning is :
16 + (16 + 10) = 62%

If the enemy infantry is in a city (size greater than 13) :
16 + (16 + (10 * 2)) = 44%
#Metropolis gives 100% bonus#

If the enemy infantry is in metropolis AND fortified :
16 + (16 + (10 * 2.25)) = 42%
#Fortified gives 25% bonus#

.....is that right? (seems low chance of winning )

 

[Tomoyo]

You also have to calculate the experience of the units. Panzers tend to get elite very quickly.

Originally posted by ImperialHR
seems low chance of winning

Not if you bring 200 artillery... Then it would be 16(5) vs. 13.5(1)

 

[DragonRunner]

I think fortifying boosts defense 50%. So, right, artillery is important.

 

[Ranos]

As far as I have ever read, experience effects combat in only one way, the number of hits a unit can take. If a unit is veteran, it gets no deffensive or offensive bonuses, just the extra hit point.

 

[anarres]

That is correct Ranos.

DragonRunner, the fortify bonus is 25%.

 

[Tom|420]

Originally posted by Ranos
As far as I have ever read, experience effects combat in only one way, the number of hits a unit can take. If a unit is veteran, it gets no deffensive or offensive bonuses, just the extra hit point.

I don't think he gets a direct bonus from his experience, but on the long run he can survive longer and on that point he might have a better chance of winning

 

[alamo]

The win/loose formula is for 1 hit point.

You need to repeat until all hitpoints exausted on one side or the other (ignoring retreat).

So for panzer vs infantry (vets w/no mod):

probability of loss =
(1-.62)^4 (straight loss)
+
c(4,1)*(.62)(1-.62)^4 (1 sucessful attack in 5)
+
(c(5,2)*(.62)^2*(1-.62)^4 (2 sucessful attacks in 6)
+
c(6,3)*(.62)^3*(1-.62)^4 (3 sucessful attacks in 7)

where c(6,3)=combination 6 choose 3 (6 instead of 7 because last one is a loss) = 6*5*4/3*2*1 = 120/6 = 20

So the total is: 0.021+0.052+0.080+0.099 = 0.252

Panzer wins 3 out of 4 times!

 

[Ranos]

Would you mind explaining what you just wrote down because all I see is a bunch of numbers and letters with no idea where they came from or what they mean.

 

[alamo]

It is a probability calculation. It looks ugly if you haven't done it before.

To start, the way a unit looses a hitpoint is like tossing a coin, except it is not 50-50. In this case it is 62-38. That means that a 1 hitpoint panzer wins vs a 1 hitpoint infantry 62 out of 100 times.

For more than 1 hitpoint you repeat the coin toss, which means multiplying the probability. A 1 hitpoint panzer wins against a 3 hitpoint infantry with probability 0.62*0.62*0.62 = 0.24, or only 24 times out of 100.

To handle a 4 hitpoint panzer vs a 4 hitpoint infantry you have to account for all the ways a panzer can loose against an infantry. I broke it down into the number of hitpoints the infantry looses - 0,1 2 or 3. Then I can do a probability calculation for each one and add them up.

For 0, that means the panzer looses 4 hitpoints in a row. The probability of that is 0.38*0.38*0.38*0.38 = 0.021.

For 1, we need to choose when the infantry looses a point - at the beginning, after the panzer looses 1 hitpoint, after 2 hitpoints, or after 3 hitpoints. That gives 4 ways. Now for any one of them the probability is 0.62*0.38*0.38*0.38*0.38. Multiple this by 4 to get 0.052.

For 2 there are 10 ways to have the infantry loose 2 hitpoints. For any one of them the probability is 0.62*0.62*0.38*0.38*0.38*0.38. Multiply this by 10 to get 0.080.

For 3 there are 20 ways, with probability 0.62*0.62*0.62*0.38*0.38*0.38*0.38. Multiply to get 0.099.

Adding it all up gives 0.252 for the probability of a panzer loosing to an infantry.

 

[rcoutme]

This is all good and well except: each terrain has a terrain modifier for the defensive unit. Granted plains, grassland, floodplain, water and tundra are small (10%) but they actually do exist.

 

[anarres]

Ranos, use Thunderfalls Combat Calc:

http://www.civfanatics.com/civ3combatcalc.html

Or the one I modded from his which allows PTW/C3C and modded units:

http://www.civ3duelzone.com/CombatCalc2.html


Note: Neither of these Calcs take in to account the retreat chances, so are slightly off when a fast unit fights a slow one. See the "utilities" forum for other calcs that do this.