Combat mechanics

[Sebed]

Originally posted by binTravkin
Raise both?
x*a / y*a = x / y

interesting, very interesting...
just wonder what doctors says about it

[binTravkin]

interesting, very interesting...
just wonder what doctors says about it

Yeah, go ask your doctors.
In their place I wouldn't let you to sit in front of computer.

[Dis]

this math looks too complicated to me in my old age.

What's the gist of it?

[Chaos Theory]

Originally posted by Chaos Theory
Thus, to calculate the true estimated probability of winning an exchange, raise both the attacker's and defender's strengths to the 4/3, and then calculate the ratio of your side's strength to the sum of the strengths.

In even simpler terms, the odds are somewhat further skewed towards the stronger unit than the ratio of their strengths would indicate.

[Deathsinger]

Are you simply trying to calculate the odds of winning a battle? I have a spreadsheet that does this. You simply input the attacker value, the defense value, the attacker's pips and the defender's pips. Would this be of any help to you?

[Chaos Theory]

What formula does it use? It's probably not correct, but if it is I'm very interested to see it.

[Deathsinger]

So harsh.

The odds that the game reports are not correct because the combat system is not a *** for tat turn. It is simply a chance to damage someone. Let me give you an example:

Attacker Value 10
Defender Value 5
Attacker Pips 1
Defender Pips 2

The game reports something like a 1:1 chance of victory for this attack. That is not the case. The following are the outcomes of the this battle, attacker takes no damage killing defender, attacker does 1 point to defender then dies, attacker does no damage to defender and dies.

The chances are calculated using the odds for the attacker or defender damaging the other, then repeating until one is dead. (There is no mutual destruction, otherwise the odds would be 50-50.)

Chance that the attacker does 1 point of damage is 10/(10+5) = 0.6666
Chance that the defender does 1 point of damage is 5/(10+5) = 0.3333

So, the attacker wins the above scenario w/o taking damage 0.6666^2 = 4/9 = 0.44444
The defender wins taking one point of damage = 0.6666*0.3333 = 2/9 = .22222
The defender wins w/o taking damage 0.3333 = 1/3 = 0.3333

The attacker wins this battle 44.444% of the time. The math gets more involved as you have more pips on each side, but luckily Pascal developed his famous triangle to solve this.

So for the following
Attacker Value 4.5
Defender Value 3
Attacker Pips 2
Defender Pips 3

Attacker wins w/o damage = [4.5/(4.5+3)]^3 = 0.216
Attacker wins taking 1 point of damage [4.5/(4.5+3)]^3*[3/(4.5+3)]*3 = 0.2592
This final factor of three is from Pascal’s triangle, because this outcome can be achieved three ways, the attacker can:
do 1 point, do 1 point, take 1 point, do 1 point;
do 1 point, take 1 point, do 1 point, do 1 point;
take 1 point, do 1 point, do 1 point, do 1 point
(Note the sequence do 1 point, do 1 point, do 1 point, take 1 point does not exist since the defender is dead after taking 3 points)
Defender wins taking 2 points of damage [4.5/(4.5+3]^2*[3/(4.5+3)]^2*3 = 0.1728
Again this can be achieved three ways, the attacker can:
Do 1 point, do 1 point, take 1 point, take 1 point
Do 1 point, take 1 point, do 1 point, take 1 point
Take 1 point, do 1 point, do 1 point, take 1 point
(Note the sequences take 1 point, do 1 point, take 1 point, do 1 point & take 1 point, take 1 point, do 1 point, do 1 point & do 1 point, take 1 point, take 1 point, do 1 point do NOT exist because the attacker is dead after taking 2 point)
Defender wins taking 1 point of damage [4.5/(4.5+3]*[3/(4.5+3)]^2*2 = 0.192
This can be achieved two ways:
Attacker does 1 point, defender does 1 point, defender does 1 point
Defender does 1 point, attacker does 1 point, defender does 1 point
(Note the sequence defender does 1 point, defender does 1 point, attacker does 1 point does not exist because the attacker is dead after taking 2 points).
Defender wins taking no damage [3/(4.5+3)]^3 = 0.064

0.216 + 0.2592 +0.1728 + 0.192 + 0.064 = 1

Attacker wins 0.216 + 0.2592 = 0.4752
Defender wins 0.1728 + 0.192 +0.064 = 0.5248

Any questions?

[Chaos Theory]

I'm not trying to be harsh, merely blunt. I'm aware of the effects of multiple exchanges of damage on the odds of winning a battle.

Originally posted by Deathsinger
Chance that the attacker does 1 point of damage is 10/(10+5) = 0.6666
Chance that the defender does 1 point of damage is 5/(10+5) = 0.3333

This is exactly what I've shown is not correct. In this scenario, the chance the attacker does 1 point of damage is about 3/4, not 2/3, and the chance the defender does 1 point of damage is about 1/4, not 1/3. The rest of your math is sound, and until recently, I believed the probabilities were as you said, but the numbers tell a different story.

[dacole]

confused here what is ment by pips? Thanks

[Deathsinger]

Pips is the number of health points of each unit, a fission reactor provides 10 pips, a fusion 20 pips, a quantum 30 pips, a singularity reactor 40 pips.

[dacole]

Ah ok thanks, how exactly did we get to call that pips as opposed to health...?

[Deathsinger]

After re-reading and downloading your spreadsheet I now understand the point. I originally misunderstood your line "calculate the ratio of your side's strength to the sum of the strengths" interpreting that to mean ratioing the health (pips). What is somewhat troublesome with your results is the dips around 0.4 and 0.6 strength ratios.

[Chaos Theory]

I have two points near .4 (reflected to .6) with slightly different x values and different, though not statistically different, y values that cause a blip on the chart. Consider the plot to be a smeared line about as wide as the upper and lower error bounds, rather than the somewhat jagged central line.

[Deathsinger]

How did you create this test in the game? Did you create two units with 1 health point each and have them fight over and over again. Then vary their attack/defense values and repeat?

[Chaos Theory]

I had bunches of units, from accelerated-start games and from old saved games, combined with the scenario editor. I pitted them against each other after noting each unit's strength and initial health, then looked at which unit won and with how much health, and recorded its damage as exchanges won by the defender, and the losing unit's initial health as exchanges won by the attacker. I varied both attack and defense across a wide spectrum, in the range .4375 to 45.