What if combat wasn't RNG dependent?

[Um the Muse]

So...1.5 rounds? A 1 str unit attacking a 10 str unit would do ~11.8 hp of damage per round using (30*13/33)...for 1.5 rounds this would do 17.7 hp of damage...actually MORE damage than the current model? IMO that's the wrong direction, since compared to the base game things like hill longbows are already gimped to some extent due to the guarantee that they take some damage (even if their first strikes makes them take a fraction of the damage other units take, they still take some).

Oops. I did say that 1.5 is only good for "close-ish" battles, but you're right anyway. The basic problem with the rule of thumb is that there are jumps in odds depending on how many rounds of combat there will be. I'm not too worried about absurd stretches like knights versus scouts, but my rule of thumb is horrible for attacking wounded units.

In short, there can't be one magic multiplier.

Getting rid of the incosistency is surprisingly quite tricky. The problem lies in the fact that in a battle damage value of attacker * number of rounds to kill <> the hp of the unit being attacked.

That's not really an issue, I don't think--the mod doesn't actually use rounds of combat, so there's no reason why the "rounds" have to be whole numbers. Take the number of "rounds" to kill from both combatants, see which one is smaller, and use that number for both combatants (you might have to round up depending on the precision allowed, I think. Sorry, not terribly computer savvy). One, by definition, should do enough damage to kill, while the other shouldn't except in the case of a tie.

On the other hand, there's an elegance to the current system. It's easy and intuitive. So what if it changes things a little? That may not be a bad thing.

[dr_s]

Originally Posted by TheMeInTeam

Now, do you have a workable formula for all strength values that gives us the answer to "average expected damage" based on previous odds values? If you have one, I would CERTAINLY forward it to my friend and it would be well worth consideration. Maybe there's something I'm missing and a nice algebraic formula will do nicely for that and make #units needed on average to kill another unit close to what the rng-based game uses.

I'm not sure it's worth trying to reproduce the results of the existing damage system. Is there any evidence that it's particularly well thought out?

Based on my reading of the thread, I think that your current test mod uses the following formula for damage. If S1 and S2 are the strengths of the two units, and S2 >= S1, then after the battle, S2 is reduced to (S2 - S1). Is that correct? If you think this is too much damage, but want to preserve mutually assured destruction when S1 = S2, then I would suggest changing this to something like

S2*sqrt(1-S1/S2)

Then a 1 strength unit attacking a 10 strength unit would leave the stronger unit at 9.5 instead of 9, a 5 strength unit attacking a 10 strength unit would leave the victor at 7, and a 9 strength unit attacking a 10 strength unit would leave the victor at 3.

[plasmacannon]

S2*sqrt(1-S1/S2)

Now, this looks better. However, it results in 0 damage, when units are of equal strength.

Perhaps, an average of TMIT's formula and this one would achieve balanced results.
Option3. A set or percentage damage done to both units. If both units were reduced to 0.1 strength, then neither would fight afterwards. The one in a city would heal. The one with a supermedic would heal.
Option4. Mutual annihilation. Both units are destroyed.

[dr_s]

Originally Posted by plasmacannon

Now, this looks better. However, it results in 0 damage, when units are of equal strength.

It's the formula for the remaining strength of the victorious unit, so it results in 100% damage for equal-strength units.

[plasmacannon]

Originally Posted by dr_s

It's the formula for the remaining strength of the victorious unit, so it results in 100% damage for equal-strength units.

ok. So, S2*sqrt(0) = 0, thus 0 strength remaining to both units or Mutual annihilation. Got it.
Thanks for the clarification. I was looking at as damage done to each unit.

What about the average option of both formulas though?
In TMIT's example, the 1 str unit attacking a 10 str unit results in a 9 str unit remaining.
In your example, it results in a 9.5 str unit remaining.
An average would result in a 9.25 str remaining.
I realize this difference seems small. It is because of these numbers being used.
When larger 40 str battleships are involved, or mods that increase unit str even higher, then the smaller amount of damage done makes for a practically invulnrable unit.
Both formulas have merit. Hence, the suggestion of an average of the two results.

[dr_s]

It occurs to me that I should elaborate a bit on my suggested formula. Using my notation above, TMIT's original formula can be written as

S2' = S2*(1-S1/S2).

Here S1 is the strength of the weaker unit, S2 is the strength of the stronger unit, and S2' is the strength of the victorious unit after the battle. This formula is the product of the stronger unit's original strength and a factor (the stuff in parentheses) that depends on the ratio of the two strengths, which is why TMIT originally referred to this as a ratio.

My suggestion is to modify the formula by raising the second factor by some power:

S2' = S2*(1-S1/S2)^n.

If you pick n < 1, then the victorious unit will survive with more health than with TMIT's formula, while if you pick n > 1, it will survive with less. By adjusting n, you can adjust how much health the victorious unit has after the battle. I picked n = 1/2 because it was the first thing I thought of. But you could pick n = 1/3 or n = 1/4 if you wanted even more health after the battle, or n = 2/3 or n = 3/4 if you wanted less.

This also suggests a couple other modifications.

One way to treat the flanking promotion would be to modify n. So if n = 1/2 normally, than an attacking unit with flanking I might get n = 2/5, and an attacking unit with flanking II might get n = 1/3, for example. Similarly for drill. A stronger unit with drill I might get n = 2/5, with drill II, n = 1/3, etc. A weaker unit with drill I might get n = 3/5, with drill II n = 2/3, etc. (I leave it as an exercise for the reader what should be done if both units have drill, but at different levels.)

You could also have n depend on terrain if you like, but maybe that's overkill, given that unit strength already depends on terrain.

[Um the Muse]

FWIW, I like dr_s's formula. I'm not sure that I like his solution for Drill, and I definitely don't think it's the right way to go for flanking. You have to both attack and win for the promotion to do anything! It better be very powerful to be competitive.

What about a 15% bonus when attacking anything?

By the way, why go from 1/2 to 2/5? Is that based on their decimal forms (i.e. 1/2=50% and 2/5=40%, 1/3 is roughly 30% so each is going down by 10%)?

[TheMeInTeam]

Originally Posted by Nick Carpathia

Post a link to the deterministic combat mod, I think the Realms Beyonders might be interested (in breaking it )

You guys break the game just fine anyway (which CFC also does, mind you ). That said, I believe my friend will release the mod when we've gone a bit further with it. If not, I'll try to talk him into it.

I'm not sure it's worth trying to reproduce the results of the existing damage system. Is there any evidence that it's particularly well thought out?

No, actually. I think ultimately the game SHOULD have some incentive to tech obviously, but balance it such that tech lead doesn't necessarily equate to a win. The strength distribution on most non-elephant units in the game actually do a pretty good job of that IMO...but damage is another matter. I'm pretty sure Firaxis didn't consider the question of expected damage because they let the RNG throw chips where they may lie. It's a new problem for deterministic combat, and it's really going to be up to a combination of balance of tech and vs preference.

S2 is reduced to (S2 - S1). Is that correct?

So far, yes. I'm still not decided on it personally.

S2*sqrt(1-S1/S2)

For non-equal strengths this is interesting (it's pretty much a wash at equal strength ). My only concern is tipping the scales too far the other way, such that a tech lead suddenly becomes insurmountable. Tweaking the n factor could make the model really good potentially though.

What about a 15% bonus when attacking anything?

What if the change in n applied to the attacker is sufficient to give the unit with flanking the ability to always survive when strengths are close enough, but not if they aren't ?

What amount to go down by in terms of % is very much straight theory at this point. We'd need to look at what actually happens in doing so.

[dr_s]

Originally Posted by Um the Muse

FWIW, I like dr_s's formula. I'm not sure that I like his solution for Drill, and I definitely don't think it's the right way to go for flanking. You have to both attack and win for the promotion to do anything! It better be very powerful to be competitive.

What I was thinking was that in the current system, flanking on average saves you hammers when you attack, because you sometimes survive when you otherwise wouldn't. I was trying to preserve that. Obviously my suggestion doesn't really capture the essence of the current flanking promotion. You could also reverse my suggestion and make flanking only apply when the attacking unit loses, but increase n to cause more damage to the victor.

By the way, why go from 1/2 to 2/5? Is that based on their decimal forms (i.e. 1/2=50% and 2/5=40%, 1/3 is roughly 30% so each is going down by 10%)?

Just picking a monotonic sequence of rational numbers with small numerators and denominators. Those were the first that came to mind.

[lindsay40k]

Been out of the thread for a while. Something occurred to me; why is the choice framed as RNG vs determinism? Combat's split into rounds, so if one wanted fewer extreme results but still retain an element of unpredictability, couldn't a 'determinism' mod have a sliding scale for how determinist the combat it? At the very least, make it possible to set it so that 0%, 25%, 50%, 75% or 100% of rounds are RNG. (Could be tricky to fit first strikes into that, and it leaves the question of whether those RNG/determinist rounds should be sequential or themselves randomly rolled.)

This would go a long way to resolving my main concern with pure determinism - the issue of equally matched foes killing each other every single time, yet the tiniest advantage to one side (easily acquired by a suicidal catapult shaving a bit of HP off all five opposing units) enabling their forces to definitely survive (yes, I know a single mounted unit could harry the 1hp survivors to death, but there's a lot of 'if' about that).

I'd be interested in playing a mod wherein spearmen never kill tanks, but the issue of closely matched foes does put me off somewhat. I'd prefer breaking a Mexican Standoff to remain something of a roll of the dice, especially with the promotions system being as it is.