Probability and Combat

[Adrien]

The following is a mathematical analysis of the Civ3 combat system.


Because there are no phalanxes in Civ3, and battleships can't directly attack land units, there is no more danger of a phalanx-battleship win.


How about something equally ridiculous, then? Say a hoplite attacking a panzer.


A panzer has an attack of 16. A hoplite has a defense of 3.


Therefore, the hoplite has a 3/19 chance, a 15% chance of winning a combat, while the panzer has a 16/19 chance or an 85% chance.

This means, under the old Civ1 system, that 15% of the time, the hoplite will kill the panzer.

As I don't actually HAVE THE GAME yet, all I can do is speculate randomly. Is there a hit-point system?

If so, how many hit points do different units have?

[jbird]

I believe you misspoke. Your example is of a Panzer attacking a Hoplite, not the converse. Just clarifying.

Jbird

[WhiteElephants]

Therefore, the hoplite has a 3/19 chance, a 15% chance of winning a combat, while the panzer has a 16/19 chance or an 85% chance.

Not true. At least the way I understand it. The hopilite would need to win 10 successfull rounds (given that I'm assuming each unit has 10 hit points) at 15% each round, which would further skew that results in favor of the Panzer given that the Panzer would most likely score 10 hits faster than the hopilite would. I'm not sure how you would express that mathematically, but I'm sure someone will take that honors.

I suppose it's similar to saying the odds of rolling a six on a six sided die are 1/6, but the odds of rolling a six ten times in a row are significantly different.

[Grunthex]

Uh, units have between 2 and 5 hp, not 10. Depending on their veterancy. (Uh, experience. Veterancy isn't really a word)

Conscripts (rarely seen, only if you draft, or upgrade a regular) have 2
Regulars 3
Veterans 4
Elites 5

Most units by the time you're fighting a bit are veterans or elites, because you have barracks. So the hoplite needs 4 or 5 of those 15% chances to kick in before 4 or 5 of the 85%. Not often. But it can happen.

[WhiteElephants]

Thanks for the clarification. I don't have the game and was basing combat on the 10 hit point system in SMAC, but I'm sure you got the jist of my post nonetheless.

[Kc7mxo]

And due to some rather whatever system that firaxis appears to be useing for their random numbers, it seems to happen a little bit too often.

[WhiteElephants]

Originally posted by Kc7mxo
And due to some rather whatever system that firaxis appears to be useing for their random numbers, it seems to happen a little bit too often.

That doesn't surprise me when we're only talking about 2-5 hit points.

[Sevorak]

Indeed, hit points is what's really at the core of the combat complaints.

Many people point to a lack of Firepower as the source of the combat troubles, but it is interesting to note the answer to this question: Which units in Civ 2 had Firepower 2?

The answers are: Cruiser, AEGIS Cruiser, Battleship, Carrier, Submarine, Artillery, Howitzer, Helicopter, Fighter, Bomber, Stealth Bomber, Stealth Fighter.

Gunpowder units in Civ 2 were NOT distinguished by firepower. They were distinguished by Hit Points. Musketeers, for example, were only 3.3.1 as opposed to the 3.2.1 of Archers - yet they made FAR superior defenders than Archers because they had 20 hit points as opposed to 10. Riflemen were only 5.4.1 - but they beat 6.1.1 Catapults consistently because they had 20 hp and the catapults had 10 and 1 firepower. Even ARMOR had the SAME firepower as a warrior - just 1! Where Armor shone through was its 30 hp, only matched on land by the Mech Inf.

Higher hit points naturally tilt combats toward whichever side has the numerically superior combat rating in the combat in question, even if both sides have the same number of hit points.

In battles of Tanks (16.8.2) against Pikemen (1.3.1), when both sides have 1 hit point (the Civ 1 System), the Tanks win a flat 84% of the time. When they each have 3 hit points, the Tanks win about 96% of the time.

The system in Civ 3 whereby all hit points are created equal and each unit has between 2 and 5 of these magical things is deliberately slanted towards giving a better chance to the low-tech unit. Not a complaint, just an observation.

However, it is interesting to note not the chances of victory, but the most likely result in each of the combats. For example, while regular Modern Armor attacking an elite Pikeman wins 95.7% of the time, it is only 55% likely that the Modern Armour will win five hits in a row, destroying the Pikeman untouched. In 45% of all cases, the Modern Armour will suffer some kind of damage, and in some cases be destroyed.

A better example would be veteran Modern Armor taking on a veteran fortified Musketman in a City. The Modern Armor wins 94% of the time, but will only escape untouched 34% of the time. Now the chances of this in Civ2 were similar, even in 15-2 battles like Veteran Armor vs. Phalanx, but due to the higher number of hit points, getting through untouched didn't mean as much since since even three or four hits-against tended to mean little against hit point totals of 30 or 40 - they hurt, but not seriously - 10% impairment per battle was livable. But in Civ3, losing a hit point is 20% of the total at minimum. What this means is that older units can sometimes pull off unusual results.

Consider the Greek Hoplite and the standard Swordsman. Assume as its adversary, the Modern Armor. One can build three Hoplites and two swordsmen for the price of one Modern Armor. Assume that the six units defend a single city, and are all veteran. Assume further that the Modern Armor is also veteran. When the Armor attacks, its chance of victory is 97.3% - but its chance of escaping undamaged in each attack is only 43.5%. It attacks three times and wins all of the combats - the most likely result being that it suffers two points of damage. Then the swordsmen attack. They have a 47% chance of inflicting one point of damage each upon the Modern Armor. The most likely result is that the Modern Armor is left with one hit point and all the Ancient era units are dead. Victory for the Modern Armor! (yet it's two full ages ahead of the ancient units, and won just barely)

When you consider this in an entire full-game context, the savings the Greek player must have gotten from skipping up to 51 technologies and building Hoplites and Swordsmen instead suggest that the Greek player would have more forces at his disposal - two to three more Swordsmen and the Armor dies.

Consider units that are less separated on the technology tree. Put a Tank up against two Hoplites and two Swordsmen (equal cost, again). Assume that the Hoplites are in the open and unfortified. The Tank attacks and kills them both, with only a 47% chance of winning flawlessly - most likely, the Tank takes a point of damage. The Swordsmen then counter - the Tank has only a 31% chance of beating off one of them without damage. Ancient units in equal cost have a 13% chance of destroying the Tank outright in this combat scenario, while the Tank has only a 2% chance of emerging unscathed.

Now of course, technology provides many other benefits in terms of city improvements and the like, such that I'd argue that any Civilization with Industrialization should be able to at least mostly make up the shield/gold deficiency they will have from pursuing technology instead of sheer unit mass. But I'm guessing that when MP rolls around, we are going to see a lot more ancient-era mass unit swarms - especially since cost/power ratio falls off in the Middle Ages (60 for a 2.4.1 musket, for example).

No complaints, just observations. I think it's interesting, that's all.

-Sev

[TCO]

Originally posted by Kc7mxo
And due to some rather whatever system that firaxis appears to be useing for their random numbers, it seems to happen a little bit too often.

Sounds pretty aenecdotal. Back it up...

[WhiteElephants]

Originally posted by Grunthex
Uh, units have between 2 and 5 hp, not 10. Depending on their veterancy. (Uh, experience. Veterancy isn't really a word)

Conscripts (rarely seen, only if you draft, or upgrade a regular) have 2
Regulars 3
Veterans 4
Elites 5

What really burns my ass is that all along I've heard these people pissing and moaning about atrillery being too weak and only taking off a hit point or two and the whole time I'm thinking that this is based on a 10 hit point system. Bah! One or two hit points is between 20 and 66 percent!

[Dis]

edit: my mistake, you did include those

[Venger]

Originally posted by Sevorak
Indeed, hit points is what's really at the core of the combat complaints.

Many people point to a lack of Firepower as the source of the combat troubles, but it is interesting to note the answer to this question: Which units in Civ 2 had Firepower 2?

Keep in mind that the other side of the FP coin is hit points - a 3 HP 1 FP unit is equivalent to fighting a 1 HP 3 FP unit, for the most part.

Also, keep in mind that HP's in Civ2 represented 10 hit points, not 1.

Venger

[Venger]

Re: Probability and Combat

Originally posted by Adrien

How about something equally ridiculous, then? Say a hoplite attacking a panzer.

A panzer has an attack of 16. A hoplite has a defense of 3.

Therefore, the hoplite has a 3/19 chance, a 15% chance of winning a combat, while the panzer has a 16/19 chance or an 85% chance.

This means, under the old Civ1 system, that 15% of the time, the hoplite will kill the panzer.

As I don't actually HAVE THE GAME yet, all I can do is speculate randomly. Is there a hit-point system?

If so, how many hit points do different units have?

Hit points in Civ2 are different than Civ3. Civ2 HP are actually 10 hit points.

Now, your percentages are way off...

The chances of a Panzer defeating a Hoplite is 92% at worst.

Of defeating a fortified Hoplite is at worst 82%. A bit low.

Of defeating a Hoplite with a 100% terrain/fortification bonus is 58% - that's too low in my opinion. But overall the balance is okay.

Having an FP or HP modifier would help...

Venger

[GePap]

All hail Sevorak!

All hail Sevorak

Finally someone has made a complete, well balanced, carefully constructed, and simple to follow argument on the vagaries of the current combat system without igniting a firestorm about whether the combat system is 'broken'. I would say that I think it was not a wise decision by Fixaris since it forces players in the late ages to have to build vast armies even to deal with much technologically backward units (which their greater industry and economies allow them too) which means horrendous amounts of micromaneging later on.

Again, good work Sevorak and that post should be put up as its own thread.

[Bubba_B]

Re: All hail Sevorak!

Originally posted by GePap
All hail Sevorak

Finally someone has made a complete, well balanced, carefully constructed, and simple to follow argument on the vagaries of the current combat system without igniting a firestorm about whether the combat system is 'broken'. I would say that I think it was not a wise decision by Fixaris since it forces players in the late ages to have to build vast armies even to deal with much technologically backward units (which their greater industry and economies allow them too) which means horrendous amounts of micromaneging later on.

Again, good work Sevorak and that post should be put up as its own thread.

I agree gj guys nice thread

and yes increased hit points would make a great difference Fraxis!!

Can this be done in the editor(by unit)??? Cant remember.