Combat Explained....

I don't think so rkyte. That's just the script for the display, not for the actual combat.
 
Arathorn said:
On first strikes (I like the term "rounds of immunity"), Drill I-III promotions appear to be relatively weak, but if you can get Drill IV, it's huge and might make up for the initial weakness. I need to run more tests -- probably just mathematical models, actually, but....

If first strikes are rounds of immunity, then for the case when both the attacker and the defender have x and y first strikes respectively, this new theory is equivalent to the old x-y theory. Am I missing something?
However, I think eg577's suggestion to give the archer unit 100% retreat chances is a good way to do further testing.

The second question is how the system works when there is a range of first strikes. Is the number of first strikes for that unit selected using a uniform distribution, or the relative strength of the units is taken into account?
 
GenericKen said:
I don't think so rkyte. That's just the script for the display, not for the actual combat.
Yes, but people were using the numbers this script displays in their calculations. The point is that they would do similar calculations everywhere. The game stores the exact number of hit points for each unit. Why would it also be storing some arbitrarily truncated strength number? It isn't. It's using the above formula.
 
Burebista said:
If first strikes are rounds of immunity, then for the case when both the attacker and the defender have x and y first strikes respectively, this new theory is equivalent to the old x-y theory. Am I missing something?

The end result is the same, but not the display.
 
Reference Material for the next post

For each 10% strength increase over an adversary
  • 00% - 50% chance of victory
  • 10% - 68% chance of victory (Combat I)
  • 20% - 73% chance of victory (Combat II)
  • 30% - 77% chance of victory (Combat III)
  • 40% - 88% chance of victory (Combat IV)
  • 50% - 90% chance of victory (Combat V)
  • 100% - 99% chance of victory

For each Drill Promotion against an equal adversary without promotions
FSC - First Strike Chance; FS - First Strike, C1 - Combat I (Free for agressive civs)
  • Drill I -- 1 FSC - 53.4% chance of victory
  • Drill I -- 1FS, 1 FSC - 60.2% chance of victory
  • Drill I -- 2FS, 1 FSC - 67.1% chance of victory
  • Drill I -- C1, 1FSC - 73.8% chance of victory
  • Drill I -- C1, 1FS, 1 FSC - 77.2% chance of victory
  • Drill I -- C1, 2FS, 1 FSC - 82.5% chance of victory
  • ---------
  • Drill II -- 1FS, 1 FSC - 60.2% chance of victory
  • Drill II -- 2FS, 1 FSC - 67.1% chance of victory
  • Drill II -- 3FS, 1 FSC - 70.3% chance of victory
  • Drill II -- C1, 1FS, 1FSC - 77.2% chance of victory
  • Drill II -- C1, 2FS, 1 FSC - 82.5% chance of victory
  • Drill II -- C1, 3FS, 1 FSC - 83.9% chance of victory
  • ---------
  • Drill III -- 1FS, 3 FSC - 67.0% chance of victory
  • Drill III -- 2FS, 3 FSC - 73.9% chance of victory
  • Drill III -- 3FS, 3 FSC - 76.7% chance of victory
  • Drill III -- C1, 1FS, 3FSC - 84.0% chance of victory
  • Drill III -- C1, 2FS, 3 FSC - 89.3% chance of victory
  • Drill III -- C1, 3FS, 3 FSC - 90.7% chance of victory
  • ---------
  • Drill IV -- 3FS, 3 FSC - 76.7% chance of victory
  • Drill IV -- 4FS, 3 FSC - 80.7% chance of victory
  • Drill IV -- 5FS, 3 FSC - 83.5% chance of victory
  • Drill IV -- C1, 3FS, 3FSC - 90.7% chance of victory
  • Drill IV -- C1, 4FS, 3 FSC - 96.1% chance of victory
  • Drill IV -- C1, 5FS, 3 FSC - 97.5% chance of victory
 
Ran a simulation of 301 Japanese Samurai (Combat I, 50% vs Melee, 2 First Strikes) vs 301 Mongolian Macemen (Combat I, 50% vs Melee). Samurai on the offense (43 stacks of 7 each).

Odds were 8.8 vs 8.8 (according to Civ's calculations).

The results were Samurai 175 Wins 126 Losses (58.1% Victory). 2 First Strikes give a small advantage when fighting a unit of equal strength (according to this data)

An 8.1% advantage doesn't seems to follow what I would mentally calculate...

On average 2 First Strikes will damage a unit of equal strength 20 HP (0, 20, or 40hp of damage being the possibilites, and assuming first strikes are calculated like regular rounds, in this case each having a 50% chance to hit and the total strength at the beginning of the battle used throughout the calculation, unlike Defensive Bombard in Civ III).

From http://c4combat.narod.ru/c4c_v0_13.htm I get 63.67% chance to win for the Samurai. 1 standard deviation = 60.898% to 66.441%, 2 sd = 58.127% to 69.212%. We are at the 2sd/3sd boundary with our data, about a 0.3% chance of happening (assuming the maths are correct in the calculator, which I think they are). Either the data are an extreme case (someone else can do this test again and compare notes) and both the calculator and first strikes are functioning properly, the combat calculator noted above is wrong and first strikes are working properly, or the calculator is correct and first strikes are not working properly.

Assuming the calculator is wrong, the new value for victory is 58.1% which gives us a s.d. of 2.84%. 68% of the time, the samurai will win 55.26% to 60.94%. If the next test is within this range (giving us 602 sample cases), it will confirm that first strikes are indeed broken or that there is some information of how they function that we do not know...

... A couple of hours later

Tested 497 more battles. For these the Samurai won 326 out of 497 (65.59%). Total for all battles is 501/798 = 62.782%. Close enough to call it good.
First Strike appears to be working properly and gives an overall ~ +7% (6.835%) chance of victory for EQUAL strength units
(62.782 - 50)/2 First Strikes = 6.391% per first strike in this simulation.

Tested 1,050 battles of Samurai vs American Knight (Immune FS) -- (Odds show as 8.8 v 10.0)
Combat Calculator above figures odds at 30.133% victory for Samurai
Actual Testing: 346 Wins, 704 Losses = 32.952% victory for Samurai
Immune to First Strike appears to be working properly

Tested 1,120 battles of Samurai vs Mongolian Maceman -- (Odds show as 8.8 v 8.8)
Samurai has 0-10 first strike chances, Combat I; Maceman has Combat I
Combat Calculator above does not figure odds
Actual Testing: 857 Wins, 263 Losses = 76.52% victory for Samurai
--------
Using an 8.8 vs 8.8 battle as 50% victory. We can work backwards and calculate that each First Strike Chance has a (76.52 - 50)/10 percent chance of increasing victory (2.7% increase per chance). This is not that far off from my estimate of 3.5% for each FSC (see below). The difference could be that not all FSCs above 7 had a chance to hit since there were in most cases 7 Samurai vs 7 Macemen. If we factor this in, and divide by 7 instead of 10 we get 3.79% which is very close to the estimate of 3.5%
Each First Strike Chance gives an overall +3.5% chance of victory for EQUAL strength units assuming FSC are 1/2 as likely as FS.

In conclusion, as I believe has been confirmed elsewhere, First Strikes work the best when the units are closest in strengths with the optimal configuration being equal in strength. For equal strength (this will be its best case), each First Strike equals approximately 7% increase in the chance for victory (3.5% for first strike chances). In all cases I would go for the Combat upgrades as they give you the full 10% strength bonus (18% increase in the chance for victory for same strength adversaries) against all units (that 7% for first strike will fall dramatically as the strength between units differ).

To make first strikes more attractive, the developers or modders, could remove first strike chances from Drill and have only first strikes. Still weaker than the combat promotion option, but better than it is now (something along the lines of Drill I thru IV - 1 FS and a 4% combat bonus for each; this would have to be tweaked to make sure FS's are not lethal, allowing for at least one round of normal combat) Making first strikes always hit would make them too powerful. As a sidenote, in my mod I have Drill modded as above (Drill requires disipline, at least that is what my drill instructors told me :) , and disipline makes a better soldier)

I think a balanced solution is to have every first strike (not first strike chance) give full damage when it hits and half damage when it misses (to simulate the element of surprise). Instead of a first strike for equal unit strengths dealing of average 10 hp of damage (0hp for miss or 20hp for a hit), they would average 15 hp (+10.5% chance to win) of damage for each strike (10hp - 20hp).

Also, make each first strike chance 50/50 for equal strength units (decide ratio by a normal battle round calculation). Then if you have an available chance, calculate the same as above, if the chance fails no damage is done. So each first strike chance on average (against equal strength units) would be 0hp for a missed chance, 10hp for a successful chance that misses (first strike), 20hp for a successful chance that hits (first strike). Averaging 7.5 hp (+5.25% chance to win) of damage for each first strike chance.

As it stands currently, the Japanese Samurai and the Chinese Chokonu have 2 first strikes available, the most of all units before upgrades. This gives the Samurai an equivalent strength rating of 9.92 (8 + 24%; Combat I and 2 First Strikes) verses other strength 8 units. A Samurai that uses it next four promotions for Drill I-IV will have an equivalent strength rating of 12.64 (8 + 58%; Combat I, 5 First Strikes, 3 First Strike Chances). A Samurai that uses it next four promotions for Combat II-V will have an equivalent strength rating of 13.12 (8 + 64%; Combat I - IV and 2 First Strikes).

Under the proposed balanced system above, a Samurai that uses it next four promotions for Drill I-IV will have an equivalent strength rating of 14.26 (8 + 78.25%; Combat I, 5 First Strikes, 3 First Strike Chances) instead of 13.12 with Combat promotions.

As the system currently is, it works out similarly for an American Maceman for instance. A maceman that uses it next four promotions for Drill I-IV will have an equivalent strength rating of 10.52 (8 + 31.5%; 3 First Strikes, 3 First Strike Chances) as opposed to 11.2 (8 + 40%; Combat I-IV)

Under the proposed system, a maceman that uses it next four promotions for Drill I-IV will have an equivalent strength rating of 11.78 (8 + 47.25%; 3 First Strikes, 3 First Strike Chances) as opposed to 11.2. This creates a choice, do I go for the long term benefit of the combat promotions or do I need the higher bonuses now, because I am fighting units of equal strength. This proposed system increases the benefit of Drill for units that initially have 1-2 first strikes also.

The modifications above would not be unbalancing because as strength differs, the value of first strikes decline, only being valuable when strength are near equal. As it stands now, first strikes are good if they are given away as freebies (obviously), but they are not worth the selection in promotions regardless of the fact that your unit may have 0-2 first strikes given to it. Drill over Combat promotion cannot be justified under any circumstances currently (v1.09). Stick with the Combat promotions over Drill , unless something changes in the next patch.
 
Something else I like about your suggestion, BomberEscort, is that the standard combat promotions open up many other possibilities. So sacrificing a bit of strength (ie not picking drill) to open up that flexibility seems only fair.

ew
 
But removing "chance" of first strikes hitting, to actual hits of varying strength, makes some fights default victories, which I think is a bad idea. This will be especially true against damaged but strong units.

This way samurai will do very well against more advanced units on the offensive, since they will probably be damaged often attacking. Not a good solution imo.

But I agree of course that first strike is one of the weakest upgrades in the game generally.
 
Luhh said:
But removing "chance" of first strikes hitting, to actual hits of varying strength, makes some fights default victories, which I think is a bad idea. This will be especially true against damaged but strong units.

If you notice in my post above, making this change results in very little benefit. It is just enough to make the Drill promotion of more value than the combat promotions under certain circumstances. For the samurai it results in an increase of 14% against other 8.8 strength units only. The value will decline as the strengths differ.

Luhh said:
This way samurai will do very well against more advanced units on the offensive, since they will probably be damaged often attacking. Not a good solution imo.

There is still a normal combat round, and the damage that would be dealt by a first strike that misses (1/2 damage) would be very small if the unit strengths varied greatly. As I also noted above first strikes could not be lethal, to guarantee at least one round of normal combat. Also any fully healed inferior unit has a good chance of defeating a severly damaged superior unit as the game is now.
 
There is another statistic that is interesting besides the basic chance to win a battle and that is the amount of hitpoints left. This is an interesting statistic when one unit has to defeat many. If the strong unit that has to defeat many units has a big chance to win the first combat but is left with only half its strength (on average) then it will not win the other ensuing battles against the other weaker units. Another example is when you're on the offensive and you don't want your offensive battles to be slowed by heavily wounded units that need to heal before they can fight again.

First strikes can be useful to avoid damage if your units are (a lot) stronger than the enemy units. This is a situation that can occur when you're technologically more advanced or if your units have large combat bonuses from cities.

To show this I used the combat calculator that you linked to.

Case 1: Unit A (St 50) vs Unit B (St 5): Average hps left when A wins: 97.6
Case 2: Unit A (St 16, 4 First Strikes) vs Units B (St 5): Average hps left when A wins: 99.0

So a strength 16 unit with 4 first strikes is better in number of hps left than a strength 50 unit against the weak strength 5 unit (not in the basic chance of winning). I bet that a strength 25 unit with 4 first strikes can defeat more strength 5 units in a row than a strength 50 unit can.

I know that this is an extreme example and will not typically occur, but it is only used here to show an advantage of first strikes. I will not try to defend that first strike promotions are better than basic combat promotions (because I don't think they are) or even that they are well balanced. But they are more useful than people might think after reading the posts above mine. I personally think that your modding might have overpowered first strikes a bit. I would go for a setting somewhere in between the Firaxis settings and yours.

Good luck with any further analysis of this difficult subject.:thumbsup:
 
I understand your points and I agree with them (except the overpowering issue). But, if you have such an overwhelming technological advantage, you are going to win anyways. Also, an advantage that is unlikely to happen is the same as no advantage at all IMO. About the waiting to heal before attacking, just get the March promotion and heal on the move. It's cheaper (available after Medic I), than Drill IV.
 
BomberEscort said:
I understand your points and I agree with them (except the overpowering issue). But, if you have such an overwhelming technological advantage, you are going to win anyways. Also, an advantage that is unlikely to happen is the same as no advantage at all IMO. About the waiting to heal before attacking, just get the March promotion and heal on the move. It's cheaper (available after Medic I), than Drill IV.

Okay, maybe it was not such a good move to provide an example that was not realistic. This example was only used to exaggerate the point that I was trying to make.

Here an example that could happen with an equal tech level. Unit A has basic strength 6 and a 100% defense bonus (castle or a unit fortified in a city on hills with a wall or some large culture defense bonus combined with fortifying bonus or...). Unit B attacking the city has strength 6.
Unit A has a 40% bonus from combat promotions -> strength 6 + 140% of 6 = 14.4 vs unit B strength 6. Expected hit points left if unit A wins: 78.6
Unit A has 4 first strikes -> strength 6 + 100% of 6 = 12 and 4 first strikes vs unit B strength 6. Expected hit points left if unit A wins: 90.7

4 first strikes help a unit more with defending the city against a horde of equal tech level attackers because it wouldn't lose its hit points and thus its strength as fast.


Unit A has a 50% bonus from city defense promotion and 20% combat promotion -> strength 6 + 170% of 6 = 16.2 vs unit B strength 6. Expected hit points left if unit A wins: 82.3.

4 first strikes help a unit more with defending the city against a horde of equal level attackers than 2 levels of the city defense promotion + 2 levels of standard combat promotions because it wouldn't lose its hit points and thus its strength as fast.


Why do first strikes work so well in this case? Simply because 4 first strikes from a stronger unit (modified strength is a lot greater) will do heavy damage to the other unit before it can actually combat the first strike unit.
First strikes become 'exponentially' stronger when a unit has more of them because the relative amount of hit points left on the opponent is very low. A unit A with one first strike might damage unit B for only 20 damage on average before real combat ensues. But a unit A with 4 first strikes will sometimes outright kill unit B before any real combat ensues. It will at least do some heavy damage against unit B before real combat ensues.

Because of the above argument, I think that Firaxis made a mistake with the first strike promotions. The first few levels of first strike should be relatively easy to acquire because they aren't worth much, but the later levels should be more difficult to acquire because these are worth much more (except when the enemy is immune to first strikes). Because of the option of immunity to first strike enemies, I think that a balanced first strike progression would be a flat +1 first strike per level of the first strike promotion, with an extra first strike at the first level of this promotion.
So:
level1: +2 extra first strikes
level2: + 1 extra first strikes (for a total of 3)
level3: + 1 extra first strikes (for a total of 4)
etc.
It would be a pretty powerful promotion type when the 'first striker' gains significant combat bonuses from a city or so, but it would still be inferior to the combat promotions in the open field (if I read your previous posts correctly) and it could be countered easily by units that are immune to first strikes.

What do you think?

edit: calculation mistake
 
bottom line of combat calculations: Dont attack with injured units.Yesterday I was in an MP game where I player bombarbed my city down to 0% defense and used his catapults to attack, but then decided to bypass it in favor of one which I was unable to reinforce. Before his stack moved on to the second target, I had bombarbed his 15 unit axe/cat stack with 6 cats. The second city had city defense 20% and on a hill w/ 2 longbow (City def I & II) and a catapult. All his units died on that attack. I checked the combat log and the percentages with ~90% win for me in most cases.
 
Roland Johansen said:
...Here an example that could happen with an equal tech level. Unit A has basic strength 6 and a 100% defense bonus (castle or a unit fortified in a city on hills with a wall or some large culture defense bonus combined with fortifying bonus or...). Unit B attacking the city has strength 6...

I agree with your calculation, but my examples above were for units of equal modified strength. I didn't say this explicitly, I said equal strength, but my examples show equal modified strength. I could have been more clear on this point. In your example above, I do not believe that an experienced player would attack with unit B in this situation. But I understand your point :)

Roland Johansen said:
...4 first strikes help a unit more with defending the city against a horde of equal level attackers than 2 levels of the city defense promotion + 2 levels of standard combat promotions because it wouldn't lose its hit points and thus its strength as fast...

Using 6.0 vs 6.0 Modified Strength

Defender = 6.0 w/ 4 First Strikes
Attacker = 6.0
Defender Win = 76.4% (63 hp left)

Defender = 6.0 w/(CG I & II; CI & II) = 7.65
Attacker = 6.0
Defender Win = 76.0% (53hp left, in a city heals at 22% per turn)

Not much of a difference, factor in that the latter promotion path is open to all units, whereas the former promotion path is open to Archery, Siege, Armor, and Chopper Units. More often that not, it will be archery units that have Drill IV since they are on the scene first and have longer to get promoted. Plus nothing upgrades to Tanks, choppers do not get a defender bonus, ships can't defend cities, and the highest unmodified Archery unit strength is 6 with 2 FS for the Chokonu (granted he upgrades eventually to MechInf, but if you are at this tech level, your probably going to win with or without first strike capability). I would say in the vast majority of examples, the fact that the second promotion path is available to more units makes it more valuable that its lacking 0.4% in survivability and the extra 10hp.

Roland Johansen said:
...But a unit A with 4 first strikes will sometimes outright kill unit B before any real combat ensues...

I am not certain that FS are lethal I will have to test this somehow. I don't think they are though.

Roland Johansen said:
...Because of the option of immunity to first strike enemies..., I think that a balanced first strike progression would be a flat +1 first strike per level of the first strike promotion, with an extra first strike at the first level of this promotion.
So:
level1: +2 extra first strikes
level2: + 1 extra first strikes (for a total of 3)
level3: + 1 extra first strikes (for a total of 4)...

This isn't far from what I've modded and suggested: 1 FS and +4% General Combat bonus for Drill I - IV [(@ Drill IV +4 FS & +16% Combat Bonus) vs (+5 FS and No Combat Bonus)] (see a few posts up)

Roland Johansen said:
What do you think?

I think for the most part we are on the same page and I believe that eventually I will turn you to the dark side!!! ;) ... In all seriousness, I think we are saying similar things, you tend to value a few extra hp more that I do, where I favor healing on the run (March). We both get the 22% healing bonus in cities though. In the end it may come down to different playing styles, but I still think Combat promotions are better than Drill promotions for the reasons listed throughout my posts. I will have to set up a city taking scenario with and without FS Defenders and see how it goes.
 
BomberEscort said:
I think for the most part we are on the same page and I believe that eventually I will turn you to the dark side!!! ;) ... In all seriousness, I think we are saying similar things, you tend to value a few extra hp more that I do, where I favor healing on the run (March). We both get the 22% healing bonus in cities though. In the end it may come down to different playing styles, but I still think Combat promotions are better than Drill promotions for the reasons listed throughout my posts. I will have to set up a city taking scenario with and without FS Defenders and see how it goes.

OK, I agree with your post all the way, except on the point that I will be turned to the dark side...:p

I think the first striker will be at its greatest strength when defending a city, that's why I used that example. Arathorn was also saying that first strikes weren't that good (he agrees with you), so I wanted to present a situation where they could be relatively good. Arathorn also argued that first strikes provided the greatest benefit when fighting units of equal strength (do you agree with this?). This is absolutely true when looking at the chances of victory. But a single victory won't win the war, so the hitpoints with which the unit is left are also important. If a unit is attacked multiple times in a turn (no time for healing), then it is very important to lose as few hitpoints as possible. I think that a unit that is promoted a lot with the first strike promotions will be very able in defending cities. The first few first strike promotions are rather worthless though, so that's why I suggested the change.

If you look at the strength of the modified first strike promotions, then our suggestions are quite comparable. I just want the first strike promotion to be very different from the combat promotions. That will make it more difficult to balance, but it might make the ingame choice between combat and first strike promotions more interesting. With both of our suggestions the first strike promotion will be valuable from the first level of this promotion. Something that is clearly not true for the Firaxis model.
I consider both models superior to the Firaxis model, but there can be only one....:ninja:
 
The following tests revealed something interesting...

The first battle was 300 Musketman (9.0) vs 300 Samurai (8.0; 2 FS)
165 Musket Wins (55%) Calc Predicts (57.4)
First Strikes work on Defense

The second battle is the strange one.

300 Cho-ko-nu vs 300 Immortals (6.0; 2 FS vs 6.0; +50% vs Archers)

Results = Cho-ko-nu win 82% (Calc predicts 63.6%). This is unusually high, I wonder if this has something to do with the way +50% vs Unit Type bonuses are handled or maybe Immortals can retreat when defending. I will confim this in the next battle.

The Third battle is 300 Cho-ku-Nu vs 300 Jaguar on Forested Hill
(6.0; 2FS; +50% vs Melee vs 6.3; +75% Tile Defense)

Results = Cho-ku-nu win 82.3% (247/300)(calc predicts 47.1%)

The previous two are strange results... Any ideas anyone??

Fourth battle
300 Samurai (2 FS; +50% vs Melee) vs 300 Musketman (8.0 vs 9.0)
Samurai wins 134/300 (44.7%) (Calc predicts 42.6%)

Summary:

Battle #1: First Strike works on Defense
Battle #2: Defender has Unit Bonus vs First Strike Attacker w/ No Counter Unit Bonus (Strange Results)
Battle #3: Attacker has Unit Bonus and FS vs Defender (Strange results)
Battle #4: Attacker has No Unit Bonus and has FS vs Defender (Results Good)
Battle #5: Defender has Unit Bonus vs First Strike Attacker w/Counter Unit Bonus (Results Good)(See First Battle Here)

There appears to be something happening with first strikes when:
a) (Defender has Unit Bonus against FS Attacker) vs (First Strike Attacker w/ No Counter Unit Bonus)
b) (Attacker has Unit Bonus against Defender and FS) vs (Defender w/ No Counter Unit Bonus)

Update: Nevermind, the Cho-ko-nu can cause collateral damage. This is why its win% is so high. This is a good unit!! Like having a 6 Strength Archery unit and a 3 strength siege unit in ONE unit!!
 
BomberEscort said:
As it stands now, first strikes are good if they are given away as freebies (obviously), but they are not worth the selection in promotions regardless of the fact that your unit may have 0-2 first strikes given to it. Drill over Combat promotion cannot be justified under any circumstances currently (v1.09). Stick with the Combat promotions over Drill , unless something changes in the next patch.

I disagree. As it stands now, first strike is better than combat in some circumstances. For instance, in city defense, i would take first strike over combat if i think that my defender can beat off multiple attackers. Archers are so powerful as city defenders that it often takes 3 or 4 opposing units for every archer taken out. With or without first strike, the archer will win the first fight or two. But with first strikes, he'll win those lopsided battles with more HP remaining, making it harder to take him out in subsequent battles. Instead of losing 3 units before killing the archer, you might end up losing 4.

Edit :
I see that Roland Johansen beat me to it. Then let me just say that i agree with him!
 
Zombie69 said:
I disagree. As it stands now, first strike is better than combat in some circumstances. For instance, in city defense, i would take first strike over combat if i think that my defender can beat off multiple attackers. Archers are so powerful as city defenders that it often takes 3 or 4 opposing units for every archer taken out. With or without first strike, the archer will win the first fight or two. But with first strikes, he'll win those lopsided battles with more HP remaining, making it harder to take him out in subsequent battles. Instead of losing 3 units before killing the archer, you might end up losing 4.

Edit :
I see that Roland Johansen beat me to it. Then let me just say that i agree with him!

Remember, First Strike is only good when you are equal to or stronger than your opponents. If they are stronger than you it is better to go for the City Garrison and Combat promotions over Drill. Plus Combat Promotions open up other avenues (Blitz, Amphibious, etc.), Drill is a dead-end.

It is possible for Drill IV to be useful IF you upgraded your Drill IV archers to MechInf (20% Intercept) AND your opponent was just as advanced and was not using Air Power. That is a big IF... By the time bombers are on the scene they can strike your offensive first strike units with impunity (unless you have SAM Infantry, but even they only intercept 40%, and unlike Civ III, inteception does not automatically destroy the air unit). So eventually your stacks will be 1/2 strength and can be easily mopped up by his Combat V units. Drill is practically worthless when Bombers arrive. Combat V is forever!!! ;)
 
I've never played a Civ 4 game (admitedly i haven't played many yet) or Civ 3 for that matter where i've seen any air unit at all. My games end long before that. In fact, the farthest i've ever been in technology in those games was getting to Cavalry in Civ 3 once or twice. So the bomber argument for me is null and void.

My games are usually decided in the ancient era. By the time this is over, i pretty much know who's gonna win. In the ancient era, archers are top notch defensive units. They can, and will, beat off many attackers. Especially if the city was put on a hill. For this, first strike can be absolutely awsome. I think you underestimate this promotion a lot. I wouldn't change it at all. For me, it's perfect as it is.
 
I think many of you are underestimating first strike. While one isn't impressive, the effects of multiple first strikes are cumulative. Think of it as free bombardment.

While generally, if a unit has inferior combat strength, combat promotions will be better, consider that your defenders will sometimes inevitably be bombarded by multiple units, and that inferior combat strength or inferior numbers will be inevitable. First strike is often the better call in these cases, especially vs units that deal collateral damage.
 
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