Barracks during axe rush?

[Habitus]

Yeah if i remember right CR3 = 75% in total, and archer with CG1 has 70% so the archer gets a 5% penalty to strength. What i can never remember is if its

Archer = 3 (Base Strength) * 1 (Strength Mods ie Combat) * 0.95 (Terrain Mods ie City) * 1.2 (Culture) * 1 (Unit Mods ie vs Melee) * 1.25 (Fortification) = 4.275

or

Archer = 3 * 1 * 1.4 (All non-Combat Mods combined) = 4.2

*edit*

Hmm 4.2? not sure how your getting that?

*edit*

LoL forgot fortification bonus

 

[ben-jammin]

Yeah if i remember right CR3 = 75% in total, and archer with CG1 has 70% so the archer gets a 5% penalty to strength. What i can never remember is if its

Archer = 3 (Base Strength) * 1 (Strength Mods ie Combat) * 0.95 (Terrain Mods ie City) * 1.2 (Culture) * 1 (Unit Mods ie vs Melee) = 3.42

or

Archer = 3 * 1 * 1.15 (All non-Combat Mods combined) = 3.45

*edit*

Hmm 4.2? not sure how your getting that?

The archer has its 50% city defense bonus, 20% from city garison, 20% from culture, and 25% from fortification for a total of 115%. I just used this as an example because that's usually the defense I look for when i'm rushing, a city that isn't on a hill with low culture bonus and the AIs better units defending or attacking elsewhere. CR3 is as you said a 75% bonus, so the archer's total bonus strength is 40%. at full health that means it's at 4.2 (3 * 1.4) against 5, though it also gets its first strike which I don't think is actually included in the combat odds the game displays.

 

[Habitus]

Yup noticed I what i'd forgotten just before you posted. But atleast i can see that it is all non-Combat mods that are added together to get final mod, rather than compared individually to modifier the strength.

As far as i know only Combat is pure Strength mod and there for applied to Attacker/Defender without being compared to each other, ie if attacked by a Combat 3 Axe instead of CR3 Axe Archer would be 6.45 vs Axe 6.5 instead of 4.2 vs 5.

In game Combat Odds do take First Strikes into account after one of the patchs (90% sure).

 

[AbsoluteZero]

That's a really disingenous argument-you need to kill every archer in the city, not just 1, and 3 axes are much better for that than 1. Combat mechanics don't even work that way- all modifiers go to the defender except combat promos.

It's hard to calculate because of the whacky way the game treats defense / attack bonuses, but there are many cases where 1 extra level can mean double or more the odds of success.

I would rather have 2 less axes and give all my axes potentially twice the odds of killing an enemy.

In any case the cost vs added effectiveness of 1 barracks is pretty low provided you get enough axes from that city.

 

[VoiceOfUnreason]

It's hard to calculate because of the whacky way the game treats defense / attack bonuses

It's not really that hard, it's just tedious. There are only a handful of outcomes (Example: Archer wins with 100/83/66/49/32/15 hp left, Axe wins with 100/77/54/31/8 hp). If the archer ends at 100, you are right back where you started, and the remaining calculations all have fewer terms to worry about (the archers are weaker, so the axe does more damage).

The actual percentages you can obtain either by calculation, or by mocking up the situation in a world builder save (with hundreds of units of each type) and then letting the combat engine tell you the answer.

In any case the cost vs added effectiveness of 1 barracks is pretty low provided you get enough axes from that city.

Which just takes us back to the beginning - how many is enough? Does a secondary city have enough time to produce "enough" axes?

 

[Dirk1302]

This is all getting pretty mathematical and doesn't take into account the convenience of whipping the barracks and have 10 H overflow to your first axe (provided you set your empire up for this correctly). Ras also made that point independent of me. It's a valid point and probably more important (for practical play at least) than comparisons between cr1 and c1.

 

[AbsoluteZero]

It's not really that hard, it's just tedious.

Given all the different scenarios it's basically incalculable.

For instance:

A 25% fortified archer in a city with 20% cultural defense and no other bonuses

vs

A CR II axe gets 63.01% odds of victory

but

A CR I axe gets only 28.79% odds of victory

However if you take away the fortification bonus then the odds of victory is almost the same for both axes ( around 60% ).

How do you know what fortification bonus you're going to be up against? You don't. You also don't know the enemies promotions, or the defensive bonuses you're going to face. They might get walls, they might not. They might get a border pop, they might not. They might get axes in a city, they might have only archers / chariots / spears.

If only combat odds were calculated in a more logical way, there would be a clearer cut answer. Building a barracks would always result in x added value to troops.

 

[VoiceOfUnreason]

Given all the different scenarios it's basically incalculable.

There aren't that many scenarios, given reasonable assumptions about the problem. And if it turns out that some interesting scenario is too close to call, then you call the decision a wash, or worry about secondary considerations like how double whipable a barracks is.

For example, the only thing that matters is the defenders net bonus - you don't care at all about 20% fortified in a 20% city or 0% fortified in a 40% city. And since we are pre-catapult, the bonus is always some multiple of 5 - so if you do 41 cases, then you've got every combination from 0% to 200%.

Likewise, the hit points of the defender matter, but not how he got there. Assuming the attackers are all alike, the chunks of damage that will be dealt can only get bigger, never smaller. That cuts out a big chunk of cases: instead of worrying about 100 different hit point levels, you only need to worry about 20 or so... maybe 30 if the archer is much stronger than the axe.

So you calculate each of those probabilities for a single axe, which produces a matrix, and then to find out how like n axes are to kill the archer, you just multiply the matrix n times.

Yeah, doing that more than once by hand sucks - so you do it by hand once, then roll it into a spreadsheet and check the result. In other words, it's a simple combat calculator that expresses not the odds of success, but the probability of how many units you need to kill the defender.

That's how you do it if you want an exact answer. If you are willing to settle for an approximation, you write a program to create a map with 1000 of the units you want, stack attack, save the map, and then parse the results to get the probabilities.


Once you have number of axes to kill one archer, number of axes to kill two archers isn't terribly difficult: you compute the the probability that exactly k axes kill the first archer and N-k or fewer axes kill the second (that's not exactly how game plays out, because it will swap the best defender around on you, but it give the same result), and add up the combinations.

What are the odds that N axes kill M archers? exactly k killing one times N-k killing M-1, summed over all K. And on it goes. The calculations not getting any more difficult, because you are re-using the same results again and again. It's just tedious.

How do you know what fortification bonus you're going to be up against? You don't. You also don't know the enemies promotions, or the defensive bonuses you're going to face. They might get walls, they might not. They might get a border pop, they might not. They might get axes in a city, they might have only archers / chariots / spears.

Bushwa -- you're writing as though to have any confidence in an answer we need to correctly evaluate every possible position to all eleventy decimal places.

Check a common case, preferably somewhere near the median of the likely candidates. Find an answer there. Take a few more cases in orthogonal directions to establish whether or not there is a gradient.



Fundamentally, the kind of question we're asking here is akin to the question of whether to train a worker first or a warrior first. We certainly don't have enough information at turn zero to calculate the odds of winning if we play worker first. Yet even in our ignorance we're able to make a recommendation that works out quite well most of the time.

 

[VoiceOfUnreason]

That's how you do it if you want an exact answer. If you are willing to settle for an approximation, you write a program to create a map with 1000 of the units you want, stack attack, save the map, and then parse the results to get the probabilities.

Umm... don't do that.

In theory, it's an excellent way to see what's going on.

In practice, it pins a CPU for I don't know how long. My quick supposition is that it really gets bogged down trying to figure out best attacker/best defender over and over again. I've done tests with 100 units vs 100 before, but 1000 vs 1000 needs a bit more patience than I have for this.

 

[oldskald]

I've followed this debate with interest and no-one has mentioned another factor which could influence whether a player might want to go for barracks spam; what the other side has!

If I'm facing a civ with the PRO trait + archery, or AGG + melee units, or perhaps an early UU, then this might influence me towards getting the best promoted units I can find for a rush. Gandhi, otoh, can be rushed with less care about promoting units.

 

[AbsoluteZero]

@VoiceOfUnreason

Most of your post is jibberish. Seems to me you're arguing for it's own sake.

Perhaps you could clarify what you're trying to argue with me about first.

Or maybe you could re-read your own posts when you sober up.

 

[ben-jammin]

This is all getting pretty mathematical and doesn't take into account the convenience of whipping the barracks and have 10 H overflow to your first axe (provided you set your empire up for this correctly). Ras also made that point independent of me. It's a valid point and probably more important (for practical play at least) than comparisons between cr1 and c1.

Let's also not forget that barracks make an easy and efficient 2-pop whip that overflows into the next unit, whereas 2pop whipping axes can be tricky and unless you super micromanage will require you to whip without any hammers already in em with the penalty.

It doesn't need to be complicated t ofigure out if the barracks were worth it. Each one pays for itself as long as two promoted axes survive where unpromoted ones would have died. It's not exact but it doesn't need to be, and IMO a city that's going to produce a dozen plus promoted axes is inevitably going to have fewer suicides. Any survivors then get CR2 and the odds snowball. I wouldnt bother with a barracks where less than half a dozen axes are going to be produced unless you've got a bunch of stolen workers and plenty of forests.

I think a more interesting question is...how many stables (if any) do you build for a HA rush?

 

[Dirk1302]

Missed that, you're right imo . I tend not to do HA rushes but i would build stables for sure if i was going for one. Cat/Phants have a reasonable window of opportunity also on deity. I tend to build a stable in the capital and sometimes in one other city and train all mounted units there while building cats in the other cities.

 

[ben-jammin]

Missed that, you're right imo . I tend not to do HA rushes but i would build stables for sure if i was going for one. Cat/Phants have a reasonable window of opportunity also on deity. I tend to build a stable in the capital and sometimes in one other city and train all mounted units there while building cats in the other cities.

I always assumed the idea with a HA rush was the same as for cavalry, that you'd use espionage to take down cultural defense if at all so they don't get slowed down. But then i've never been much good at any kind of early rush above emperor.

 

[Mantic0re]

I'm not in the same league as most of you guys so this may be a moot point.

Axe rushes come early...and generally the capital and second city tend to be decent producers throughout the game. It makes sense to build a barracks in a city like this for future wars. The question really seems to be more about timing and whether you build the barracks before the axe rush or after during the recovery phase.

If I have reason to think the combat odds will be this narrow and the margin of victory so small I shouldn't be going to war.


I think the ideal answer depends more on your leader traits (how difficult can recovery get) the target, surrounding AI's, space and quality of land available, etc,.


As a general rule of thumb I like Dirk1302's mention of 2pop whipping. Hell if we are gonna do it, lets build them early and use our overflow hammers. It gets hard to work the overflow magic when building only units (as you do in war). This way seems to earn two birds with one stone.


Macro generally trumps Micro right?

 

[Dirk1302]

@ben
Cav Rushes can be done without espionage. Lb's and pikes are not a big problem for c2 cavs. It gets a bit harder against muskets and you'll lose some against grens. The last 2 are relatively rare however since they can't be upgraded from lb's. Lately there have been some examples of cav rushes against (protective) rifles here on the forum, be sure to have enough cavs in that case, you also need Zeppelins in that case to weaken the defenders 20%.

 

[VoiceOfUnreason]

Umm... don't do that.

In theory, it's an excellent way to see what's going on.

In practice, it pins a CPU for I don't know how long. My quick supposition is that it really gets bogged down trying to figure out best attacker/best defender over and over again. I've done tests with 100 units vs 100 before, but 1000 vs 1000 needs a bit more patience than I have for this.

On the other hand, I was going to sleep anyway, so I let the game run over night. At some point, it did actually produce an answer.

Archers, 83hp, defending with 115% bonus, against 100 hp Axemen with no promotions.

The displayed combat odds that you see are 5.00 vs 5.35, 39.3%.

Doing the experiment, we see
390 Archers killed (that's a match)
127 Archers alive with 11hp
162 Archers alive with 29hp
143 Archers alive with 47hp
124 Archers alive with 65hp
54 Archers alive with 83hp

Do this experiment 5 more times, and you have the data you need to correctly calculate the odds that two vanilla axes will kill a healthy archer at 115%.

Do it 20 more times (approximately) and you can calculate the odds that any number of axes you want will be able to kill any number of healthy archers at 115%

And yes, if you next wanted to know how it would come out with promoted axes, you'd have to do another 20+ experiments....

OR

You realize that the empirical results match the theoretical results, and do the calculations in a spread sheet. Then, when you want to know how things change when the archer has only 3 turns of fortification instead of 5, or the city has walls, or whatever you like, you change one number in the spread sheet and read the new answers.

You build one spreadsheet
You tweak the defensive bonus 41 times, recording the answers
You change the axe from Level 1 to Level 2, and record another 41 answers.

Now you have everything you need to work out your base cases. Start with a simple one - 4 archers defending a city at 115%. How many unpromoted axes do you need to have a 99% chance of capturing the city in one turn? (grind grind grind DING!) How many promoted axes will get the job done? (more grinding). Hey, it's fewer! Is the difference enough to justify a barracks?

Now do it the same work at 135% If the promoted vs unpromoted decision gets easier, then you don't need to worry about testing all of the other higher bonuses, the answers not going to come back. You go the other way, and test a few points to see if the answer becomes too close to call.

As another test, you add an archer to the defenders, and see if that changes the barracks/no barracks result.


The calculations require a non trivial understanding of probability and combinatorics, and they are tedious to do, but not difficult, and they are finite. I don't recommend the exercise to anyone who just wants to play the game for fun.

But it's not "incalculable".

 

[amanbe]

Macro generally trumps Micro right?

On lower levels generally yes, on deity early game micro is crucial. 1 turn earlier or 1 more unit can very well be the tipping point.

 

[VoiceOfUnreason]

A couple other points:

I'll immediately concede that as soon as you open up the possibility of a second turn of combat, the complexity of the problem explodes - you have to start worrying about how the XP are distributed, and what promotions the AI might choose (or at least what promotions the AI should choose) between turns, and the possibility of counter attack, and reinforcements.... Yuck.

Too many combinations.


You can simplify the problem of discovering "which is better" by recognizing that as the number of hammers invested by a city goes up, the barracks case gets stronger (the expense of the barracks gets amortized over more units).

On the other hand, if you fix the number of hammers, then as the defense gets stronger the odds favor the non barracks case.... 11 level 1 axes might kill 10 level 2 archers in one turn, but 9 level 3 axes never will. That's a somewhat impractical case, as either the odds of success are small enough that you shouldn't make the attempt, or you need to reasonably account for the fact that you can finish off the last couple units on the next round.


In the case where the results are too close to call, you can presumably break the tie by looking at the expected value of the surviving stacks, using any reasonable heuristic.

 

[pi-r8]

This is all getting pretty mathematical and doesn't take into account the convenience of whipping the barracks and have 10 H overflow to your first axe (provided you set your empire up for this correctly). Ras also made that point independent of me. It's a valid point and probably more important (for practical play at least) than comparisons between cr1 and c1.

How about this as a rule of thumb:

First, take a good look at what you'd expect the opponent to have. Can you beat them with an axe rush? If not, don't axe rush! (shocking advice, I know...)

Assuming you can beat them... how difficult will it be? Will you need every possible axe, or can you scrimp a little? If they're protective, you'll probably need everything you can get, but someone like Pacal Gandhi is a lot easier.

If you really need every possible axe that you can produce, I wouldn't make a barracks. I really doubt there's any circumstances there where the barracks will be worth the cost (unless you can make it before hooking up copper, obviously).

However, if you think you can win with slightly fewer axes, than a barracks starts looking good. It reduces losses, reduces upkeep, and it'll be useful later.