03-04-2002 13:39									#31
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quote: Originally posted by Sir Ralph One of the best ancient times army I ever had was one with 2 Horsemen and 1 Impi. That's a great mix. I used it in a lot of wars and it remained even useful after I had Knights. Later, the Impi and 1 Horseman died while the last Horseman survived, and I was able to add 2 Cavalries. This army served me well till I got Tanks.

I haven't read the whole thread, so maybe this was discussed before, but...

I don't recall ever losing any units in an Army till the whole thing died. I've had Armies with 4 units go to 1 HP total for the entire Army. Still all 4 units alive. I can't recall losing all but 1 HP since 1.17f. Did they change this?

	03-04-2002 15:15									#32
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Seems so. I was also surprised, that after a tough battle with a 1 hp army left I was suddenly able to add units again. Although it was with 1.17, it could not be the stack move exploit, because in that case the Impi should have remained and not one of the Horsies.

By the way, what I added were in fact Knights and not Cavalries as I wrote above.

Last edited by Sir Ralph on 03-04-2002 at 16:57

	03-04-2002 16:06									#33
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Hmmm. I've been able to inadvertantly move units out of an Army. But I've yet to see a unit die if the Army didn't die.

Like I said. I haven't seen an Army go to 1 HP with 1.17f yet.

	03-04-2002 17:57									#34
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quote: Originally posted by Dominae Zachriel, your numbers are correct. So are mine. I was just trying to give the odds of getting one or more GLs with a high probability (75%) and near certainty (95%). Saying that you get a GL 50% of the time every eight victories with Elites doesn't mean much to me, to tell you the truth; if it helps you to think of those numbers, so be it. In any case, my post focuses on what you can expect from Heroic Epic, not how likely it is to generate your first GL. Dominae

Good post Dominae. Your numbers were accurate and interesting, no doubt -- with the at least one qualifier. But the qualifier is important. For instance, with 22 elite combats, there is indeed a 75% chance of at least one Great Leader, but there is also a 40% of at least two Leaders, and a 1/6 chance of at least three! I find this very pertinent to your main point.

	03-04-2002 18:11									#35
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Playing today as Japan on deity, the same elite horseman managed to generate 3 GLs in about 5 combats. That's the best I've ever seen, I'd gone all out military and by about 500BC had 3 wonders (Forbidden Palace, Sun Tzus, and Great Library). So to all you who aren't getting GLs - you must really be doing something wrong! Early combat seems to generate almost a guaranteed early leader for the palace, and sometimes you get bonuses like these.

	03-04-2002 19:49									#36
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DrFell,

Sometimes it happens like that. Your example is extreme, but I've seen stuff like it. Failure to generate even one GL is probably equally as likely. Luck 'o the draw.

I've decided on my preferred situation for an early warmongering style game - and it has to do with geography. I want an oblong continent, with me on one end, with three more civs inhabiting the rest. I can then march systematically through these civs, hopefully putting down the forbidden somewhere in the second civ's (former) territory, and end up with a 4-civ (and hence 4 luxury) continent.

Forbidden Palace placement drives me nuts sometimes. I was messing around with a game last night (Japan again) and was on a "Y" shaped continent. I was in the NW part, China in the NE and India in the S. I destroyed China and got a leader, so the FP is in Beijing, but the reality is that my Indian provinces (well, not mine yet...) will always be corrupt. Nothin' I can do. The "Y" shape just doesn't lend itself to the corruption model. It isn't terrible, because at least you have two non-corrupt core areas, but the water inbetween the arms of the Y is wasted. If it was land, it would be partially productive. This is why the barbell shape is best.

Dominae & Zachriel - good stuff on leader generation. I would argue that making an early army is more worthwhile on larger maps, because you will have more units and battles on those maps.

-Arrian

	03-04-2002 19:50									#37
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quote: Originally posted by Zachriel Good post Dominae. Your numbers were accurate and interesting, no doubt -- with the at least one qualifier. But the qualifier is important. For instance, with 22 elite combats, there is indeed a 75% chance of at least one Great Leader, but there is also a 40% of at least two Leaders, and a 1/6 chance of at least three! I find this very pertinent to your main point.

Very true Zachriel. As I'm sure you know, I calculated the stat by figuring out how likely it was to get no GLs with 22 victories, then substracted this number from 1; this gives the figure of getting at least one GL, as you pointed out. I simply neglected to point this out. However, I was trying to analyse the Heroic Epic in terms of guarantees (95% certainty), which (I don't think) is immediately obvious (to me anyway). The only thing my numbers guarantee is getting at least 1 more GL (or at least 2 more, etc.).

Again, thanks for pointing this out.


Dominae

	03-04-2002 20:04									#38
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quote: Originally posted by DrFell Playing today as Japan on deity, the same elite horseman managed to generate 3 GLs in about 5 combats. That's the best I've ever seen, I'd gone all out military and by about 500BC had 3 wonders (Forbidden Palace, Sun Tzus, and Great Library). So to all you who aren't getting GLs - you must really be doing something wrong! Early combat seems to generate almost a guaranteed early leader for the palace, and sometimes you get bonuses like these.

My best score with GLs is with a non-militaristic civ - but with HE, 3 leaders in the same turn (rush 1 wonder and 2 factories). This was at Monarch level with 1.16f.
When I am at war - I start real war only after I have cav. - 1 GL per turn is not unusual.
As it was said before the trick is not to 'sacrifice' the elites in first wave attacks. Keep them for the kill blow against wounded units.
My feeling is also that you increase your GL probability
- if you fight/kill twice in the same turn (you need at least tanks for this);
- if you kill a unit with better (modified) defense than your attack :kill a 1hp infantry (in city) with your 5hp elite cavalry; GL prob. could be based on the attack/def ratio;

	03-04-2002 22:07									#39
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quote: Originally posted by Dry My feeling is also that you increase your GL probability - if you fight/kill twice in the same turn (you need at least tanks for this); - if you kill a unit with better (modified) defense than your attack :kill a 1hp infantry (in city) with your 5hp elite cavalry; GL prob. could be based on the attack/def ratio;

I was under the impression that nothing increases GL probability other than the Heroic Epic. Anyone care to set the record straight?


Dominae

	04-04-2002 01:14									#40
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This thread is excellent. It made me totally revise my view of armies and GLs. Thanks guys.

As as result of my renewed interest, I did some army combat calculations to verify some of the things mentioned here.

1) rpodos' method of mixing units from different eras in an army is much more effective than I thought. When reading about using hormen in armies when cavalry is available, my first reaction was that this would not change the combat results much compared to if the army had only the cavalry units without the horseman. I mean, if you are down to using the horseman to defeat a fortified rifleman in a city, you'll probably lose anyway, no? I was surprised. An army of two cavalries (V), one knight (E), and one horseman (E) wins 84% of the time attacking a rifleman (V) with a 100% defender bonus. Without the horseman, it wins only 76% of the time!

2) Calculating the effective strength of an army by taking the average of the strengths of its units, is surprisingly (to me) accurate.

Examples: (all veteran with defender 50% terrain bonus)
Average strength 3
2 Immortals + 1 pikeman vs pikeman win 90% of the time
3 swordsmen vs pikeman win 91% of the time
Average strength 4.67
2 cavalries and a horseman vs rifleman win 80% of the time
1 cavalry and 2 knights vs rifleman win 80% of the time

As a result of this useless experiment, (since you guys already knew this stuff by intuition and/or experience) I now have a useless combat calculator for armies.

Attachment: armycombat.zip
This has been downloaded 12 time(s).

Last edited by alexman on 16-08-2002 at 03:54

	04-04-2002 01:52									#41
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quote: Originally posted by Arrian I would argue that making an early army is more worthwhile on larger maps, because you will have more units and battles on those maps. -Arrian

I agree. Plus it is even more important to get the Epic when playing larger maps.

	04-04-2002 02:33									#42
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quote: Originally posted by Dominae However, I was trying to analyse the Heroic Epic in terms of guarantees (95% certainty), which (I don't think) is immediately obvious (to me anyway). The only thing my numbers guarantee is getting at least 1 more

Ah, so! Certainty is certainly a very tricky question.

	04-04-2002 02:34									#43
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quote: Originally posted by Zachriel Gotcha! Certainty is certainly a very tricky question.

Especially when dealing with probability

	04-04-2002 02:40									#44
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... and sombreros.

R

	04-04-2002 02:46									#45
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And the probability of sombreros

	04-04-2002 02:49									#46
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I'm no expert, but from what I've learned, 95% to 99% probability is "certain enough" in the stats world (depending on the domain, of course). After winning 50 battles with Elites and not getting a Great Leader, it's somewhat comforting to know that you're in the top (or bottom!) 5% of the population.


Dominae

	04-04-2002 03:45									#47
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Responding to alexman’s analysis of mixed-unit Army success rates:

I think one of the real benefits of adding progressively stronger units to Armies, aside from lengthening the service of the given Army, is the incrementally improved availability of hit points.

Imagine the following: You start with a 1-unit Horseman Army. You add a Knight, and finally Cavalry. Assume they are all vets, and at full health. You attack that bastard Hun Musketman that’s protecting evil Berlin, and, woe is me, the guy is just a rock. Thankfully, however, you kill him, squeaking by with 1 hp.

Now, what really happened?

Cavalry went first, and used ALL 4 hps. Same for the Knight.

You pick up one more usable hp for all but the last unit, and they get utilized in descending order of strength. So, in the above example, that’s 10 “points” of additional firepower.

Look at some offense totals / usables:

[Note: assume all vets, and “points” are attack strength times hps]

HOMOGENOUS

Army: 2 X Horse = 16 pts total, 14 usable = 87.5%
Ind: 2 X Horse = 16 pts total, 12 usable = 75.0%

Army: 3 X Horse = 24 pts total, 22 usable = 91.7%
Ind: 3 X Horse = 24 pts total, 18 usable = 75.0%

Army: 2 X Knight = 32 pts total, 28 usable = 87.5%
Ind: 2 X Knight = 32 pts total, 24 usable = 75.0%

Army: 3 X Knight = 48 pts total, 44 usable = 91.7%
Ind: 3 X Knight = 48 pts total, 36 usable = 75.0%

Army: 3 X Cavalry = 72 pts total, 66 usable = 91.7%
Ind: 3 X Cavalry = 72 pts total, 54 usable = 75.0%

MIXED

Army: 1 Horse + 1 Knight = 24 pts total, 22 usable = 91.7%
Ind: 2 X Knight = 32 pts total, 24 usable = 75.0%

Army: 1 Horse + 1 Knight + 1 Cavalry = 48 pts total, 42 usable = 87.5%
Ind: 3 X Cavalry = 72 pts total, 48 usable = 66.7%

Army: 1 Knight + 1 Cavalry = 40 pts total, 36 usable = 90.0%
Ind: 2 X Cavalry = 48 pts total, 36 usable = 75.0%

Army: 2 X Knight + 1 Cavalry = 56 pts total, 52 usable = 92.9%
Ind: 3 X Cavalry = 72 pts total, 48 usable = 66.7%

Actually, as a sidenote, this makes the point that Armies, in one sense, have the most positive impact later, when those extra hps are a higher absolute number (look at the lost hps for 3 Cavalry).

What I find so interesting, however, is that due to combat order, the mixed-unit Armies hold up so well.

The difference in usable between an HKC Army (42) and 3 individual Cavalry (48) is not that great, considering how long the Army has been around at that point.

Now build the Pentagon… the HKCC Army goes to 66 usable pts, and the 4 individual Cavalry go to 64 usable pts!!!

Interesting as well, the older untis often get promoted to elite, as they are usually finishing off a damaged unit.

All the more reason to create that first Army as soon as possible.

R

	04-04-2002 04:03									#48
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Rpodos, based on those stats you just posted, it's hard to justify burning a GL on an early army, if done strictly in exchange for the slightly higher kill rate. You'd have to view it as the down payment for the HE.

	04-04-2002 04:14									#49
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One more thing:

I just realized that this applies to mixed-unit offense-defense Armies as well.

On offense:

Army: 2 X Immortals + 1 Musketman = 40 pts total, 38 available
Army: 3 X Immortals = 48 pts total, 44 available
Ind: 3 X Immortals = 48 pts total, 36 available

On defense:

Army: 2 X Immortals + 1 Musketman = 32 pts total, 30 available
Army: 3 X Immortals = 24 pts total, 22 available
Ind: 3 X Immortals = 24 pts total, 18 available

Wow! That's why it's the Incredible Hulk!!

R

	04-04-2002 04:20									#50
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Txurce:

I agree, the whole point of early (2-point offense) Armies to win 1 battle, so you can go for the HE as early as possible.

If I create a 2-point early Army, I'll use just one unit and pick a battle with a redlined Warrior. After that, I put'em away someplace safe until I can augment them with more advance units.

I'm just really pleased that augmenting works so well, and that the resulting mixed-unit Armies maintain value for such a long time.

In response to Dominae's question, I think Soren confirmed somewhere that the ONLY thing that can increase the chance of GL creation is the HE.

R

	04-04-2002 06:14									#51
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rpodos, I'm not quite sure I understand your analysis of mixed Armies. Particularly, what are "usable" points?

A Veteran Horseman gets to "roll the dice" four times in combat; once at full health, again at 3HP, again at 2HP, and finally one last time at 1HP. By your "point" system, the Horseman gets to use its 2 attack power four times, for a total of 8 points. A duo of Veteran Horsemen therefore have 16 points when fightning individually.

For a 2 Vet Horsemen Army, the same applies. The first Horsemen "rolls the dice" up to 4 times. Regardless of whether the Army survives or not, the second Horsemen gets to "roll the dice" up to 4 times as well.

The only advantage that I can see for Armies is that you don't lose the first Horsemen if your Army collectively loses 4-7HP.

I'm beginning to wonder if I really understand how Armies really work. The FAQ on the Civ3 site confirms what I've said above. Has this changed with any of the patches?


Dominae

	04-04-2002 09:20									#52
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Dominae, sorry, I wasn't being clear.

Using the 2-Horseman vet Army as an example, the benefit is that all but the last Army unit can use the 4th HP and even if the respective unit loses the "roll of the dice," it survives.

So I guess, to put a fine point on in it (pun intended), my definition of "usable" points is that they are "survivable" no matter the outcome of that roll.

I think this is extremely valuable... besides keeping your own units alive to fight another day, it keeps the opposing defensive unit from being promoted. This has become more important post-1.17f, as retreat has become less likely.

Your point is correct, that even individual units "use" that last hit point; I just hate when it gets "used" to die!!

I think we are on the same page about how Armies work.

	04-04-2002 11:05									#53
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I have the same lack of luck getting GL's. As Rome, 114 elite victories, ZERO GLs. The victories were pretty evenly defensive and offensive. On games when i do get a GL, the first one is for an army the rest are to rush build wonders. My favorite armies are 2 tanks(mod armor) and 1 mech inf

	04-04-2002 11:15									#54
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quote: Originally posted by ALPHA WOLF 64 I have the same lack of luck getting GL's. As Rome, 114 elite victories, ZERO GLs

Mars had judged you as unworthy. Sorry. Try another civ. Or get some M&Ms.

I get 1 about every 10 or 20 Elite combats.

Is it going to drive you nuts to know that I usually have one hanging around the capital waiting for something useful to do? I thought so. Forget I mentioned it.

	04-04-2002 20:04									#55
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quote: [SIZE=1] I think this is extremely valuable... besides keeping your own units alive to fight another day, it keeps the opposing defensive unit from being promoted. This has become more important post-1.17f, as retreat has become less likely.

Good observation, I hadn't thought of that.

quote: [SIZE=1] I think we are on the same page about how Armies work.

Agreed.


Dominae

	04-04-2002 21:38									#56
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nye,

Be careful about keeping GLs hanging around... you can't ahve two at once.

This was one of the reasons I initially started playing around with Armies so much... if I don't have a Wonder to build, I will always use the GL to build an Army.

This happens probably once or twice a game, on average.

R

	05-04-2002 01:02									#57
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I started a new Japanese game, and have had some good fortune with GL's. Ironically, though I eventually built the Heroic Epic, all of my GL's to date came before it was done.

I started on a 5-civ continent, although I was able to block a choke point and prevent India from contacting everyone else for quite some time. I destroyed Babylon, China, Persia (no iron, hehe) and then India with horsemen (the last stages of the Indian campaign did involve some Samurai). I maintained a force of roughly 25-30 horsemen at all times, of which maybe 10 were elite at any given time. I generated six great leaders. #1 = forbidden palace. I had captured the Pyramids, didn't have literature, and had a good location for the FP. #2 = Great Library. Largely to deny it to the AI's on the other continent, which would have helped speed tech development over there (I think... then again, the trading goes so fast anyway...). #3 - get this, the Hanging Gardens. Why? Whim. I had Babylon... I just HAD to have the HG there. By this point, I knew I had a good run going, so I figured why not? #4 = Sistine Chapel. #5 = Army, #6 = Leo's. The sixth leader showed up 3 turns prior to completion of the Epic. I have fought since, using some elites, to finish off India and then to pounce on Zululand for their wines and spices. No more leaders.

The main problem I have with the army/HE route is the uncertainty. Good effort, Dominae, at trying to calculate a "sure thing" GL creation. Still, it all comes down to luck. And when the choice is luck vs. an absolutely sure Wonder of the World...

By the way, I came within 1-2 hp's of losing my 3 horseman army twice, against defending spearmen. Starting at full hp. BAD uber spearman! I fear the RNG more when attacking with an army, because a string of bad rolls happens pretty often, and normally you would just lose a unit, and be done. But as I watched in horror, my army lost 9 straight hp's to a spearman in a size 2 town w/o walls, on grassland. That's a bad string for ya.

Also, you know that free shot a fortified defender seems to get at the start of combat? When an army gets down to its last few hp's, it starts cycling through the individual units. The attacking unit withdraws, and the next one comes up. It seems to me that the defender gets its "free shot" again each time that occurs. Anyone else notice this?

-Arrian

	05-04-2002 01:36									#58
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quote: Originally posted by Arrian Good effort, Dominae, at trying to calculate a "sure thing" GL creation. Still, it all comes down to luck. And when the choice is luck vs. an absolutely sure Wonder of the World...

"Trying"? What do you mean by "trying", eh!?!?

Honestly, the numbers I posted don't mean all that much to me either, other than give an idea of what a "sure thing" GL entails (with and without the HE). What I got from my little analysis is that, in the long run (say, with a Huge map with 16 opponents), you'll generate 3 GLs with the Heroic Epic for every 2 GLs without it (this is "in the limit", so it's as certain a figure as you can get). So, if you're going to fight a lot, you'll almost always see the benefits of the HE. Whether you think it's worth it is a matter of preference, I think.

I'm a Builder at heart, so I love to get Wonders just like any other Builder. But sometimes when I play Militaristic civs, it's just fun to form an Army (which is strategically significant, but not amazing), build the HE, and rest assured that my conquests will yield better "spoils of war" (read: Great Leaders) than they normally would.

As an aside, does anyone know if the AI ever builds Small Wonders? I never use the 'Investigate City' option, so I've never had the opportunity to check. It seems that the AI does build the Intelligence Agency because I've caught it trying to steal my techs in the modern era. What about the Heroic Epic, or the Forbidden Palace for that matter?


Dominae

	05-04-2002 02:20									#59
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quote: Originally posted by Dominae What I got from my little analysis is that, in the long run (say, with a Huge map with 16 opponents), you'll generate 3 GLs with the Heroic Epic for every 2 GLs without it (this is "in the limit", so it's as certain a figure as you can get). So, if you're going to fight a lot, you'll almost always see the benefits of the HE. Whether you think it's worth it is a matter of preference, I think. Dominae

Three compared to two -- in the long run. Good stat summation.

So, warmongers should benefit; people who play big maps should benefit; and builders like the cultural benefits of the Epic. If you are going to build the Epic, it is best for culture and for war to build it as soon as possible.

Exceptions, smaller maps?

	05-04-2002 02:28									#60
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Dominae,

I have seen the AI build small wonders. I have seen the Ironworks, the Forbidden Palace and I think the Intelligence Agency... oh, and Apollo.

Of course, the AI has no concept of where to place a Forbidden Palace, so it will never be as good as we are at that. I laughed my ass off when I discovered the Persians had built it in Parsagradae (#2 city, right next to Persopolis). This was on Marla's map, and it's true that they were a bit boxed in, but really.

Again, has anyone else noticed the "first free shot" thing I was talking about above, or am I nuts?

-Arrian