View Full Version : The Other Domination Limit


superslug
Jun 27, 2005, 05:23 PM
EDIT: It turns out my little theory is only that, a theory. The practical application just didn't pan out, so remember that while you read it. I've left the article up, however, for anyone interested in such reading, even if false.

Introduction

Standard milking theory within the Hall of Fame holds that you should expand to within one tile of the territory domination limit, grabbing the 66% of the map with the most food and then ramping up your population as high as possible while keeping one AI city quarantined in order to hold off on actually triggering any win condiditons. This strategy has been employed for years, as conventional wisdom dictated this was the best way to ensure the most points scored.

Iíve recently discovered this may not be entirely true.

Based on another thread, I began to wonder what would happen if the human player stayed under the population limit instead of the territory limit. Instead of having as much population as possible, you could then grab as much territory as you wanted. In order to avoid the population domination, the player would have to ensure that the quarantined AI stayed at 34% of the mapís total population.

HOF Milking Application

It was time to do some number crunching from Huge maps, where serious milking is done. Specifically, I wanted to look at an archipelago, and for sake of thorough calculations, the game in question needed to have been milked to the best possible degree.

That of course left only once choice: Moonsingerís Sid #1 (http://hof.civfanatics.net/game_info.php?entryID=869), the highest scored game in HOF history.

A CRpMapStat scan of her final.sav shows that Moonsinger had a domination limit of 4562 tiles, 4561 tiles within her territory, 4626 happy citizens and 3347 specialists (with no content citizens). Per the score formula of one basepoint per turn for each tile and specialist, and two basepoints per turn for happy citizens, Moonsinger was gaining 17160 basepoints per turn during the post-growth milkphase.

Now, assuming full irrigation, rails, harbors, ag civ, etc, 100% city coverage and cultural borders covering two tiles of water (all coast and sea), the total map's available food is approximately 20800. 34% of this is 7072. Divide that by 4 (railed irrigated grassland) and you can get 34% of the total map food with 1768 grassland tiles. That would be given (via fully improved and grown cities) to the quarantine AI. The player would then take the other 66% of the food and all the territory you want.

In the case of Moonsingers map, that would be 13728 food over 6970 tiles.
Since that's barely under 2 food per tile, we can assume no content citizens, nor specialists. Since happy citizens require 2 food and give 2 basepoints, the player would get 13728 basepoints per turn from citizens. Add the 6970 basepoints from tiles within borders, and the player would accumulate 20698 basepoints per turn.

20698/17160=20% more score during growth-cap milk phase!!!

100,000?

Some weeks back in the HOF forum, I made the claim that 100,000 points was possible in an HOF legal game of Civilization III. At the time, I didnít back up the statement. Now, perhaps I can.

As a general rule of thumb, 60% of a milked gameís points come from the milking. This means that 53131 of Moonsingerís 88553 final points were from the milk phase. Boosting that by 20%, the map would have been theoretically capable of 63757 milk points, putting the final score at 99179 points.

Whatís the catch?

The proposed milk method isnít without complications:

The quarantined AI should remain quarantined, eight units surrounding each city. If so much as a single worker gets out of their cities and mines a tile, they drop their food and you have to drop yours. To make matters worse, it means cleaning up their pollution for them.
That obviously means that you should be in good enough standing with the last AI that you can have a constant right-of-passage.
It also means keeping military units around, more than the usual milkphase. While unit support isnít an issue, there would be a slight loss of disbandable shields for milk improvements in your own towns.
An Ag civ is best for the AI in question. They should also have a preferred government that doesnít offer poprushing.
The territory domination warning bell on CRpMapStat will go off everyturn. Disabling it is tempting, but for other games, perhaps a bad idea.
Thereís not a true population domination warning in CRpMapStat, so I had to rely on the Victory Status Screen. 65% was rarely safe, but 64% was. This meant constant trimming of my own population.
Said trimming has to be done carefully. Cash rushing workers/settlers might be best, as poprushing and drafting done too much could hurt happiness. I did use Communism for my editor test though, and by rotating the drafting through all the cities I never saw unhappy citizens.
Keeping multiple AI cities around might mean some cultural border pushing. Itís okay to push back, as youíll already be over the territorial domination limit. Just remember not to step into their 34% of the food.


20%? Are you sure?

Er, almost. I did make a few approximations:

I rounded the theoretical food per tile to 2, it was actually 1.97~.
60% of scores being milk points is a rule of thumb. For Moonsinger, I wouldnít be shocked to determine itís higher.
For the equations, I assumed that the AI would be on all irrigated grassland, and thereís enough on that map to do it. However, their cities would only produce 3 food per tile, not 4 as the equations assume. On the other hand, that could possibly be compensated for with bonus foods.
Speaking of bonus foods, I didnít factor that in.
Setting up a map for milking via the traditional method takes time. Itís possible that setting up the AI for this new method would take longer, thus shortening the milk phase.
I assumed a 1:1 ratio of coast:sea tiles.


A Funny Consequence

Since territorial domination is irrelevant under the theory, you'd want to push all your coastal city borders out two tiles to grab as much food as possible. Actually, my equations assumed that. That means The Internet might actually have a practical use. :lol: :eek:

Conclusion

Even if the differential isnít fully 20% on a huge archipelago, itís obvious from both the numbers and the test map that staying under the population domination limit can yield more points than staying under the territorial limit. However, it does carry the burden of complex AI/map manipulation, and does result in even more micromanagement than the traditional method.

Then again, true milkers wonít mind that much. A point is a point.

superslug
Jun 27, 2005, 05:24 PM
This may go without saying, but I'll state it anyway: I used Moonsinger's #1 game as an example not to criticize her milking ability, but actually quite the opposite. In order for the math to provide valid results, the test subject needed to be the best milked game ever.

Article edit1: Shrunk 2nd picture.

Gyathaar
Jun 27, 2005, 05:35 PM
Very interesting....
and I still have a nice map sitting idle halfway though conquest phase... :)
I might put this to the test when I start my vacation next week..

bed_head7
Jun 27, 2005, 05:43 PM
This discovery may just be enough to deter me from ever doing a serious milk run. But, whoa. Amazing that there is something this huge which hadn't been thought of until now. Amazing how complex a game this is. Amazing.

superslug
Jun 27, 2005, 05:46 PM
But, whoa. Amazing that there is something this huge which hadn't been thought of until now.
Indeed! You can well imagine my disbelief when I discovered this. The game's been out how long? It'll be interesting to see if CivIV's domination is again a double-limit. If not, this tactic may have a short shelf-life.

bed_head7
Jun 27, 2005, 05:55 PM
I just realized that the effect of your discovery will completely unbalance GOTM again. Jason scoring needs to be completely revised, or your method will put up unbeatable scores.

superslug
Jun 27, 2005, 06:02 PM
I just realized that the effect of your discovery will completely unbalance GOTM again. Jason scoring needs to be completely revised, or your method will put up unbeatable scores.
For what's worth to the GOTM staff, causing them headaches certainly wasn't my intention. ;)

I would like to point out that for a 10x10 pangaea, the differential was 8%, and 20% for a huge/archipelago. For standard sized maps, the percentage increase will probably land in between, with some variation for how the maps are designed.

Svar
Jun 27, 2005, 06:33 PM
I'm sure the math is right but how do you get the AI to cooperate? I haven't played in a month but I seem to remember that I have over 66% of the population long before I get to 66% of the territory. People will have to completely rethink their strategy to implement this, like only settle in plains and desert areas to keep the population down. The biggest problem will be keeping the AI reined in for the whole game.

superslug
Jun 27, 2005, 06:57 PM
I haven't played in a month but I seem to remember that I have over 66% of the population long before I get to 66% of the territory.
For HOF milk runs, I'd say this is pretty factual, yes.

I'm sure the math is right but how do you get the AI to cooperate?
I'd think you'd have to wipe out all but one AI and take the last one down to one city, just as before. During that time, your 66% of the population can be in the grassland towns you're constructing for them. Then simply gift them. After that you can build the rest of your cities.

DaveMcW
Jun 27, 2005, 07:46 PM
Your city layout in Test #1 is sub-optimal. Try maximizing sea tiles and avoiding mountains.

superslug
Jun 27, 2005, 07:58 PM
Your city layout in Test #1 is sub-optimal. Try maximizing sea tiles and avoiding mountains.
:blush: You're right. I'll run another test tomorrow.

Bartleby
Jun 28, 2005, 02:39 AM
I'd never thought of it in that way, but I have staved off AI domination by maintaining 33% pop in peaceful xCC games.

That means The Internet might actually have a practical use.

For me the internet is usually useless because it would probably force a culture win. I'm almost addicted to finishing with exactly 160k culture.

eldar
Jun 28, 2005, 06:11 AM
I presume the way to go with the quarantine AI would be to set up their "prison" with your own cities, gift them those cities, and wipe out their remaining core (before you're at the tile domination limit)?

Timko
Jun 28, 2005, 08:29 AM
You would be pretty unhappy when they launched their spaceship though, wouldn't you? If they got to the latter stages of the tech tree you would have to switch back to milk-method 1, and reduce them to 1 city, and reduce your land to 65%.

Also, on the higher levels, what are the chances that an opponent (with 34% of the population on a huge map) wouldn't build up enough troops to decide to attack?

Gyathaar
Jun 28, 2005, 09:22 AM
You would be pretty unhappy when they launched their spaceship though, wouldn't you? If they got to the latter stages of the tech tree you would have to switch back to milk-method 1, and reduce them to 1 city, and reduce your land to 65%.

Also, on the higher levels, what are the chances that an opponent (with 34% of the population on a huge map) wouldn't build up enough troops to decide to attack?
Just keep a MPP running and they wont attack

Offa
Jun 28, 2005, 10:17 AM
This is entertaining.

I suggested this in another thread, and no less a milker than Moonsinger shot me down, and I didn't think any more about it. It seemed like too much work to me anyway, and I really don't like milking.

I had rather envisioned using tricks like gifting the AI bloated cities as required, kindof like a dogpile for the AI, while keeping 80+% of territory for myself. It probably wouldn't actually infringe the rules as they stand.

As you would need to be completely in charge to run a game like this, I think lower difficulty levels would be easiest.

superslug
Jun 28, 2005, 03:08 PM
Well, this is definitely turning out to be a work in progress. I appreciate all the feedback thus far.

:blush: You're right. I'll run another test tomorrow.
In progress.

For me the internet is usually useless because it would probably force a culture win.
In this case it would not only grab all the available sea tiles, it could prevent the AI from getting a culture win. If they do have a huge culture lead, their cpt will drop from being restricted to x amount of cities, and all the human has to do is stay above half their total. Then 160,000 is irrelevant.

I presume the way to go with the quarantine AI would be to set up their "prison" with your own cities, gift them those cities, and wipe out their remaining core (before you're at the tile domination limit)?
Setting up the prison cities on your own and gifting them is critical to the theory, in order to ensure proper placement. As far as wiping out their remaining core, I'd personally prefer to do it before the gift, but either way could work I suppose.

I just think knocking them down to one town first would be easier, in case some of their quarantine cities might need to be on grassland once owned by them.

You would be pretty unhappy when they launched their spaceship though, wouldn't you?
No, I'd have exercised preemptive aluminum denial.

This is entertaining.
You're welcome, I guess. :confused:

I suggested this in another thread, and no less a milker than Moonsinger shot me down, and I didn't think any more about it. It seemed like too much work to me anyway, and I really don't like milking.
I'd be interested in reading that thread. I don't recall every reading something quite like this before.

I had rather envisioned using tricks like gifting the AI bloated cities as required, kindof like a dogpile for the AI, while keeping 80+% of territory for myself. It probably wouldn't actually infringe the rules as they stand.
HOF rules? Certainly not. I can't speak for GOTM though.

As you would need to be completely in charge to run a game like this, I think lower difficulty levels would be easiest.
A well executed traditional milk game assumes the player to be completely in charge of the map anyway.

superslug
Jun 29, 2005, 04:57 AM
I've finished the second test on the same map. When properly milked via the traditional method, the map gives a higher score to traditional milking, not the theoretical way.

Offa
Jun 29, 2005, 05:30 AM
You're welcome, I guess. :confused:


I'd be interested in reading that thread. I don't recall every reading something quite like this before.


HOF rules? Certainly not. I can't speak for GOTM though.




I meant entertaining as a compliment :goodjob: . I look forward to Moonsinger's comments.

The other thread was this one:

http://forums.civfanatics.com/showthread.php?t=118422

As you can see my remark was a bit of a throwaway one liner, nothing like your clever analysis. The thoughts about reverse dogpiles etc I kept to myself, as I didn't really think there was much mileage in it, at least the way I play. Frankly I thought the whole thing might be tricky to set up, only to risk a game either not scoring all that well or getting banned retrospectively.
I haven't attempted to do this at all myself, not having milked a game in years.

I didn't know the rules stop you gifting the AI a huge city? Clearly you could easily change them to make sure they do.

I can't believe this sort of game will be easy on Sid, but perhaps Gyathaar can show us it is possible.

Dianthus
Jun 29, 2005, 05:37 AM
I've finished the second test on the same map. When properly milked via the traditional method, the map gives a higher score to traditional milking, not the theoretical way.
I think you're going to have to change your test map to prove the point. You really need to minmize the amount of territory the AI requires for it's 34% pop, which means all of it's territory should be railed-irrigated-grassland. The AI had quite a bit of coast in your example.

superslug
Jun 29, 2005, 01:51 PM
As you can see my remark was a bit of a throwaway one liner, nothing like your clever analysis.
I should have seen that link coming. Your throwaway one liner was the inspiration for me to look into this. ;)

superslug
Jun 29, 2005, 01:53 PM
I think you're going to have to change your test map to prove the point.
You're right, but I think I'm going to have to take it a step further and use a randomly generated map and milk it both ways. I can't be certain that I'm subconsciously rigging the map.

Dianthus
Jun 29, 2005, 02:06 PM
You're right, but I think I'm going to have to take it a step further and use a randomly generated map and milk it both ways. I can't be certain that I'm subconsciously rigging the map.
If you're feeling really brave you could take Moonsinger's 10AD .sav and see if you can use this new method to beat her score ;).

Gyathaar
Jun 29, 2005, 02:46 PM
If you're feeling really brave you could take Moonsinger's 10AD .sav and see if you can use this new method to beat her score ;).
Just take the 2050AD save and use the huge amount of settlers and armies available to do it then.. you just need to see if you can get the internal score per turn higher than it is in 2050..

Pentium
Jun 29, 2005, 02:52 PM
The AI probably don't have many population in 2050 AD.....

Dianthus
Jun 29, 2005, 03:28 PM
The AI doesn't matter too much as the idea is that you gift the fully populated cities to the AI. The 2050AD .sav has 504 workers and 39 settlers ready to go. Probably need a few turns to build some more and get back to the same population level.

Gyathaar
Jun 29, 2005, 03:46 PM
The AI doesn't matter too much as the idea is that you gift the fully populated cities to the AI. The 2050AD .sav has 504 workers and 39 settlers ready to go. Probably need a few turns to build some more and get back to the same population level.
You are forgetting the 631 slave workers and 101 slave settlers (140 total settlers)

superslug
Jun 29, 2005, 07:13 PM
Just take the 2050AD save and use the huge amount of settlers and armies available to do it then.. you just need to see if you can get the internal score per turn higher than it is in 2050..
I think you may be onto something. Give me a few days. ;)

Svar
Jul 01, 2005, 12:58 PM
I have looked at my Regent high score game and tried to get the numbers to show how to work this strategy. That game had a domination limit of 3756. Near the end there were 3810 happy citizens and 3041 specialists. That yields a score potential of 14,417. I looked at how many tiles I would have to add with a ratio of 1.015 happy citizens per tile to make up for the loss of 3041 specialists, it was 1008. 1008 tiles plus 3756 is 4764, or 83.7% of the available 5693. That leaves 929 tiles for the AI population. If the AI can maintain 1.8 citizens per tile like I can they will have 1672. Assumming I only have 1.015 population per tile on my 4764 tiles I get a population of 4835. 4835 plus 1672 is 6507 and I have 74.3% of the population. In conclusion, to make up for my 3041 specialists I would need to add enough territory that would give me 83.7 % of the available territory and 74.3% of the population. This strategy doesn't seem to work.

Dianthus
Jul 01, 2005, 01:38 PM
This strategy doesn't seem to work.
I've just had a look at your .sav, and my calculations are open to interpretation.

First I calculated the food available and the potential territory/population:
http://www.civfanatics.net/uploads10/svaremp.png

The interpretation bit (unless I got any of the above wrong ;)) comes when estimating the number of those citizens that will be happy.

If all are happy then I make that:
4222 + (2*5710) = 15642 base points/turn

If only 3810 are happy (the amount you had with 66% of the territory):
422 + (2*3810) + 1900 = 13742 base points/turn

I guess the number of happy citizens will be somewhere inbetween. superslug was expecting all citizens to be happy for the figures he used with Moonsinger's game as there was only around 2 food per tile for the remaining tiles. For your game it's 2.71 food per tile for the remaining tiles, so maybe all happy won't be possible? I guess this is down to the difference between pangea/archipelago. With an archipelago map there will be a higher number of tiles remaining after giving 34% of the food to the AI, but those tiles will be of lower quality food-wise.

Svar
Jul 01, 2005, 03:06 PM
If all are happy then I make that:
4222 + (2*5710) = 15642 base points/turn

I guess the number of happy citizens will be somewhere inbetween. superslug was expecting all citizens to be happy for the figures he used with Moonsinger's game as there was only around 2 food per tile for the remaining tiles. For your game it's 2.71 food per tile for the remaining tiles, so maybe all happy won't be possible? I guess this is down to the difference between pangea/archipelago. With an archipelago map there will be a higher number of tiles remaining after giving 34% of the food to the AI, but those tiles will be of lower quality food-wise.

I just looked at my Emperor game and get 1.016 happy citizens per tile so for a traditional game that looks like a good number but probably less than half of the available sea tiles were used. If I use 1.04 happy citizens per tile I still only get 12,784 base points per turn. To get to your 4222 tile number with happy citizens that will match the actual 14,417 base points per turn you will need 5097 happy citizens. 5097 divided by 4222 yields 1.207 happy citizens per tile. A 1.207 happy citizen per tile ratio will require 875 sea tiles be worked. This strategy should work much better on an archipelago world with the AI trapped in the interior.

superslug
Jul 02, 2005, 07:20 AM
I've been thinking things over and I think giving the AI 34% of the food isn't enough. Even if they keep their population maxed out, the human can still hit 66% and trigger domination.

Even though the test map was flawed, I did discover that if the Victory Status screen said 65%, there was a very good chance you'd trigger Domination. Since I didn't want to pile on massive numbers of reloads, I stayed at 64%, which seemed to do it.

Another thing to take into consideration is the number of cities and placement. On a huge/pilego, the human player would have hundreds of cities. An Ag city provides three food for that tile, which is an increase for what you would otherwise get on hills, tundra, etc. This may have had some impact on the test map.

For now, I'm going to start assuming the quarantine AI needs 36%.

superslug
Jul 08, 2005, 07:30 PM
Well, time for my moment of humble pie. The practical application just doesn't match the theory. The initial equations had assumed the AI having 4 food per tile (railed irrigated grassland), but there's problems with actually implementing it. Mountains, plains and hills interspersed throughout. The AI cities themselves only getting 3 food.

Furthermore, giving the AI sufficient tiles simply can't be done internally, away from coasts. Maintaining that long a cultural border exactly where it needs to be is simply impossible. The only bet is to keep the AI in one mass, sharing only a single-sided land border, but that means the AI eats up a lot of the map's coast and sea.

That 20% just kept shrinking and shrinking until it was just a few percentage points. At that point, I gave up. It would have taken well over 100 cities to the AI on Moonsinger's map. Fully quarantined, that would take 800+ units. The units probably would be no problem after a Deity/Sid combat phase, but the loss of those shields for the initial aqueducts?

Meh, I'm just going to load the game and play it however the hell I feel like. I've had enough strategy for now...

Thanks for your input everyone.

Methos
Jul 08, 2005, 09:50 PM
Great work Slug. I'll have to admit it was a great idea and at least you looked into it. Thanks for letting us know your outcome.

occam
Aug 12, 2005, 04:32 AM
Your math about how many tiles the AI will need assuming they receive all their population from grassland carries the flaw that ocean cities for the AI help add pop without burning a grassland tile.... esp. those one tile islands. (In particular your math about the HoF game.) Later comments seem to indicate that everyone understands water=free food for the AI, but my point is your original totals can reasonably be viewed as merely the floor for what is possible.

In theory, the AI could have tons of single tile islands, leaving 90+% of the 'good' tiles for milking.

In ANY case, a very original and thought-provoking read.