Maximizing Your Score

Normally I skip Monarchy and go directly into Republic - is that worse than going Monarchy and then into Democracy?

Depends on your playing style. If you really want a tech lead (or you are playing on the lower levels), Republic is definitely the best. Republic makes more money than a monarchy, so you have more money to invest in science, but you will probably need to build the cathedrals and colleseums. In monarchy, you don't need the cathedrals and colleseums because of the military police, so you can start building more military units instead of buildings. And a monarchy is more ideal for someone who wants to wage a continous, non-stop war. You can literally be at war with someone the entire game, with no war-weariness. To get a gigantic score you want to control as much territory as early as possible, so in a monarchy, you can continue to keep grabbing more and more territory by taking over your neighbor's cities.

Monarchy is much better IMHO on the more difficult levels, where it is nearly impossible to gain more than a 1 or 2 tech lead, so people put their science rate at 0% and just buy techs off the AI. With no spending going to science you can make a ton of cash or support hundreds of units.

Democracy is a little better than republic in corruption, but because of intense war-weariness Republic is far better. If you are totally safe from wars go to Democracy so you get the bonus worker speed.

If you really are striving to be in a democracy, then choosing the government prior to it depends on the situation. Republic is so similar to democracy that the transition will be much smoother. If you go from Monarchy to Democracy you loose the contentness from the military police so you might not be able to handle the new unhappiness in your cities. Make sure you have access to several luxuries and marketplaces in most of your cities before switching over to republic or democracy.
 
A question for those with more experience on maximizing score...

When milking the game for score, clearly the most important goal is to utilize every tile possible without triggering a domination victory (and of coure all happy citizens :D ). My question: is it more effective to have:

1) many cities of size 12, each using roughly 3-5 tiles or

2) fewer cities of 25+ size, each taking close to the full 21

My guess is that the size 12 cities would produce higher scores, since when city population is more than 21 all extra citizens become specialists and thus cannot become "happy", which produces a higher score. Is there someone out there who has tested this and can confirm my suspicions?
 
I would go with choice 1. More cities are the big difference. Means more terrain is under your control which also means more score.
 
Terrain isn't the issue; I already have all the land I can get without triggering domination. I'm pretty sure that more cities is the way to go, just trying to get some confirmation from one of the players with experience on it here.
 
It is a difficult comparison, because with smaller cities, the maximum population may be smaller, and the "working" (happy/content/unhappy) population is always smaller. I've been trying to work out a comparison and the results are interesting. A bit of a long read, skip to the end if you just want my conclusions.

First, let's consider a case where all the land is grassland. Suppose that we have an area which is all grassland, irrigated and railroaded. So each "worked" tile will produce 4 food and can support two citizens. Each tile which is used for a city will produce 2 food and will support only one citizen.

If there are 18 such grassland tiles on the map and we compare using them as one city vs. using them as three cities then:

One city: 18 tiles total. 1 tile for the city supports 1 citizen, 17 worked tiles support 34 citizens. Best possible result with maximum happiness is 17 happy citizens plus 18 specialists.

Three cities: 6 tiles per city. 1 tile in each for the city supports 1 citizen. 5 worked tiles support 10 citizens. Best possible result with maximum happiness is in each city 5 happy citizens plus 6 specialists, for a total of 15 happy citizens plus 18 specialists.

Using the smaller cities we ended up with 2 less happy citizens in the final result. We lost 2 citizens because of less food produced by the extra city tiles. The 2 we lost were happy citizens because there are two less tiles which can be worked.

For this simple grassland case the scoring potential is as follows. Using the formula:
NumberOfCities * ( HappyCitizens * 2 + Specialists + TileCount )
One city: 1 * ( 17 * 2 + 18 + 18) = 70
Three cities: 3 * ( 5 * 2 + 6 + 6 ) = 66

Although the above shows that a single large city can score better in theory, the small cities might still score better in practice for a number of reasons:

1) They may grow to their maximum much sooner in the game. They don't need to wait for hospitals, and each one benefits from a smaller independent granary. Total cost of building may be smaller, depending on the need for Aqueducts. (Large city needs Hospital + MassTransit = 360 shields. Two additional small cities in worst case need MarketPlace + Aqueduct each = 400 shields.)
(Edit: I just realized that for cities this small, with just 5 working citizens, there is no need for the Marketplace given enough happiness improvements, e.g. 8 luxuries and JS Bach's. So at this size there's definitely less building with small cities. When the city's terrain is poorer a size 12 city may or may not need a Marketplace, depends on the number of working citizens.)

2) In outlying corrupt regions it may not be possible (certainly not easy) to keep all working citizens happy. In this very large single city that's probably not an issue since it can have 18 specialist entertainers. But on less ideal land (including some hills, tundra, etc.) there often are not enough entertainers to do the trick. If the single city has 15 happy + 2 unhappy citizens instead of 17 happy, then its scoring potential is the same as the three city approach. More unhappy citizens than 2 means it actually performs worse.

Then there's the question of what happens if the terrain is worse?

If we use the same case as above with all irrigitated+railroaded desert the result is I think:
One city: 1 * ( 17 * 2 + 1 + 18) = 53
Three cities: 3 * ( 5 * 2 + 1 + 6 ) = 51

It is interesting to note that desert can reach 75% of the scoring potential of grassland!

Now what if we place the cities themselves on poor land?

Suppose that the 18 tile region we're looking at contains 15 grassland tiles and 3 hill tiles (or tundra would be the same), and that our cities are always placed on the "bad" tiles:
One city: 1 * ( 17 * 2 + 15 + 18) = 67 (Edited, original post said 68)
Three cities: 3 * ( 5 * 2 + 6 + 6 ) = 66

A final note on a related subject: What is the scoring potential of hills/mountains/tundra? These tiles cannot fully support the citizen that works them. But these tiles are worth 3 points each when worked - 1 for being in our sphere of influence, 2 for the happy citizen working on them. I think that when there are hills/tundra/mountains already within your sphere of influence, it pays to arrange cities so that there are cities at the edge of these regions with food-rich tiles. Those cities can then support the happy citizens working the food-poor tiles, increasing the scoring potential. In large hill/tundra areas where there is no nearby food source, I try to place one town per four tiles, so that 2 out of 4 of the tiles in the area get happy citizens working on them.

Conclusions

1) Larger cities have a theoretically higher scoring potential.

2) The difference in scoring potential is small when comparing maximum size cities to size 12 cities. It would become a bigger difference if we considered even smaller cities again in the comparison - small cities should probably not be carried to an extreme, around size 12 is likely to be optimum I think.

3) The difference in scoring potential becomes smaller again when the cities themselves are built on food-poor terrain.

4) The difference disappears (or even favors the smaller cities instead) in cases where large cities are not large enough or rich enough to have all of their citizens happy. In large empires most cities are likely to fall into this category - outlying high corruption cities are likely to always have some unhappiness.

5) Desert (and plains of course) have surprisingly high score potential. Less than grasslands, but not by as large a factor as one might think.

So it seems to me that careful building of size 12 cities is likely to score best in most games, being careful to put the cities on poor food terrain where possible. And making sure to place cities which include hills, tundra, and mountains in their area so that there is a citizen working each of the food poor tiles.
 
Wow - thanks a lot! :goodjob:

I think the general idea is pretty clear, that it doesn't make all that big of a difference between the two. Obviously the terrain makes the biggest difference. I think the lesson here is that it's not that important how many cities there are, just that every tile is worked by a happy citizen and everything is irrigated/railroaded. Much thanks to SirPleb for all of the number crunching done to maximize score! :cool:
 
You're welcome Sullla! I have fun exploring this stuff :)

I continued a bit after posting prior note. One more interesting case to work out a limit:

What would be the scoring penalty for the most tightly packed cities possible?

The tightest build possible is one city per 4 files. In a case with 20 irrigated+railed grassland tiles:

One city: 1 * ( 19 * 2 + 20 + 20) = 78
Five cities: 5 * ( 3 * 2 + 4 + 4 ) = 70

The difference still isn't large, a 10% loss in score. And that gets smaller as the terrain gets worse. The scoring penalty for a very tight build, although noticeable, sure isn't as large as one might guess.

So your conclusion is the right one I think, "it's not that important how many cities there are, just that every tile is worked by a happy citizen and everything is irrigated/railroaded". Those are clearly more important factors than the city density.
 
Also excluded from the calculation is the speed of border expansion through the increase in culture. Given that the small cities/large city are located in unclaimed territory, the smaller cities should be able to "push" the borders further out than one large city within the same number of original tiles.

In already claimed territory the calculation stands though, although the difference seems to be small.

Or am I totally up the wrong alley?

//
 
Originally posted by Kipner
Given that the small cities/large city are located in unclaimed territory, the smaller cities should be able to "push" the borders further out than one large city within the same number of original tiles.
In a way I guess that is true, but, if you are going for territory then using the same number of settlers for completely non-overlapping cities would of course be better again than having small cities. I'm not sure what the best trade-off is early in the game, between getting more territory early on vs. setting up for other factors which will improve score later (and contribute to winning :lol: )

In the milking stage of a game this factor won't matter at all of course - at some point you are just barely under the domination threshold and then you don't want your borders expanding further.
 
It is interesting to note that desert can reach 75% of the scoring potential of grassland!

What would you say about coastal squares then? They produce the same food as a railraoded/irrigated desert (if you have a harbor in the coastal city of course). But also, you usually get 'free' sea squares. In most cases, there is a strip of coastal tiles, then a strip or two of seas, then the ocean. The first strip of sea squares would be worked (happy people), and those are tiles that helps in score, but doesn't add to the domination threshold. Plus if the culture borders push far enough you can grab more free sea tiles (but won't be worked on, so not as much free points).

So theoretically, if you had 1 sea tile for each coastal tile, is that the same, or better, than claiming a grassland square? Because 1 coast + 1 sea = 4 food (for 2 happy people) + 2 tiles, but only counts as 1 for domination. You would have the added expense of harbors, though, but no loss to pollution.
 
Originally posted by Bamspeedy
What would you say about coastal squares then?
Edit 2002/6/3: Originally when I wrote this note I thought that sea tiles counted toward one's territory score. They don't. I've now reworked the note to allow for this.
I really like the coastal and sea regions, and try to include as much of them as possible in the sphere of influence. I also like to grab islands to include the surrounding sea, and large bay areas. I've been doing this because it intuitively seemed right. Time to try analyzing it a bit :)

Suppose that a coastline is completely straight. The coastal water region is usually one tile wide. So a city placed on the coast will have one sea tile in its workable region for each coastal tile.

For each coastal tile the resulting scoring potential is 5. (Before the difficulty multiplier.) 1 for the coastal tile plus 4 for the two happy citizens. (There isn't another point for the sea tile - it doesn't count toward territory score. Before the 2002/6/3 edit of this note I thought that it did.)

If we build inland instead, the best we can normally do is a grassland tile. Just one grassland, since we are only using one coastal tile in the comparison. (One grassland eats up the same amount toward the domination threshold.) A bonus tile (cattle, wheat, etc.) can do a bit better but they aren't common enough to include here I think. One irrigated+railroaded grassland has a scoring potential of 4. 1 for the tile, plus 2 for the happy citizen working it, plus 1 for the specialist supported by the extra food.

So coastal tiles with sea beyond seem to have a 25% higher scoring potential than grassland. (5 vs 4) And higher again when compared with plains (5 vs 3.5), desert (5 vs 3), or hills (5 vs 2.5? hard to be sure how to count hills - I'm counting it as subtracting from a specialist to feed its worker.)

Expanding the sphere of influence to sea tiles which are further out and cannot be worked by citizens does nothing for score. (I used to do this, thinking it increased score, know better now :) )

Irregular coastlines seem to reduce overall the coastal/sea tile ratio, and that will work in the other direction, reducing scoring potential. On running mapstat against my final GOTM5 map I have 471 coastal tiles and 321 sea tiles. I haven't counted them individually but I'm fairly sure that over 80% of the sea tiles are worked by citizens. Multiplying it out this works out to 3.8 points per coastal tile. Not quite as good as grassland, but better than plains. On that particular map there wasn't much grassland so it seems to have been a good move.

Islands: Looking at my final GOTM5 map, there's a small island near the south edge of the map, west of the middle. That island has 9 poor land tiles and 20 coastal tiles around it. I had 3 towns there with a sphere of influence including 33 sea tiles, 19 of which were worked by citizens. Total points: 29 (territory) + 2*38 (happy citizens) + 1 (content citizen) = 106. The same amount of territory as prime grassland would I think be 2 cities on 29 tiles: 29 (territory) + 2*27 (happy citizens) + 29 (specialists) = 112. So the island with poor land is scoring just a bit worse than the best of land. (And on the GOTM5 map there was very little prime land.) Smaller islands should do better I think. And islands with a bit of workable land will also do better of course - this island was nearly the worst case in that regard.

In summary:
After editing this note to allow for sea tiles not counting toward territory score, it seems that grabbing a lot of sea area may or may not be a good thing for score, depending on the map. My previous thinking that grabbing coastal+sea areas is always good does not seem to be justified.
If a map has lots of prime real estate (grassland) it makes sense to grab that before taking coastal areas. Coastal areas will usually be at least as good as plains.
If you do take coastal areas, try to take them in such a way that the row of sea tiles beyond the coastal tiles can be worked by citizens. If you do this then the net result should be a score for each coastal tile which is about as good as a grassland tile. In the best cases, where the coastline is regular and has just one row of coastal tiles, these tiles can increase score even more than grassland.
 
I just checked in again... there has been some action here SirPleb. I gotta start reading this again...
 
Nice job Sir Pleb with the score calculator. I love it. Right now its prediciting my score to be in low 6000's. That means i can knck of Beameuppy in the Regent HOF for 3rd place. :goodjob:
 
Originally posted by SirPleb
Finally, something I like to do in milked games which has nothing to do with score, but seems right to me for this kind of game: Improve the landscape. After the last war I use my military to destroy all the so-called "improvements" in territory which I won't be settling. I then use workers to plant forests, create a simple rail system, and create lots of paths (roads) through the woods. It doesn't take much longer to do this and the end result seems more satisfying to me. :)
I like that!:goodjob: Thanks for the milking tips.:)
 
Originally posted by SirPleb
I continued a bit after posting prior note. One more interesting case to work out a limit:

What would be the scoring penalty for the most tightly packed cities possible?

The tightest build possible is one city per 4 files. In a case with 20 irrigated+railed grassland tiles:

One city: 1 * ( 19 * 2 + 20 + 20) = 78
Five cities: 5 * ( 3 * 2 + 4 + 4 ) = 70

The difference still isn't large, a 10% loss in score. And that gets smaller as the terrain gets worse. The scoring penalty for a very tight build, although noticeable, sure isn't as large as one might guess.
It might even be less then 10% in practice.

I'm gonna do some practical tests on this matter, I will start on a map, alone, NO Rival's and try this out. Both ways, and see what the difference in score can be.

EDIT: This map will be a "Clean Map" with only Grassland Bonus tiles.

As there will not be any Rivals, all research will be done on my own, but I will make the map a Tiny map so the Test will go quick.

EDIT: Turn off "Conquest" and you can play alone on any map.

I will try and keep as many detailed notes from the two games as I can.


EDIT: I'm gonna do this test with the Egyptians.
 
Btw, I just started the test... and I think I will have to restart.

The difference will be to big when it comes to research speed so I think I will have to lower the Tech costs first.


EDIT: I lowered the tech speed, and gave Egypt 2 more techs; Alphabet and Bronze Working for starters.
 
Great thread.

I was discussing "milking" with Aeson and others over at Apolyton, and I got to thinking about culture. I just can't help myself. I build all those improvements. It's in my nature. So I was thinking... how can I do that and yet still drag the game out as long as I can?

The answer: mobilization. Once you are done building city improvements and the like, mobilize. It cuts culture production per turn in half. It's not going to save you if you have 90k culture already, but it will buy you some more turns.

----

As we all know, score is not adjusted for map size. But we do know how many tiles are on each size map, right? Roughly speaking, anyway. Population is harder to figure, but I wonder if someone with Civ on the brain and far too much time on their hands could devise a basic conversion factor so that we could compare a game played on a huge map to one played on a standard (my preferred setting).

Sir Pleb,

The one time so far that I really tried to "milk" a game, I found that although I played well past the time I could have won, and built hospitals and irrigated my land and all of that, my score was barely higher. I originally won via domination by mistake, score 5950. I reloaded, avoided that, and played on for centuries, and then again won via domination (I broke an AI city and my borders expanded... I forgot they were holding me in check), score 5970. It made me question whether or not it was worth it.

-Arrian
 
The one time so far that I really tried to "milk" a game, I found that although I played well past the time I could have won, and built hospitals and irrigated my land and all of that, my score was barely higher. I originally won via domination by mistake, score 5950. I reloaded, avoided that, and played on for centuries, and then again won via domination (I broke an AI city and my borders expanded... I forgot they were holding me in check), score 5970. It made me question whether or not it was worth it.

Yeah, what size map was that? Tiny, small, and some standard maps, there aren't enough tiles to milk to compensate for the early win bonus. And earlier in the game, the early win bonus keeps up pretty well with the points/turn you're earning by milking. When you get to the the 1700's and later, is where the early win bonus is so small, that's when the milking really kicks in. For example, on Regent if you win in the 700 A.D.'s the bonus is 30 pts/turn, after 1950 A.D. the bonus is 3 pts/turn, so if you gain say 15-20 pts/turn from milking you will really notice the difference in the last couple hundred turns.
 
Originally posted by Arrian
The one time so far that I really tried to "milk" a game, I found that although I played well past the time I could have won, and built hospitals and irrigated my land and all of that, my score was barely higher. I originally won via domination by mistake, score 5950. I reloaded, avoided that, and played on for centuries, and then again won via domination (I broke an AI city and my borders expanded... I forgot they were holding me in check), score 5970. It made me question whether or not it was worth it.
Could it have been a fairly early date when you did this? There are odd curves involved between the early-finish bonus and what can be gained on a turn by turn basis through milking. In games where an early enough win is possible, the curves have a cross-over point - you might have been around that point.

I think this is an unfortunate effect of the game's score calculation. It leads to some rather undesirable results.

For instance, at 500AD the early finish bonus is going down by 10 * Difficulty for each additional turn played. Let's say we're using Emperor level, so that would be 50/turn. The gain per turn from milking depends on the map size, and whether we have control of the bulk of the map yet of course. Let's say we're gaining about 50/turn at that date by milking. In this case milking would appear to not be doing any good.

But in the long run the milking will increase score a lot in this case. By the time we reach 1250AD, the milking increase might be slowing down a bit due to approaching maximum territory and happy citizens. (Or it might still be rising, but let's suppose it is slowing down.) Say it has dropped to a gain of 45/turn. But at 1250AD the early finish bonus drops to 5 * Difficulty, i.e. 25/turn. So now milking starts gaining noticeably each turn. At 1750AD the gain per turn from milking increases again. And at 1950AD when the early finish bonus drops to 5/turn, the ongoing milking will far exceed the lost bonus in each turn.

To make this example worse, suppose we were gaining at 40/turn in 500AD. At that point, for every turn we continue milking up to 1250AD our score for finishing at that date goes down. But if we milk to 2050AD the score will be much higher than if we'd stopped at 500AD. So there's a point in some games where milking just a bit makes the score worse but milking a lot more makes the score better. To me this seems a very undesirable scoring algorithm.

IMO the scoring algorithm would be better overall if the early finish bonus were based on number of turns instead of number of years. E.g. the bonus could be (540 - TurnsPlayed) * 10 * Difficulty. So an Emperor level win in 1500AD would get 250 * 10 * 5 = 12500 as the early finish bonus. A bonus like this would largely eliminate the non-linear benefit of milking. It would still be possible on large maps to gain more by milking than by finishing early, but at least the gain or loss from milking would be clear from turn to turn, instead of the current situation where the largest benefit from milking is at the back-end. I guess a turn-based finish bonus might introduce other problems I haven't thought of. But it seems to me they'd at least be less severe. :)
 
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