Great People Points: Focus in one city, or distribute across many?

Discussion in 'Civ4 Strategy Articles' started by Vol, Nov 22, 2005.

1. aryahChieftain

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thx!
thats a good point, but his first chart seems to say that the racing condition between cities, discounting the effect of National Epics, under reasonable distributions is not problematic, it alone only affects some random walk +-8% around the mean. Since its the argument, as I understand it, that the debalance by National Epics is what makes the situation so very inefficient, the significantly diminished effect of National Epics probably relieves a substantial portion of the worry about issues with such distribution, because of the racing conditions.
The potentially added total population of specialist due to more area being worked for them (in all cities) should be more than able to make up for this (smaller) inefficiency it terms of total efficiency of the use of the empire & its territory, just as much as a commerce in a non-Oxford city is still worth it even though such distribution of commerce between cities is technically less efficient than putting them all in that city - only in this aspect did I draw a parallel.

Point is a concept of distribution of specialists across cities seems to imply that one is like actually choosing whether one would put 10 specialist around your empire or somehow migrate those populations to once city; just like with commerce resources found or built on tiles, the food resources and the city population is not free to move in this way, but this doesnt imply its wasteful to use them in such cities anymore than it would imply so for the commerce resources, with even potentially worse multipliers in comparison to that fictive alternative.
It doesnt seem to me to be the most useful way of investigating about specialist distributions. Im thinking perhaps finding some ideas about how to distribute such specialist so that those outside the National Epics city are not aditionally hampered by the racing with it more than say their relative GPP multipliers, or even say, to around 2/3 , like it is with commerce..

I would like to understand more about the mathematics used for that chart+-8% chart, I tried analysing the racing situations, but couldnt come up with a way to reason about situation with multiple cities. Im particularly interested in what exact situation does a city loose the race with a larger city forever, under what kind of a concrete scenario? Though Id intuitively expect this to happen, I couldnt understand exactly how when I tried thinking about such situations, it allways seemed it would catch up eventually with the moving target, even if in game-impractical amount of time, it seemed their GPP points grew quadratically due to accumulation, while the 'border' moved only linearly...

2. Roland JohansenDeity

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I just skimmed over the article again. I had read it some years ago and had forgotten its exact argumentation. The article was written shortly after the release of the game and not every detail about the game mechanics was completely understood then. The article explains a small part of the effects of the way the game generates great people and does so with nice graphs, but it isn't the the definite article on great people generation (and wasn't meant to be so).

The point that I was making in my previous post is not really included in detail. The article is more about the effect of the National Epic. Of course, when you are able to focus all of the great person point generation of an entire empire in a single city with the heroic epic, then you will generate about twice as many great people points then when you focus them outside of the city with the National Epic (or a smaller factor than 2 with the philosophical trait or the pacifism civic). That's the factor 2 that you see in the second graph (60% on the right versus 120% on the left).

The article doesn't really explore the effect of spreading great people points generation over many cities. The analysis is done for 3 cities, for d=1, the great people points are spread over 3 cities, for very small values of d, the great people points are focussed in a single city, for very high values of d, the great people points are focussed in 2 cities. If you're generating all of the great people points of an entire empire in 1, 2 or 3 cities, then you're still focussing them and not spreading them.

I'll try to show the results of spreading them in an example. You'll have to do some minor calculations. You can't hope to really understand the mathematical effects of game rules without doing some calculations. But I'll keep the numbers simple so as not to complicate matters unnecessarily.

But first of all, I want to remove a misconception shared by many namely: doubling the number of great person points generated by your empire will result in double the number of great persons after the same amount of time. This is not true. This has to do with the number of great person points needed for the next great person. It is a number that increases as follows (normal speed values):
100, 200, 300, 400, 500, 600, 700, 800, 900, 1000,
1200, 1400, 1600, 1800, 2000, 2200, 2400, 2600, 2800, 3000,
3300, 3600, etc.

Say for the sake of simplicity that all of the great person points are generated in a single city, so no loss of great person points in a city that is not going to generate a great person. Then after generating 1000 great person points, you'll have created 4 great persons, the ones for 100, 200, 300 and 400 great person points. It will take you 2100 great person points to generate 6 great persons, more than double the amount to generate 4 great persons.

(If you're mathematically inclined: the function describing the number of great person points needed to get n great persons starts of behaving like a quadratic function and even speeds up to a polynomial of the third degree after the n=10. This means that the number of great persons generated after a time T (at a constant great person point generation) starts of behaving like sqrt(T) (4 times as many great person points gives you twice as many great persons) and slows down to T^(1/3) (8 times as many great person points gives you twice as many great persons).)

Let us now discuss spreading great people points vs focussing them in one (or a few) cit(y)(ies).
First of all, there is an opportunity cost to using specialists to generate great people. It means that you will need more farms (to feed the specialists) instead of mines and towns which usually means a lower output of the city. The representation civic and small cottages might temporarily give an advantage to the specialist situation, but once the cottages mature a little, they will even outproduce a specialist under representation. You can have multiple cottages for each specialist because the specialist needs farms to feed him. In return for this opportunity cost, you expect to gain great people which make it worth the investment. If the return in great people is low or the time it takes to get great people is very long, then the investment wasn't worth it. The opportunity costs were too high for the limited return.

The best way to show what happens when you spread great people is an example. I'll try to use simple values in the example so that the calculations are relatively simple.

Situation 1:
The player created one Great Person farm specialised entirely to create great person points. It's generating 50 great person points per turn. Obviously this is unlikely in the early game, but it is very possible in the late game.

Situation 2:
The player created the same great person farm. Additionally, the player chose to create 5 great person points in 10 other cities effectively doubling his output in great person points. What will be the effect of this?

Situation 1:
Great People will be generated after this many turns:
2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 134, 162, 194, 230, 270, 314, 362, 414, 470 (game end)

Situation 2:
Great People will be generated after this many turns:
2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 134, 162, 194, 230, 270, 314, 362, 414, 470 (game end) all in the great person farm. Hmm, really? Yes, the other cities never in the entire game produce one single great person. Yes, they do produce many great person points, but they can never finish a great person before the great person farm has finished its next one and the amount increases again.

I'll show a few of the calculations to hopefully convince you that I didn't cheat with the numbers.
It takes 1000 (100+200+300+400) great person points to create 4 great persons in the single great person farm. That takes 20 turns at 50 great person points per turn.
To create the fourth great person in another city takes 400 great person points. But after 20 turns at 5 gpp's per turn, these cities only have 100 great person points.

It takes 23500 great person points to create 19 great persons in the single great person farm. That takes 470 turns at 50 GPP's per turn. The 19-th great person costs 2800 great person points. But after 470 turns, the 5 GPP's per turn producing cities have just accumulated 2350 GPP's.

Does this mean that these small cities will never produce a great person even if the game would play on indefinitely? No, not never, but it takes longer than the length of a game to produce one.

What this shows is that if the difference in great person point generation is too big, then the additional cities are useless for generating great persons.

If the 10 cities would be producing 10 GPP's per turn (tripling the empire wide output of great person points), then one of them would generate a great person after 100 turns and another after 160 turns (didn't calculate any further). In this case, there is some return of the investment, but producing 1600 great person points in 10 cities (16000 great person points in total) for 1 great person after 100 turns and another after 160 turns while the great person farm created 11 in the meantime shows that tripling the output of great person points has a very low revenue in this case. In my opinion, definitely not worth the opportunity costs.

If you can get a few cities which produce high amounts of great person points, then that is okay. But if you add numerous other cities which only add small numbers of great person points, then those aren't going to help generate great people. Try to concentrate the generation of great person points in a few cities (1, 2, 3, maybe 4) which have a roughly equal output (differing no more than a factor of 2 or 3 in output).

Of course, you should focus the production of great person points in those cities that have multiple food resources. Not only can you get a higher food output in these cities than in normal cities meaning that the total number of specialists and the total generation of great person points in such cities has the potential to be much higher, but also the opportunity cost to support these specialists is low as each food resource can support several specialists already very early in the game. You don't need many farms to get a decent number of specialists in these cities.

I hope this helps.

3. ColfoxChieftain

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This has been a fascinating read, even if I'm too lazy to do all the math.

I just have one question. If I want to create a GP city, then I want high food production to support the specialists. I'd also like to build lots of Wonders there for the "free" GP points.

Cities with high food production tend NOT to be good production cities. How am I building all the Wonders? There are only so many forests around.

I'm relatively new to this forum, and I'm sure the answer is here somewhere. I need to keep reading...

4. Roland JohansenDeity

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It's not that hard to create a city that produces enough food to support 10 specialists and if you pick the city where you want to create specialists right, then this city will be able to support many more specialists by the late game. 10 specialists create as many great person points as 15 great wonders. If you're able to get anywhere near 15 great wonders in a single city, then you're playing at a difficulty level that is clearly not challenging you.

So the idea is that the great person farm is creating great persons by having many specialists, not by having many great wonders. It might have some (by chopping forests as you say or by temporarily changing terrain and focussing on production), but this city is typically not having many wonders as it doesn't have the production to create them.

Some other cities that are focussing on a high hammer output will (try to) build the wonders of your civilization, not for their great person point bonuses but for the other benefits of the wonders.

5. ColfoxChieftain

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That makes sense. I've just made the jump from Noble to Prince (I know...I'm a piker...that's why I'm reading the boards). I'd been playing industrious civs, and I knew is was time to step up when I was building 4/5ths of the Wonders and founding 5 religions. Needless to say, Prince has been a bit of a shock to my system. From reading the boards, it looks like building a Wonder is a rare achievement at the higher levels. I need to get out of the habit now, and learn other ways to get ahead. Anyway, thanks for the reply.

6. Roland JohansenDeity

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At the levels that are really challenging someone (doesn't really have to do with the actual difficulty of the level, just the relative difficulty for the player), the player doesn't have the luxury to go for many world wonders. Especially at the start of the game where expansion and claiming good city tiles is very important, going for a wonder can be a luxury that you can't afford. One will have to choose between building a wonder like the pyramids and building several cities. If the level is really challenging you, then you probably can't afford to miss those cities.

Not everyone likes to play at a difficulty level that challenges them so much that it is hard to build a world wonder. Many just like to build an empire with many beautiful cities with many wonders. In that case, maybe the world wonders can be a substantial source of great person points. Usually, I won't have many world wonders in my great person farm.

7. InvisibleStalkeEmperor

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See Obsoletes games for a strategy on producing Great People and wonders. You settle the great people (usually priests) in your capital to provide more hammers to build more wonders which produce more Great People. Its a pretty nice virtuous circle and he plays it at Immortal/Diety.

Wonders don't produce as many Great People as specialists, but you can have both specialists and wonders in the same city.

8. WodanDeity

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And, wonders don't eat food.

Wodan

9. Roland JohansenDeity

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Personally, I think settling great persons is a relatively pretty poor investment of the great person. Many of the great persons also don't provide a great number of hammers when settled. Still, if you want to create a super city, then that's the way to do it. Super cities work better on smaller maps where their relative influence is bigger. On huge maps, one single super city is unlikely to have a big influence on your empire.

10. WodanDeity

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If you have Pyramids and are running Representation, settling an early GP is a very good option. Otherwise, I tend to agree. Save them for a golden age, if nothing else.

Wodan

11. Roland JohansenDeity

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I must admit that the representation bonus on settled great persons is pretty significant. I just don't like to go for the Pyramids in my games. That wonder is so expensive and there is always some industrious AI or an AI that starts near stone. To get it first, you'll have to build it fairly early. If you have stone yourself or play with only a few AI opponents on a small world, then it's probably less costly to try and get that wonder after some expansion of your empire. On the lower difficulty levels, it's probably also not that costly to get it first.

12. WodanDeity

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Yeah but even if you don't get it, you get a very efficient translation of hammers to gold which can allow you to run a deficit economy and increase your tech speed.

Look at it this way: if there was something that allowed you to research at 125%, would you do it? I think you probably would.

Wodan

ps I pulled the 125 number out of my rear; it would be interesting to do an analysis to see what that number really is.

13. Roland JohansenDeity

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It can be an efficient transition of hammers to gold if you have stone or are industrious.

And no, I won't always go for research at 125%. Not if it would seriously harm my expansion. So if I can build the pyramids without seriously harming my expansion, then I'll try it.

On huge maps at immortal or deity level with the standard number of opponents, a decent rate of expansion would give one more than 10 cities before 0 AD (without war, with war it's hard to tell).
The pyramids cost 500 hammers, a settler 100, so building the pyramids is a rather costly affair (or 750 and 150 at the epic speed at which I usually play).

14. WodanDeity

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10 cities before 0AD seems to me is way too much. That's crippling to your economy, no matter what size map. When do you usually get Currency or something?

Regardless, personally I feel that with CIV, expansion at all costs is not the best way to go. That's a good way to get yourself in trouble. It always has to be a balance of economy, military, expansion, and research.

Wodan

15. Roland JohansenDeity

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I agree that you should balance your economy with your expansion. It's quite easy to overexpand and ruin your economy. That has been true since the first version of civilization 4.

Usually, claiming some resources and using hereditary rule so that my cities can grow a little and use multiple cottages per city helps to prevent a catastrophic stagnation in my economic expansion.

The balance between economic expansion and normal city expansion is a little different on the different map sizes. For instance on huge maps, city upkeep costs are typically a little lower. This is done intentionally as otherwise only a tiny fraction of the map could be settled at the start of the game. The high difficulty level does increase the city upkeep again.
I won't say that it's very easy to create an economy that can sustain more than 10 cities at 0AD, but as I usually play that way, it is certainly possible.

If you don't expand at a fairly fast pace at these settings (immortal/deity, huge map, standard number of opponents), then you will see that the AI will claim a significantly larger part of the map than you do and you will have to compete with AI civilizations twice your size. That can be a problem. Especially if you also use the aggressive AI setting as they will see you as a weak civilization that can be conquered easily.

By the way, we're derailing this thread a bit. It is a thread about great people points, so maybe we should continue this discussion elsewhere if you want to continue it.

16. WodanDeity

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Nah, let's just drop it. Thanks for your thoughts.

Wodan

17. Roland JohansenDeity

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Thank you for yours.

By the way, we have almost the same number of posts (at the moment).

18. WodanDeity

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You're right. Neck and neck.

Anyway, back to the OP... lately I've been focusing in one city, but not worrying about GPP "purity" like I used to do... so I get the mixed bag of GP to feed golden ages.

Wodan

19. BureaucracyChieftain

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You are certainly right, that losing 5 settlers can hurt your expansion. But on the other hand, who can build 5 more cities from the start, and not run their economy into the ground by doing so?

Of course, the math isn't so straight forward. Some Civs get settler building bonuses, and others get wonder bonuses, and then there are resources to make the case more complex. So the base value comparison is a little hard to guide by.

Back in the days of Civ 3, the Land-is-Power ideal was pretty much dead-on. It still has certain valid points, but there are at least a couple deity builders who get along fine by focusing on vertical growth instead.

20. Roland JohansenDeity

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I didn't want to say that not building the pyramids would allow one to build 5 more settlers and I purposefully didn't say so. To create new cities, you also have to create units to defend them and workers to improve the area around them. Furthermore, you will want to grow your cities vertically a bit so that your economy doesn't stall.

I just wanted to say that building the pyramids will cost me a lot in expansion speed, usually too much for my taste. If you start near stone, then it's less of a problem, but that depends on luck.