A theory of interest for Civ2

[Peaster]

Interesting questions, which I have not analyzed mathematicly. But in most GOTMs, we can IRB in rows 1 and 2 very early in the game without effort. Often, we start with either BW or HBR. If not, I usually choose BW as the off-path tech towards monarchy. And sometimes you get these techs, or WC or Writing, from huts or even from AI contacts.

I'd guess that getting a second off-path tech mainly to make IRB's easier is not worthwhile. You don't have a lot of gold early in the game, even with maxed taxes, so you can usually spend all you have just on rows 1, 2 and 4 (or whatever rows are available).

 

[Ali Ardavan]

It would be interesting to see the math comparing the "cost" of stressing science (in delays to earliest expansion through limited rush buying) vs. the "cost" of delaying monarchy (delaying the accelerated food growth) a bit later because science was not stressed.

Here is my take on this:
Because of oedo years any delay in discovering Monarchy that does not change the date you switch to Monarchy are worthwhile. If you miss the oedo year, Monarchy is delayed 4 turns. The benefits of Monarchy are:
1. Extra food per turn per city on grass. Extra food per food special (wheat, fish, oasis, pheasant, spice, fruit, ...)
2. Extra shield on shield specials (Peat, Oil, ...)
3. Extra arrow on arrow specials.
4. Less corruption
5. More flexibility with the Tax/Lux/Sci setting
6. Better unit support system (3 per city as opposed to 1 per citizen)

2,4, and 5 above are of negligible practical significance in the early part of the game (my focus is on -4000 to -1000). 3 is of practical significance when you have a Whale within city radius. Since whales are fairly abundunt and the most valuable special to have, this occurs on a frequent basis. 6 matters when there are no closeby huts or the hut does not give you a None unit. In either case your first city gets stuck with a supported unit and when it produces its first settler and goes back to size 1, it has to pay 1 shield of support while the settler is making its way to its city site. 1 is the most important benefit.

Unless one gets a significant number of start up techs, one has about 4 cities by the time one discovers Monarchy (Peaster probably has more). I assume that all cities are on grass, two have access to a whale, and one has access to another food special. (I believe this assumption is reasonable as we seek the specials out and try to build cities that take advantage of them.)The benefits of 4 turns of Monarchy through numbers 1 and 3 (ignoring 6) above are thus: 4x4 food + 4x1 food + 4x2 arrow = 20f + 8a.

Now let us look at the benefit of establishing a city earlier. Again I assume that the city is on grass and give it a 50% chance of having a whale, and 25% chance of having another food special. The food special does not matter sicne we are in despotism (unless it is fruit, but that is negligible). The city produces 4f+2s+1a without special (assuming shielded grass) and 4f+3s+3a with a whale for an expected value of 4f+2.5s+2a. 2f are consumed so it leaves us with 2f+2.5s+2a per turn.

Given that most often I can switch from shielded grass (2f+s) to forest (f+2s) the above become equivalent to 20s+8a (for Monarchy) and 4.5s+2a per turn for a city.

The conculsion: Delaying Monarchy by an Oedo cycle (4 turns) is justifiable if you can get 5 or more settler-turns in return (for example produce two settlers one two turns earlier and another three turns earlier)

 

[Ali Ardavan]

While I enjoyed doing the above analysis, let me also point out that I believe in over 90% of the games the decision to delay Monarchy depends heavily on the paticular circumstances of the game. One aspect of this is presence/lack of a None unit. Another is the ability to rush buy 2nd and 3rd rows as pointed out by ElephantU. Another is the availability of cash through huts (why would I want to delay research if I have already gotten a lot of cash from huts).

My instinctive opinion is that most of the time delaying Monarchy is a bad idea.

 

[Andu Indorin]

While I enjoyed doing the above analysis, let me also point out that I believe in over 90% of the games the decision to delay Monarchy depends heavily on the paticular circumstances of the game. One aspect of this is presence/lack of a None unit. Another is the ability to rush buy 2nd and 3rd rows as pointed out by ElephantU. Another is the availability of cash through huts (why would I want to delay research if I have already gotten a lot of cash from huts).

My instinctive opinion is that most of the time delaying Monarchy is a bad idea.

A good rule of thumb , with many with many of the games-theoretic options cited. But when are the circumstances right to bypass Monarchy and go straight to Republic?

And, perhaps more pertinent to the discussion, how does when measure long-term infrastructural development (eg., labor-intensive irrigation) in terms of a "per turn" investment.

Which is to ask: "How exactly should one calculate a per-turn return on investment so early in the game?" There is something to be said for capital investments ...

(Granted, given my appreciation of the power of Engineers, I do tend to underestimate the powers of the Settler.)

 

[Peaster]

Ali - I am more comfortable with my quick analysis. But I think your analysis leads to the same conclusion. You concluded that one oedo cycle is worth about 4-5 settler turns. Let's continue....

Suppose monarchy is the 5th tech, which costs about 60 beakers (is that about right?) and you are getting an advance every 8 turns. So, one oedo cycle costs you about 60b x4/8 = 30b = 30g (in approx 2500BC). Suppose a typical city makes 2.5s/t, as you said, and you can spend 30g on IRBing a Settler [actually it would be spread across time, and several cities]. Then 30g buys 15s (if you do it right) so you can save 15/2.5 = 6 settler turns, which is good.

And this omits an important idea that makes the taxes+ IRB plan twice as attractive. That is, beakers do not compound like gold does (30b in 4000BC = 30b in 2500BC, IMO). So, you should imagine that the 30g is spent as soon as it arrives (not in 2500BC like the beakers) - let's say 3200BC, as an average year. So it saves a settler 6 turns in 3200BC. But that settler will produce a baby by 2500BC [and then both of them are 6t ahead], so you have actually saved 12 settler turns!

I admit that getting monarchy 4 turns early has a side benefit, that you may also get the next tech 4 turns early too. Probably other minor factors have been left out, and an exact analysis of this question seems very difficult. I started on it as a noobie 2 years ago and gave up, but my rough estimates and experience indicate that early IRBs count more than a few turns of monarchy. Someone else (maybe SlowThinker?) should get the credit for the early taxes aspect - I don't remember quite where I got that part anymore.

Why not try a practice game or two, to see for yourself if early taxes work well for you? The 4000BC to 2000BC period doesn't take very long. BTW - I agree that factors in a specific game must be considered. But you have to start this strategy in 4000BC to get the full advantage.

 

[Ali Ardavan]

And this omits an important idea that makes the taxes+ IRB plan twice as attractive. That is, beakers do not compound like gold does (30b in 4000BC = 30b in 2500BC, IMO). So, you should imagine that the 30g is spent as soon as it arrives...

Not quite true. Gold spent on rushing does not compound till the unit is actually produced either. Whether you spend the gold this turn on row 1 or 10 turns later on row 3 (assuming you can) is the same. Likewise, there is the compounding effect with techs as well. The sooner you get Monarchy out of the way, the sooner you can get Trade, and so on with other needed techs.

Why not try a practice game or two, to see for yourself if early taxes work well for you? The 4000BC to 2000BC period doesn't take very long. BTW - I agree that factors in a specific game must be considered. But you have to start this strategy in 4000BC to get the full advantage.

Great suggestion. I would.

 

[TimTheEnchanter]

Not quite true. Gold spent on rushing does not compound till the unit is actually produced either. Whether you spend the gold this turn on row 1 or 10 turns later on row 3 (assuming you can) is the same. Likewise, there is the compounding effect with techs as well. The sooner you get Monarchy out of the way, the sooner you can get Trade, and so on with other needed techs.

The 'payoff' for both spending gold on settlers, and spending taxes on science is not truly compounding every turn in the financial sense. They both have payouts at thresholds. You don't get the benefits of the gold until your settler founds a city, and you don't get the benefits of the science until you learn the appropriate techs. However, I think the fact that the gold pays off in smaller thresholds does allows for more compounding than the beakers. Compare getting 5% per month to getting 60% (5%*12) per year. In 6 years, the monthly compounding will give you double what you get from the annual compounding.

Investing in gold has a very real effect on getting cities planted sooner. Investing in beakers doesn't really show a benefit until monarchy is learned. After that, you don't get much benefit until Trade (do camels justify the cost in this analysis?). OTher than that, your next payoff might not be until either map making and/or one of the Att 4, Move 2 units is available (and I don't even want to think about trying to quantify the value of war yet.)

This brings up another question. This analysis really doesn't address the "value" of the techs very well. The beakers themselves are treated as having value, but what is the real "payoff" or value of the techs? Since value is basically translated to beakers=arrows=sheilds=settlers, there is an additional layer of indirection trying to establish the value of the technology. What is the value of map making (depends on size of land, location of other civs etc)? What is the value of trade? What is the value of Polytheism? How to you quantify the difference in riot factor between despotism and monarchy? How do you quantify the effects of knowing these things earlier vs. later? Etc.

 

[Ali Ardavan]

However, I think the fact that the gold pays off in smaller thresholds does allows for more compounding than the beakers.

Good point; but only because at that stage of the game advances other than Monarchy are of no value yet. But even that may not be the case. In GOTM63 we all ran into Greeks pretty early on. I got two techs towards Monarchy (Ceremonial Burial and Bronze Working which is off path but I was stuck with it due to tech hiding) from them through tech exchange. If I did not have techs such as Code of Laws to offer, the exchange would not have happpened.

This brings up another question. This analysis really doesn't address the "value" of the techs very well. The beakers themselves are treated as having value, but what is the real "payoff" or value of the techs? Since value is basically translated to beakers=arrows=sheilds=settlers, there is an additional layer of indirection trying to establish the value of the technology. What is the value of map making (depends on size of land, location of other civs etc)? What is the value of trade? What is the value of Polytheism? How to you quantify the difference in riot factor between despotism and monarchy? How do you quantify the effects of knowing these things earlier vs. later? Etc.

Good points; but as far as I am concerned these go far beyond the scope of anything we are trying to (or are even capable of) analyzing here.

 

[Peaster]

The 'payoff' for both spending gold on settlers, and spending taxes on science ... both have payouts at thresholds.

Good explanation. Gold compounds much faster than beakers, with the exception of a few threshold periods (eg monarchy, trade, corporation).

(do camels justify the cost in this analysis?).

You are asking whether a camel is worth 50 shields (or 125g)? I think so (usually). Suppose you need a boat (100g) and 10 turns to deliver it, and it pays 200g + 200b = 400g (ignoring the ongoing benefits). So, 225g pays back 400g in 10t, which is an excellent return of about 8% (IMO.... too lazy to reach for a calculator). Of course, all this depends on city size, celebration, commodity demand, water safety, whether you need beakers as much gold, etc. But you can use the boat more than once, and you can often get bonuses well over 200g, so I think camels are a good idea 90% of the time.

I don't usually make camels in a strict EC game, because I don't really need the beakers, but I have been experimenting with them more lately. They may make sense even there.

This brings up another question. This analysis really doesn't address the "value" of the techs very well....

Most of these questions seem too hard for me. IMO the rule of thumb, 1b = 1g, is good enough. The equation must be approx correct, because we have so much trouble deciding which side is worth more.

Also, IMO exact answers would have to depend on the player's style and goals. In my EC games, for example, I mainly need Mon'y, Trade, Poly and MapM - the rest is icing. And I almost always get them "in time" (my conquests are delayed more often by shield production than by slow science). So, for practical purposes, all these techs (except monarchy) have negligible value to me. That's an oversimplification - I do raise my science bar above 30% sometimes. But I don't need a numerical evaluation of these techs, to play EC.

Also - I am no expert on landing games, but I imagine that the overall goal should be to make X beakers (enough for all the pre-reqs of fusion power or whatever). And most of these are made towards the end. The early goal should be to build a civ that can produce beakers quickly [thru an SSC and trade]. So, in my (almost only) game, I tended to ignore specific techs, and to concentrate on the growth strategies we've discussed in this thread (with some assets siphoned off into the SSC and cities).

 

[Ali Ardavan]

Also - I am no expert on landing games, but I imagine that the overall goal should be to make X beakers (enough for all the pre-reqs of fusion power or whatever). And most of these are made towards the end. The early goal should be to build a civ that can produce beakers quickly [thru an SSC and trade]. So, in my (almost only) game, I tended to ignore specific techs, and to concentrate on the growth strategies we've discussed in this thread (with some assets siphoned off into the SSC and cities).

Your results have always been impressive, but what impressed me most was the speed with which you launched in GOTM63. Before this, I always had doubts on how applicable your style is to a landing game. Timewise, you beat at least 2 seasoned landing players (Grigor and I) by a long shot.

 

[Peaster]

Thanks, Ali. That GOTM was uncharted waters for me, so I wasn't sure if I was playing well or not. But I remembered that Zenon (one of the great landers and also a strong conquest player) once said there's not much difference in how you start a landing game and a conquest game. Also, DaveV's ICS philosophy (bigger/faster) has always made sense to me, and I thought it should apply to landing games too.

 

[Prof. Garfield]

But when are the circumstances right to bypass Monarchy and go straight to Republic?

Short answer: Go for Monarchy in Emperor, Diety and Diety plus one. Go for republic in most other circumstances. (At d+2, you need a reasonably high lux rate and acces to ocean with most or all cities to make it work, but the elimination of riots with cities should more than compensate.)

Addmittedly, I skimmed over all the fine mathematical points of this discussion, but I noticed a couple of small problems with the general strategy:
It looks like it falls apart at higher difficulty leavels with their higher riot factor and fewer content citizens. What hapens to your investment when you have to wait ten turns for your city to have two citizens to stop rioting? Then add 20 turns to build the settler and 10-20 more turns for the riots to end...

Furthermore, few games give you a huge river system to streamline transportation, and even in that case inland transportation also takes away from valuable whale possibilities. Your double the civ sise every 14-18 turns is also comprimised after a few cycles due to the fact that it may take that many more turns to move your centrally produced settlers out to the fronteer to build cities. This strategy sounds like the basic expansionist diety strategy applied to lower levels. A group of us played a succession game a while ago on a low level with tons of rivers, albeit a map with more land than water and somewhat swampy terrain. I'll find the name and you can see what hapens when diety players end up playing warlord with rivers. It looks more or less like this strategy sounds.

The real lesson of this thread is why a planned economy doesn't work in the real world...

 

[Prof. Garfield]

It was called "succession game, join in"

 

[TimTheEnchanter]

Addmittedly, I skimmed over all the fine mathematical points of this discussion, but I noticed a couple of small problems with the general strategy:
It looks like it falls apart at higher difficulty leavels with their higher riot factor and fewer content citizens. What hapens to your investment when you have to wait ten turns for your city to have two citizens to stop rioting? Then add 20 turns to build the settler and 10-20 more turns for the riots to end...

I'm not sure how Peaster approaches deity since so few GOTM's are done at that level and that's where I've seen his games, but this strategy was originally designed to specifically deal with the problems of deity. A few turns spent on a quick garrison warrior or maybe a horse for more mobility and you're back to cranking settlers. The key is that you get the citizens out of your city as settlers because otherwise you have to spend more keeping them happy. Would you rather spend money just keeping citizens content, or keeping citizens content while growing your base? If you play it right (or get lucky with the timing), a handful of units can move between cities and provide relief as needed. Then, after a bit more of churning out new cities, the riot factor kicks in and you start getting citizens in the black. At this point you should be about ready to build Hanging Gardens (because you knew you were in deity and that this was going to happen) and suddenly the black hats are your dear friends. It sometimes seems harder to manage this type of expansion at levels lower than deity because it takes many more cities to start getting black hats.

Furthermore, few games give you a huge river system to streamline transportation, and even in that case inland transportation also takes away from valuable whale possibilities.

I don't see why whales are excluded as they can still be reached from coastal cities. :?

Your double the civ sise every 14-18 turns is also comprimised after a few cycles due to the fact that it may take that many more turns to move your centrally produced settlers out to the fronteer to build cities.

We discussed this earlier in the thread. By building the cities very close together, you save several turns in transit. If you build spread out, you will have trouble, but if you pack them into a tight pattern, it's not that far to the frontier for the first several rounds of expansion. You also can build a continuous road network to the frontier with only a few roads, taking advantage of the free city-square roads.

This strategy sounds like the basic expansionist diety strategy applied to lower levels. A group of us played a succession game a while ago on a low level with tons of rivers, albeit a map with more land than water and somewhat swampy terrain. I'll find the name and you can see what hapens when diety players end up playing warlord with rivers. It looks more or less like this strategy sounds.

Not sure what you're getting at.

The real lesson of this thread is why a planned economy doesn't work in the real world...

???

 

[Peaster]

The main point of the thread is that Civ2 is mostly about investing. You want to invest in whatever gives the best return It pays off to have some rough idea of the "interest rate" for each of your options. Usually, the best rate is approx 5% from building settlers, but well-planned caravans can pay more.

I consider it a decision-method, rather than a full strategy. Though it was almost certainly the main idea behind the ICS strategy. That was developed for Deity level, but IMO the level of play (and the govt etc) doesn't really matter too much.

At Deity level, I make a just-in-time warrior for each growing city, and build HG ASAP (eg standard ICS play). You have a point - this slows down growth, which implies a slightly lower interest rate. But it's still over 4% IMO. This difference could affect some borderline decisions, but not many.

If you want to poke holes in the theory, or at least in the 5% figure, you could mention maps with poor terrain. They can slow down growth much more than Deity level does. So, on those maps, I often invest in exploration units, for huts and AI contact. Hard to estimate the return on that, though.

 

[rysingsun]

no i won't poke any holes in the theory. i find it quite fascinating reading. i've spent years trying to shave a turn here and there off the empire doubling time. so i find it fascinating that i indeed left out this one strategy of ultra-tight city spacing. now i like going for high scores on large maps where i run into that 255 city limit, so for me to implement this in the early game means i have to start disbanding cities in the midgame ... something a bit of a pain in II.

You've mentioned that the settler "interest rate" goes down on poor terrain maps. agreed. now you have approached this concept of interest in the context of number of cities and with it the settler-producing capability. now once republic / demo comes along the rate of settler production can go through the roof providing an interest rate of about 15 percent as long as WLTK can be had and unlimited cash can be provided for rushing settlers. This again would demand a 15 percent interest rate on gold in particular. and how is that done? it requires some combination of highly lucrative caravans and very short delivery times. i guess that has been my forte over the last few years.

but i feel i cheated myself. because while i learned to grow my gold by 15 percent per turn (for a short time) it never even occured to me that i was spreading my cities far far too wide. heck, if i had cramped them all together even my caravans would have reached their desinations on average a couple turns earlier increasing the gold interest rate too.

 

[ElephantU]

Just a note to rysingsun that caravan delivery to your own cities suffers a 50% reduction in bonus payment, over and above the short distances between the cities likely in an ICS style strategy. Better plan would be to find a decent-sized AI on another island about 20 tiles away and set up a boat chain to deliver as many demanded caravans as possible. Explore for another AI civ in the neighborhood and fork or expand the chain.

 

[Ali Ardavan]

rysingsun, keep in mind that the analysis was done for the rapid expansion phase of before -1000. The closely spaced cities will not grow much in the long run and are ill suited for much of any infrastructure.

That this approach allows a faster finish in conquest games has been known and is undisputed. Peaster's result for GOTM63 shows that this approach also allows faster finish for space ship games. But if your goal is to maximize score or build a large empire or go through all 255 future techs (did I miss anything here?) then this is not going to help you.

Having said that, your theory of building cities close by initially and abandoning them midgame is fascinating.

Another theory I would like to try, once I get a chance, is a mixture of small and large cities planned apriori. Up to now my approach, and probably yours too, is to place cities far enough apart that they share little, if any, tiles. This assumes every city is going to grow to its max size and have full infrastructure. The ICS approach, is the exact opposite with the exception of one city: the science city. I wonder how a mixed approach would compare. Some cities (most notably the ones with 3-4 specials) spaced such that they get all their 21 tiles and others spaced closeby. The large ones would get all infrastructures and the small ones very little.

 

[rysingsun]

perhaps i should explain the method a little more clearly.

lets assume for now a large world map starting as the americans so that we can all visualize the map.

i will rapidly build about 6 cities ICS style, although previously i had always built them with a wider spacing. i will then build a science city somewhere around nova scotia (a nice place where all 21 tiles can generate trade arrows). with caravans i will rush collosus here and hanging gardens somewhere. if i can get lighthouse that will be excellent too. after this it's just a matter of building settlers caravans and triremes. the triremes bring the caravans to europe. the ICS allows me to have many cities that can support ships to carry caravans and the tight spacing allows not only settlers to quickly get to new city destinations but also caravans to quickly get to the science city and rehome to it. incidentally the fact that i rehome all the caravans to the science city means for me that it is almost irrelavent at this stage in the game that my other cities are cramped and unproductive. for a long time they have little purpose besides building settlers and caravans.

edit ... i should also point out that strictly speaking this is not necessary in games that have no goal besides high score, because high scores are almost entirely dependent on population. the quick-finish bonus is so minor for it that it comes down to little more than getting the largest land-area map possible and then working down every single tile to grass for max population, meanwhile placing cities so that there is no overlap and as much of the workable area as possible is land, rather than ocean. but my kick is converting my world to grass with an earlier completion date than before ... sort of my own version of "beating my previous best" and hence the interest in super-fast expansion phases.

 

[Nick Garai]

By the time you can build factories, all the good city sites have long since been taken. Are you suggesting building cities on Antarctica, or what? I guess you could build them in between your existing cities, but all that does is turn one good city in to two worthless cities.

Nothing wrong with building cities in Antarctica. Use engineers to terraform the land into fertile grasslands and you have room for another 20-50 cities up there and each one can also be used for making a navy. If they have offshore oil platforms and you convert each one to Capitalism, you have free money from these areas. Don't knock the poles, they have lots of potential later in the game.