12-01-2001 23:25									#31
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Agree that much remains to be researched.

But from my visits here to date I would say you are very far from being alone in feeling the desire to subject different aspects of the game to rigorous analysis.

William Keenan's Barbarian Paper is a particularly striking example.

And try searching the threads for some of the analysis on combat outcomes.

The fortnightly OCC comparison games have led to a good deal of well backed up work, by Tonic and others.

But you are right that many of us, myself included, rarely if ever turn to the cheat menu and embark upon a systematic examination. Nevertheless the sheer volume of Apolytoners' experience built up during play regularly generates an insight or a useful/interesting quirk.

I value contributions whether based on science or intuition. Speaking for the intuitive tho', I am very glad that the scientists such as yourself are generous enough to share with us all the fruits of your labours.

So let the walls of Carthage tumble yet a few more times and if you refine your marginal rate of return notion I will gladly hear your further exposition of it.

	12-01-2001 23:46									#32
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I’ve been following this thread for a few days and find it very interesting, being an accountant in real life and an avid Civilization player in cyberspace. But perhaps you could address the following questions:

Money in Civilization doesn’t seem to have a measurable discount rate. In real life, it can be invested (various stocks, bonds, etc) but that function is not available in Civilization. Nor is the game designed as a money making game, so money goals are not built into the process, as they are to varying degrees in a corporation that manufactures a product or provides a service for the public. In Civilization, one can calculate the cash flow in a given project (a Caravan, for instance), but discounting future revenues is not appropriate. Therefore, if net present value is just an arbitrary number with no meaning, what is the point of trying to calculate it?

On the other hand, the concept of “opportunity cost” is very valid in Civilization. Building a Caravan, for example, means one has forsaken the opportunity to build something else. Thus, different builds should be evaluated against one another. I’m not sure, however, that $ (or francs) is the proper measure. The most critical element in Civilization is time. How do you meet all your goals, or objectives, in the amount of time you have? Critical path analysis helps out in this case.

One final thing. In my opinion, rush building a Caravan should only be done in an emergency, such as when you need to use it to help build a wonder. One will rarely recoup the money used in the rush build. For example, if it takes 10 turns for a city to build a Caravan and you pay X amount of gold to get it done in 2 turns, then you have saved 8 turns with X amount of gold. If you want to calculate how much gold you gain by rush-building, you have to do it over just 8 turns (after the Caravan connects with its objective city). Everything after that, you would have gotten without rush building. Of course, you should also consider that the city might build something else in those 8 turns – this is “opportunity.” Despite my profession, I usually follow my gut feeling on this. Don’t most of you use this criteria, the gut feeling?

	13-01-2001 00:05									#33
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How do you handle the situation where you build a caravan, look at the trade demand screen to decide whether to assign it your hides, or coal or gold, then send it off to the foreign city which is 25 squares away overland with no roads...then as you get to London or Delhi, you check their trade demands to find that when you assigned your caravan to carry coal to London 25 turns ago, now London only wants Spice, Gems and Silver? It seems this happens to me a lot in my games both OCC and otherwise.

Knowing that the coal going into London will only yield 28 gold and 28 science beakers, I have at times turned the caravan around and headed it back to Rome or Veii to put it to work in a Wonder building project. That may be too shortsighted to me, but in my mind, if I can't get at least 50 gold/beakers upon delivery of a commodity, it is more valuable to use in building a Wonder.

Your comments?

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	13-01-2001 00:41									#34
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Poppawoppa, I've turned a few back, too, but usually I look for another city that's within a reasonable distance. Also have to consider if the caravan might be destroyed before it reaches another objective. In most cases, the bonus is lost and I might as well just get what I can and build another caravan.

	14-01-2001 15:47									#35
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Monsieur La Fayette!

It was not my intention to disregard your effort. On the contrary, I found it very interesting and impressive! Let me quote someone on these forums you know much better than I do.

quote: Originally posted by La Fayette on 01-12-2001 10:36 AM I'm pretty sure that you have noticed what I have noticed when reading the archive to this forum: many many posts stressing the importance of this and that, and long term effects and the like.

Yes, I have!

quote: I feel somewhat on the same line as (I suppose) Scouse Gits (with GL and starting techs), oedo (with statue and unfinished) or Slowthinker (with dips and spies): much has been said and achieved by the 'masters' (I won't name any, since you know them better than I do), but much remains to be tested and researched by those interested. That is one of the numerous reasons why this game is GREAT.

I couldn't agree more!

quote: That is also why I published this case study: trying to make some people react otherwise than saying "I use home trade and I'm glad with it" or "a settler is better than a caravan".

I agree with you on this too, especially since I am one of those people who post stuff without running experiments first and man do I wish I had in some cases! .

Looking forward to read about your continued tests and the results!

Carolus

	16-01-2001 10:04									#37
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Carolus
I never never thought you disregarded my efforts. Your post about NPV is thoughtful and deserves a more specific answer than the one I gave at first. I'll try.

EST
Shall we say that all the authors mentioned in SG's Great Library are great thinkers and great players?
I shouldn't have named anyone, since naming a few means forgetting many (I'm a humble man studying on a cobble-stone street and would be very glad if something I wrote came to be considered valuable enough to be mentioned up there some day).

Poppawoppa
I agree: risks (of wrong or delayed or no delivery) must not be forgotten. Please, let me answer Hawkman first.


Hawkman
Perhaps Carolus explained NPV better than I did.
The basic idea is precisely to introduce time (and side effects and long term effects and opportunity costs) into the picture, using a "rate of discount", which you might consider arbitrary, but which in fact reflects your will (shall I be long sighted or short-sighted?).
In civ2 the unit of time is the turn. Anyone knows that any gold obtained next turn is better than the same amount of gold obtained 20 turns later. Then, if you choose to be short-sighted, you consider that 20 turns later is very far and you give it a low value by choosing a high "rate of discount" (and the reverse).
This leaves us with the main problem: how to deal with opportunity costs, side effects, and so on?
To make it short, I would answer that, in most cases, no one can do it properly but it's worth having a try.
Our problem is decision making. Then, when a decision is to be taken playing civ2, I suppose we all use our intuition (our guts, our rules of thumb,...) but that always implies some kind of wisdom behind it (in fact almost no wisdom at all if I am a newbie playing chieftain for the first time in my life )...
Sorry, time to go, I post again to-morrow.

	16-01-2001 21:34									#38
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Hawkman
Sorry I had to stop in the middle yesterday.
1) No need to have any Market Place or Bank or interest rate in your civ for using the discounted cash-flow. Perhaps it's even better just forgetting them and imagining that the "rate of discount" is a trick that we economists use to show that time indeed has a value (actually, I don't know whether "rate of discount" is the right technical name in english; in french we name it "taux d'actualisation").
Let me take an example:
I build 2 settlers; #1 is finished next turn, #2 is finished 10 turns later. If I'm short-sighted, I give a small value to settler #2 (for example V2= V1/(1+r)power 10, where V1 is the value of settler #1 and r is the "rate of discount"). If r=8%, then V2=0,43V1 .
If I'm long sighted, I choose a lower rate, giving V2 a higher value; if r=2%, then V2=0,82V1.
Those values can be measured in shields if I will. No need for gold or $, or anything like that.
I agree with you: it is arbitrary, but it is far from useless (since it helps greatly giving a value to the time that passes, and that is precious in decision making).
2) Net Present Value (NPV)
(Carolus, tusen takk for navnet paa engelsk; min förste kone var norsk, derfor er jeg saa glad aa kunne bruke et skandinavisk spraak for aa takke deg - og jeg er ikke helt sikker paa den svenske rettskrivningen)
NPV=Discounted Revenue - Discounted cost
The calculation should be quite simple, but defining Revenue and Cost is not so easy, because you always find someone who points out that you have forgotten some side effects, or long term effects or opportunity costs.
3) Opportunity costs
They are so numerous and tricky in civ2 that one would need huge simulation models to handle them all. Then, don't bother: if someone tells you you might have chosen to build a settler or a knight when you start building a caravan, just say "OK, you are right, I build one next turn in another city".
It is generally advisable to handle opportunity costs by defining 2 solutions (I do this , and I do that), then giving them a NPV each, then comparing NPVs.
For example, if I am building a WoW (let us say HG=200 shields) and hesitate between rushbuilding it and rushbuilding caravans then bringing those caravans to my capital, I can forget settlers and knights for a while, as soon as I have decided that I want HG.
I know that rushbuilding the Wow is going to cost me about 800 gold (with 1 shield in the box to start with), and building a caravan stepwise costs 125 gold, then 125(1+r)power n (n being the number of turns travelling between the city and the capital or waiting somewhere if I built it too soon) is the discounted cost.
And I conclude: unless r or n is very very high, it is generally advisable to build a wonder with caravans rather than buying it (except of course when I start thinking about that wonder when reading the well-known message about "the Romans...", and also except when I notice that I can get so rich when sending those caravans to a fat foreign city ... but that brings us back to the start).

3) Side effects and long term effects
I wished to write a quite short and simple post when I started this thread. That's why I didn't mention them. I thank you all for posting about them (risks, building ships for foreign trade, citizenry, and so on) and I stick to one short answer "the true value is never true, but, in many cases, it may help taking right decisions without daylong calculations".


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	17-01-2001 10:22									#39
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Sir

Your English is awesomely good. And now you casually start using Swedish?

Is it a gift which you have or do the teachers of Albi specialise in foreign languages?

By the by, "rate of discount" seems fine to me but I am doubtful about "power n". "Power 2" in this sort of context usually means "multiplied by itself, "power 3" multiplied by itself twice etc. That doesn't seem right in the context of your posts. Do you mean something like "discounted to allow for". If so I expect there is another symbol for that. Unless I am dmonstrating exactly how shallow my grip on maths/economics is, of course.

	17-01-2001 02:33									#40
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La Fayette, I still don't see that NPV has a place in Civ II in the traditional way that we use it, because the game does not have the investment alternative built into it, nor is inflation very obvious. However, I think I am closer to using an accountant's view while you are closer to using an economist's view towards this. In other words, your view is broader and therefore it could be fitted to the game in some manner. But (there is always a "but"), to play the game and track the various values of caravans would require a second computer, something I've often thought about and seldom tried to implement. I prefer to follow my instincts and if I'm not exactly right then I just build more caravans.

My instinct tells me the short-term value of a trade route early in the game is relatively small, so I don't try to establish lots of them. Each city I view as a manufacturing unit, producing goods and also having a need to build up its productive capacity. Production therefore has to be balanced between these two conflicting priorities (for each city). One thing I do fairly early in the game is start City A to building the Colossus, while other cities produce three caravans which are sent to City A where ownership is transferred (to City A) and the caravans are then sent overseas to establish trade routes for City A. With the Colossus and three trade routes, this city is on its way to becoming an economic powerhouse. Add two more wonders (Cop's Observatory and that College that comes later) and the city is a powerful research center. Meanwhile the other cities may not have many trade routes until about the time that factories become available.

You can say that I would have more cash if more trade routes were established early, and that is true. But I need relatively little cash until I have to build factories, while my need for military units and city improvements is much higher. Would more cash help me to build more of these things? In the short run, yes, but in the long run I would never have enough cash if I pursued that strategy.

Wouldn't it be nice if we could capture caravans? That would be the ultimate solution.

	17-01-2001 18:58									#41
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EST
It wasn't swedish. It was norwegian (I fell madly in love with a norwegian girl many many years ago, that's why). But I know Carolus is going to understand me (and danish readers too, if there are any on this forum nowadays) since norwegian is somewhere between danish and swedish (as a language, not on the map).
Power 3 means exactly what you wrote.
Then 1/(1+0,1)power 1=0,91
1/(1+0,1)power 2=0,83 (and so on)
These are to day's values of 1$ you receive next year or 2 years ahead, if you choose a "rate of discount" of 10% (which is rather short-sighted, but, as I tried to explain, you are perfectly free to choose it, if you think it helps you taking wise decisions).

Hawkman
Rehoming caravans in a capital with Colossus, then sending them faraway is something I would consider quite profitable (it happens to me to do exactly that now and then). Go on playing the way you like. This is a game and I wouldn't like people to be playing it with computer #2 behind their back (though I heard it said that some people do exactly that, when playing MP; but I haven't bought MGE yet, so I don't care).
...


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	17-01-2001 20:35									#42
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You speak norwegian?! Now, that was a surprise!

Moi, je suis né à Grenoble. Mon père est francais et ma mère était suédoise. Ils se sont divorcés quand j'avais deux ans et nous (maman et moi) sommes retournés en Suéde. Chaque été je suis allé voir papa, mais il y a long temps maintenant que je ne l'ai pas vu, donc ca fait au moins six ou sept ans que je n'ai pas parlé ou écrit francais. Alors, ne vous vous mocquez (?) pas trop de moi et ces petites lignes.

BTW, where on the keyboard do you find the little line that should be attached to the "c" in "francais" and "ca" to make it sound like an "s" instead of a "k? Also, I always confuse "ou" and "où". Which of them means "where" and which means "or"?

Carolus

	17-01-2001 20:39									#43
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And yes, I did understand the norwegian!

Carolus

	17-01-2001 21:00									#44
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And I understand your French, Carolus Rex, surprising to me since it's been over 25 years since I spoke that language (I could read and write it better than speak it). My languages are English, German, and French but it's been too long since I've used any German, too. Also know a little Thai and Japanese. One problem I have is mixing the languages, so I sometimes throw in a word from the wrong language and my family is quick to correct me.

La Fayette, I agree with the reasoning that early trade routes can be very profitable. My reluctance to build many caravans for trade is simply the high cost (50 shields) for a small city. The game was well designed in this respect, to force the player to think about the hard decisions and realize there is a cost for each one.

	18-01-2001 21:35									#45
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Carolus
ççççç...this is named "c cédille" in french . On my french keyboard it is situated under 9.
ou=or
où=where (ù is under %, right to m, on my french keyboard).
Hils din far fra meg, hvis du faar anledning (og din mamma med det samme).

(Ming
Please, excuse me for those few lines off topic. I forgot that we have a possibility of private messages).

	18-01-2001 21:58									#46
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If you don't have a French keyboard you'll have to use an alternative method to get the cedille. You can either copy and paste it or use the ascii code. You press the alt-key and keep it down while you type the ascii code for the character on the number-pad at the right of your keyboard. Unfortunately I don't have a list of codes at hand, but I'm sure someone can tell you where to find them.

	18-01-2001 23:18									#47
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I have a list of the "additional characters", as they're labeled, but it's from a DOS manual that's about 20 years old. My best suggestion is to try all the codes (127-255); the letters are grouped mostly at the beginning (ç = 135, ù = 151).

	27-07-2003 02:52									#48
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Bump

(at long last !)

I just reread it and find

	27-07-2003 02:53									#49
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quote: Originally posted by La Fayette Bump (at long last !) I just reread it and find it interesting

	27-07-2003 12:19									#50
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quote: Originally posted by La Fayette

LF - as you say interesting and worth reading - thanks for bumping it.

After reading it a number of things strike me.

1) The value of trade as a game winner is much better appreciated now than it was then - particularly for early landing.

2) Discounted cash flow is a useful tool for analysing some decisions in the game, but as you and others have pointed out it is not always appropriate.

3) The appropriate time value of money (or cost of capital or discount rate) to use in DCF analysis is not clear. You used 2% and 8% in some of your examples; I would go as high as 20%. This seems to remain an open question.

4) To take account of non cash flows (eg shields and beakers) it is necessary to convert them to cash. For example you used 1 beaker equals 1 gold but this is an approximation that can sometimes be wrong. (The beakers from a trade delivery when you already have sufficient for your next advance are completely lost.)

5) The attraction of Civ II is that the game contains so many closely balanced trade-offs that we are still discussing strategy years after it was launched.

RJM at Sleepers

	29-07-2003 00:50									#51
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I agree with RJM -- good Bump.

Great thread.

Multiple decisions -- from the start -- search or settle? Since the settler/engineer is a “developing unit” (more later) searching with a settler is very expensive in terms of opportunity costs -- thus only search for a bit then settle (and/or maybe build a road first then settle).

Next decision is the level of search activity. It is an open question to be deferred at this time.

What to build? the active question in my mind has always been the same from my economics training -- maximize the expected present value of the long run profit stream. This thread has discussed in part the “present value”; the “expected” was touched upon (the notion of risk) and the long run profit stream is assumed as a game win, but might be better defined. For some players, it might be a high score, others, a rapid win. what we have yet to see is the shortest time to collect $30K -- where $30K might be an easy representation of other achievable goals further down the line. (Although the tech activity might be slowed after trade, republic, banking or democracy -- the open questions being growth to fill the continent in question (especially since the ai is poor with invasions), and the value of additional technology may be small in attempting to achieve $30K.)

La Fayette simplified the discussion by setting aside the uncertainty aspects of risk reduction via building offensive & defensive units. The discussion of “value of conquest” might also be the subject of some other thread. Similarly, I have yet to see a definitive experiment as to the value of conquest vs bribery of ai cities. And finally the relative value of white goods compared to units can be discussed later, but needs to be discussed with a notion of time.

Yes, an opportunity cost of four camels is five settlers, but the settlers come with carrying costs and the settlers them selves have varying degrees of value. Open nearby sweet spots with specials? -- plant new cities ASAP. Distant marginal sites, or limited (ICS mode) sites -- hmmm less clear decisions. Use the developing unit to actually build roads/irrigate (intensive development vs. extensive development) is another choice of when & how much -- especially with the increased “cost” of unhappiness and with primitive governments, corruption & waste.

How to use the resources, citizens, for each city & the slider bar for the economy = more decisions.

I’d like to discuss all of those at some point, but I think that a simple question can be focused upon -- domestic vs foreign trade.

La Fayette, I think that the initial data can be reexamined with the new trade information that Solo and others have developed. The 16 turn refresh cycle opens up the thoughts of more camels “sooner” so we may not be limited to ‘just’ three routes -- what we have with the fourth and beyond routes is a potential marginal improvement in the ongoing gain of arrows. Similarly, growing our source city (or for domestic trade both cities) and adding infrastructure can improve the arrow count -- thus affecting our answer. On the other hand I recall seeing some where that there is a cap on the initial cash payout of 2/3 of the total beakers required for the next advancement -- thus in the very early game, a delivered camel may only yield 133 beakers/coins if 200 were required for the next advance -- and thus may not be worth any sort of rushed activity.

In the early to mid -game, this may be less of a concern -- five turns on a road and two turns of boat may yield payoffs of 800 offshore to foreign lands compared to 150 or so for domestic deliveries from the same source of the same demanded product (as exemplified by my current Cfc GOTM). In this second stage, rushing looks to be well worth it and delivery to foreign lands also looks to be the best decision.

I remember in other games where the payoffs later were much more often netting 1000 to 1400 coins per truck for a serious trip across the world, circa the late tech stage (maybe 65-70 techs or so). Again, rushing & foreign markets look to yield the best results.

Note that in addition to the turn number, there is a sense of time with the techs discovered (but that is also another discussion.)

If we were to just simply take turn numbers in question, then we could estimate the “average” interest rate based upon a simple score as the “long run profit stream”. Using some high scoring games as an example, I saw a table where 15,000 looks like a reputable score. With 400 turns, an interest rate of about 2.45% should get close; about 3.27% will get there in 300 turns (about 1900 AD in emperor) , and about 3.95% can do it in 250 turns (about 1850 in emperor). Since the better players seem to get reasonable scores in a shorter time, I think that they are exhibiting better rates of return than 4%.

	29-07-2003 11:32									#52
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quote: Originally posted by Old n Slow maximize the expected present value of the long run profit stream. This thread has discussed in part the “present value”; the “expected” was touched upon (the notion of risk).

I admit it's rather a long time since I learned about DCF but the idea of the expected net present value is new to me and very interesting. I'm used to npv calculations that assume the return is certain or else increase the discount factor to take account of risk.

Is the word "expected" being used in its statistical sense or does it have its normal English meaning? Introducing a risk factor into the future returns would certainly help with one of the difficulties I have with dcf - that it can give too great a weight to returns that are far distant in the future. ("too great" and "far distant" are of course subjective )

Incidentally, I wonder if it should be "maximise the present value of the expected long run profit (cash) stream". A real statistician (like Dr Spike?) would have to comment on whether maximising the expected present value ... is the same as maximising the present value of the expected ...

My brain hurts; I must go away and think about how to apply this to Civ II.

RJM at Sleepers

	29-07-2003 17:49									#53
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Let me help your brain pain --

Iirc, with a few assumptions (constant interest rate, independent distributions, etc.) the math should work through the expectation calculations -- if not it is close enough relative to the other errors that loom. But I think that you are correct. Technically, one calculates the profit for a given period, adjusts that based upon risk and uncertainty, and then discounts the value and sums it up. Yes the “expected” is in the statistical sense, dealing primarily with risk, but equally yes, the “expected” can be expanded to include uncertainty -- one simply adds assumptions and then treats the uncertainties as quantifiable risks.

The risk and uncertainties justify in part the war materiel; of course there may be other justifications for such investments…

	29-07-2003 19:58									#54
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How are you going to define the "expected" value?
Although sending a camel on a boat to visit another civ will pay far more in both a straight bonus and in long-term trade arrows, the risks of your camel falling prey to barb pirates or even irate enemy civs is far higher the longer the camel is out in the open.
Sometimes it will be better to send your caravans to nearby Rome with a shorter shipchain for a smaller bonus than to send it halfway around the world to Babylon for more money but having to enter hostile territory controlled by the Mongols. The long-term prospects of your target city should also be considered when weighing up where to send a freight. The trade-special AI city may seem to be a good destination but given its location on a land-link between three other civs renowned for their bloodthirsty reputations, then might it not be more sensible to send your caravans to a city that does not have the potential for such a large bonus payment, but is likely to grow larger and remain in the game longer, meaning you will have better value from your trade route and not have to reestablish it when the city is destroyed.

	30-07-2003 11:27									#55
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quote: Originally posted by duke o' york How are you going to define the "expected" value?

Roughly speaking, the expected value is the value of a particular outcome multiplied by the probability of achieving it summed over all possible outcomes.

So if your caravan has a 60% probability of making a delivery with a bonus of 100 gold and a 40% probability of being killed on route, the expected value of the bonus is 60 gold.

Estimating the probability of achieving the outcomes may not be too easy and if the range of outcomes is infinite you will have to resort to a little gentle calculus.

RJM at Sleepers

	30-07-2003 13:12									#56
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A little gentle calculus or a little rough guesstimation?

	01-08-2003 11:51									#57
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quote: Originally posted by duke o' york A little gentle calculus or a little rough guesstimation?

If your guestimation is good enough - go for it.

On reflection, most of the infinite sums that come up in Civ II don't require calculus, they are (hopefully convergent) series.

The real problem is estimating the probablities:

a) when (indeed whether) a caravan will be delivered
b) whether the goods will be demanded
c) how many trade arrows the city you deliver to will have (particularly an AI civ).

The whole thing gets a lot easier when you can deliver on the same turn that you complete to a city that you have delivered to before.

RJM at Sleepers

	02-08-2003 02:24									#58
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quote: Originally posted by rjmatsleepers c) how many trade arrows the city you deliver to will have (particularly an AI civ).

My rule of thumb: one trade arrow for each population point.

Add two extra if city next to Whale.

	02-08-2003 11:36									#59
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quote: Originally posted by Elephant My rule of thumb: one trade arrow for each population point. Add two extra if city next to Whale.

It's a good rule of thumb, but there is always the possibility that the city will build a settler just before you deliver not to mention the possibility that some other civ or barbarian will occupy a key tile at the wrong moment.

Of course you still have to use some rule of thumb, however the uncertainites are sufficiently large that it's not worth trying to be too precise with the dcf calculations.

BTW can a worker be displaced from an ocean tile when it is occupied by another civ's ship? (I should probably know the answer to this, but I don't.)

RJM at Sleepers

	02-08-2003 12:49									#60
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quote: BTW can a worker be displaced from an ocean tile when it is occupied by another civ's ship? (I should probably know the answer to this, but I don't.)

No

SG[1]