30-04-2005 17:47									#1
	Kramsib's Value Theory Suffering from ads?

Although I want to participate in the Theory Contest, my lack of time prevents me from following that thread as often as I wish. So I have opened this thread to discuss my theory point by point til we reach an agreement or even other theory.

Firstly, I want to discuss the theoretical bases of the theory before passing to practical examples.

Let's start:

First Statement: an approach based on economic theory.

In real world, producers combine productive factors to transform resources into final production.

So we have:

Productive Factors: There are three kind of productive factors.

N Nature: where raw materials are (ground, forests, hills, ...)
L Labour force: workers or number of worked hours per year depending on some authors.
K Capital: machines, buildings, ... anything which improves production.

Resources

Raw materials, or other products used in the middle of the productive process.

Final Output

Final Production, products which don't need no further transformation to be used.

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Once we have the basic concepts, let's see where we can find them in Civ.

Cities are the only productive units in the game, they use the following productive factors to transform resources in final production:

Productive Factors:

N: Terrain Tiles
L: Citizens
K: City and tile improvements.

Resources

Cities get resources (food/shields/trade arrows) from terrain tiles which are worked by citizens. These production can be improved by capital investments on city or tile improvements.

The quantity of food / shields / trade arrows depends on the number of tiles worked by citizens and the presence of city or tile improvements.

Final Output

Food is used to get more citizens.
Shields are accumulated to build city improvements, units or wonders.
Trade arrows are used to get science, luxuries or gold for our treasure.

That is to say, terrain Tiles, Citizens and Capital investments are used to get food / shields and trade arrows which are used to get more citizens, more terrain tiles (by building new cities -settlers- or conquering -military units-), and more capital investments (buildings, terrain improvments), and the cycle goes on.


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¿Do you agree?. Let's discuss it before the second statement.

Last edited by Kramsib on 30-04-2005 at 18:35

	30-04-2005 18:52									#2
	Inflate your Upload Space

If you are talking about real Civ2 rather than our contest, you should include gains from huts, tribute, trade bonuses and so on.

But you will never get a practical set of Civ2 formulas this way. I can't take your approach seriously if you can't handle the highly simplified position in the theory contest.

	30-04-2005 19:03									#3
	Support Apolyton, buy Alpha Centauri

Also in the Kapital category: gold on hand for rushbuying.

	30-04-2005 20:19									#4
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quote: Originally posted by Peaster If you are talking about real Civ2 rather than our contest, you should include gains from huts, tribute, trade bonuses and so on.

Huts give extraordinary "stock" of gold, science advances and units. They mean extra final production which don't affect on value (as we will see during this exposition).
Caravans give extra "flood" of trade arrows. Their effect is similar to building a road, and can be included in capital investments.

quote: But you will never get a practical set of Civ2 formulas this way. I can't take your approach seriously if you can't handle the highly simplified position in the theory contest.

I don't think so, if you remember my past exposition I had several formulas, but I think I need to establish a strong theoretical base to be understood. In fact, my future examples can be arranged in not a such simplified position, my theory applies whatever the situation, so I can apply from the beginning of a standard game, and this is one of the aims of this thread. Once the theoretical statements are discussed, I will start a practical example to show how this theroy works and how powerful it is.

	30-04-2005 20:28									#5
	Support Apolyton, pre-order Civilization IV

quote: Originally posted by Grigor Also in the Kapital category: gold on hand for rushbuying.

Gold on treasure is not a productive factor, it doesn't affect production directly.

Rushbuying doesn't affect value directly or at least, present value, but it affects on timing.

The cost of shields under rushbuying was a first approach to shield value, but we must think, that such a value has a penalty for "bringing" production from the future. So this value is distorted. It is more related with value through time and consequently with "interest rates", than present value.

All these interesting questions will be answered in the future as the theory develops.

	01-05-2005 11:43									#6
	Support Apolyton, buy Civilization 2

I'm not sure whether it is relevant to the discussion, but there may be a fourth factor of production. It is somewhat similar to the economic idea of entrepreneurship or enterprise. (Perhaps it is somewhat old fashioned to consider this a factor of production these days ) Anyway, it has to do with the tactical skill and micro-management ability of the player - for example manipulating your workers to gain that extra shield that completes a build even though it means a short term food deficit.

I regularly observe that some players get more out of the game's raw materials, labour and capital than others do. But as I said at the begining - I'm not sure how relevant this observation is.

RJM at Sleeper's

	01-05-2005 18:29									#7
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quote: Originally posted by rjmatsleepers I'm not sure whether it is relevant to the discussion, but there may be a fourth factor of production. It is somewhat similar to the economic idea of entrepreneurship or enterprise. (Perhaps it is somewhat old fashioned to consider this a factor of production these days ) Anyway, it has to do with the tactical skill and micro-management ability of the player - for example manipulating your workers to gain that extra shield that completes a build even though it means a short term food deficit. I regularly observe that some players get more out of the game's raw materials, labour and capital than others do. But as I said at the begining - I'm not sure how relevant this observation is. RJM at Sleeper's

Very interesting observation, I think it was Schumpeter who stated the relevance of the entrepeneurship as one of the most important factors for surviying among economic cycles.

But, as far as we are describing mechanic aspects of the game, personal features of the players are out of the model.

	03-05-2005 18:28									#8
	Help yourself to an AD-FREE life

And one other factor. At Raging, 150 gold for a barb king, early in the game, can be quite a boost, so resources spent on king chasing/traps must be considered.

	07-05-2005 19:14									#9
	Second Statement: Cost of production Tired of ads?

Production factors have costs.

In real world:

N: The cost of natural resources are related to the cost you pay for purchasing them or the rent you pay for ground.

L: Salaries and wages per unit of time worked.

K: The cost of capital is related to amortisations, depreciation and rent depending on the cases.

In civilization, tiles has no cost except cost of oportunity (the cost of choosing one option and no other):

Example:

Let's imagine we have 2 tiles to place 1 citizen to work.

Tile A) produces: 2 food, 1 shield and 1 trade arrow.
Tile B) produces: 1 food, 2 shields and 1 trade arrow.

Choosing Tile A) has a cost of 1 shield per turn, but it gives 1 extra food in exchange.
Choosing Tile B) has a cost of 1 food per turn, but it gives 1 extra shield in exchange.

Depending what is more valuable 1s or 1f, Tile A) is cheaper than B) or viceversa.

In civilization there is no salaries nor wages, but there is a "cost of time" for citizens. According to Adam Smith, every worker should receive a salary in proportion of the hours worked. As in civ time is divided into turns, the salary for one citizen per turn is the same for every citizen wherever he works.

Note: citizens become unhappy by working on glaciers, it seems salary is unable to compensate for working in such extreme conditions.

Finally, city improvements has a very clear cost, maintenance. But tile improvements have a different cost, the cost of maintaining a settler during the turns a tile improvement is built. That comes from 1 to 2 food per turn, and 0 or 1 shield.

The sum of all these costs (opportunity cost / salaries / maintenance) determines an internal cost of production for our civilization in game.

In other words, the cost of transforming food, shields and trade arrows in final production, is determined by the sum of costs of opportunity, salaries and maintenance.

	15-05-2005 02:43									#10
	Third Statement: Technical Efficiency Support Apolyton

Let's assume we always work on the most efficient tiles.

If plains produce 1f / 1s / 0a
There is no way to produce on a desert 0f/1s/0a

So between producing on plains or on a desert we will produce on plains.

This statement reduce the cost of opportunity of producing on uneffiient tiles.

	15-05-2005 03:15									#11
	Fourth Statement: Trade arrows are money Support Apolyton, buy Call to Power 2

Trade arrows turn into three different outputs.

1. Taxes which increases treasure (stock of gold).
2. Science.
3. Luxuries.


It is obvious that taxes means money. Liquid money on your stock of gold.

We can consider science as money invested on science. So scientifical researching is a purchase of technology.

Luxuries can be considered money returned to people under the form of government expenditure, charity, etc., ...

Conseqently, trade arrows can be considered as money, that is to say, 1 trade arrow is equal to 1 gold.

(In fact, in CivIII there aren't trade arrows, there are coins and they are used in the same way as trade arrows in Civ II).

	15-05-2005 04:00									#12
	Fifth Statement: fc = sc = ac Support Apolyton buy from Amazon

And the most controversial statement.

As a consequence of what I have stated before.

In one turn, a city exploits its squares, its citizens and its buildings to transform food, shields and trade arrows into final production.

To transform food, a city employs X citizens, Y squares and Z buildings.

To transform shields, a city employs the same quantity of citizens (X), the same (Y) squares and the same number of buildings.

To transform trade arrows, a tity employs the same quantity of citizens, squares and buildings again.

Consequently, in one turn, the transformation of every element uses the same productive factors.

As productive factors has a cost, the cost of employing those productive factors is the cost of transforming the three elements (food/shields/trade arrows) into final production.

So, the cost of transforming food is the same as the cost of transforming shields and the same as the cost of transforming trade arrows, as three of them were transformed by the same quantity of productive factors during that specific turn.

That is to say:

fc = sc = ac

(food cost) = (shield cost) = (trade arrows cost)

Sixth Statement

According to 4th and 5th statements:

food cost = shield cost = trade arrow cost = money

As trade arrows are directly convertible into money we can quantify how much gold the cost of each element is.

Dividing the number of trade arrows directly convertible into gold by the number of other item we get the unitary cost of that element.

An example:

Here is Berlin City, it is transforming 24 f / 9 s / 10 a (one trade arrow comes from trade by caravan).
It is employing 8 citizens in 8 tiles.
Those tiles are technically efficient as they produce 4 items minimum, and there is no other tile with more than 4 items without a citizen on it.

The cost of transforming a trade arrow is:

10 / 10 = 1 gold per trade arrow

The cost of transforming a shield is:

10 / 9 = 1,11 gold per shield.

The cost of transforming a unit of food is:

10 / 24 = 0,41 gold per unit of food.

IMPORTANT NOTE: This is cost, and not the real value yet, but it is the minimum "price" for each item.

Attachment: berlin.jpg
This has been downloaded 66 time(s).

Last edited by Kramsib on 15-05-2005 at 04:05

	15-05-2005 04:03									#13
	Re: Fifth Statement: fc = sc = ac Got spare money?

DOBLE POST

	15-05-2005 10:25									#14
	Re: Fourth Statement: Trade arrows are money Support Apolyton or Terrorists Win

quote: Originally posted by Kramsib Conseqently, trade arrows can be considered as money, that is to say, 1 trade arrow is equal to 1 gold.

But until you reach democracy you cannot get 10 gold from 10 arrows, unless the roundings are working in your favour. And with a market (bank, etc) you get more than 10 gold from 10 arrows. My conclusion is that the "value" of a trade arrow depends on the form of government and the infrastructure that you have built, but it is very rarely 1 arrow = 1 gold.

RJM at Sleeper's

	15-05-2005 10:38									#15
	Re: Fifth Statement: fc = sc = ac Lose 30 kilos (of popups)

quote: Originally posted by Kramsib Those tiles are technically efficient as they produce 4 items minimum, and there is no other tile with more than 4 items without a citizen on it.

I'm not sure what you mean by "technically efficient". If you move 1 of the workers that is producing no shields on to the forest and another on to a plain, you would get a 10 shield surplus which is much more efficient for producing units. These 3 additional shields would be at the cost of 3 food and 1 arrow, but would eliminate any shield waste in the final row of a unit build - great for rushing vans.

RJM at Sleeper's

	21-05-2005 01:07									#16
	Support Apolyton, buy Galactic Civilizations: Deluxe Edition

That's why these types of forumlae are mental masturbations.
There will always be turns where an adjustment will have to be made to maximize the city. I.E. in any perfect formula let's say it's kicking out 7 shields. after 7 turns you have 49 shields. that's seventh turn you could have adjusted to 8 to finish that caravan and not wasted the 6 shields the next turn. Despite the less then optimal use of food or trade.

That turn your going to be one beaker short of making monarchy in an odeo year.

That turn you need to finish the wonder before someone else does.

The turn you crank down all science and trade to delay getting a tech that you plan to steal from a neighbor when he develops it so you can leap frog.

The turn you crank your money so you can bribe that barb before it destroys a key city.

The turns you maximize food to the city will be size two prior to an attack.

The turns you minimize food to keep the city from growing and going into revolt.

The turn were you maximize trade for celebrating or delivering caravans.



There are hundreds of situations where your not going to be using that perfect combination. It depends on whats going on in the game around you. So you can all waste your time argueing over theoritical things (especially the vague nature of this one). I'll spend my time playing MP games by the seat of my pants. And I bet my results will be better than yours.

It's always about what is most important to you for that turn. And you don't need a complicated formula to figure out.

	21-05-2005 10:50									#17
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quote: Originally posted by rah There are hundreds of situations where your not going to be using that perfect combination. It depends on whats going on in the game around you. So you can all waste your time argueing over theoritical things (especially the vague nature of this one). I'll spend my time playing MP games by the seat of my pants. And I bet my results will be better than yours. It's always about what is most important to you for that turn. And you don't need a complicated formula to figure out.

If I'm the I'm the person you're betting against, you'll win your bet easily.

But thanks to Solo investigating "theoretical things" we now know about which trade goods a city will supply and how to keep it supplying them. There are a lot of other examples I could choose. You yourself mentioned an Oedo year - another example of investigating "theoretical things". Progress comes from a combination of good practical play and good theoretical analysis.

RJM at Sleeper's

	21-05-2005 23:32									#18
	Re: Re: Fifth Statement: fc = sc = ac Support Apolyton buy from Amazon

Sorry I wasn't able to answer till today, I had a lot of work to do.

quote: Originally posted by rjmatsleepers I'm not sure what you mean by "technically efficient". If you move 1 of the workers that is producing no shields on to the forest and another on to a plain, you would get a 10 shield surplus which is much more efficient for producing units. These 3 additional shields would be at the cost of 3 food and 1 arrow, but would eliminate any shield waste in the final row of a unit build - great for rushing vans. RJM at Sleeper's

When I speak about "technical efficiency" I mean a kind of "absolute advantage".

Grassland 2 f / 0 s / 0 a = 2 items
Bonus Grassland 2 f / 1 s / 0 a = 3 items
Plain 1 f / 1 s / 0 a = 2 items

A bonus grassland is more efficient than a grassland or a plain as it produces 1 extra shield compared to simple grassland or 1 food compared to plains.

But a square with grassland has the same technical efficiency as a square with plains. Which is better?, it depends on the "value" of 1 f against 1 s. If 1s = 1f, both are equally efficient, if 1s>1f, plains are more efficient and viceversa.

Under technical point of view, squares with the same number of items are equally efficient. Different values for each kind of item make efficience varies. So I'm talking about two concepts, technical efficiency and global efficiency. Ok?

In the example above, if you move 1 citizen from no shield grassland to a forest you are "changing" 2 f + 1a for 2 s in exchange. That is to say, 1 f + 1/2 a for 1 s.

You can change it to plains "changing" 1 f for 1s, which is a cheaper option.

The example was given intentionally to show, in the future, how my theory can be useful to maximize production or even decide were to produce to maximize "value", so be patient.

The picture shows the AI's decission, the distribution of the citizens by clicking the city square on the resource map.

	21-05-2005 23:37									#19
	Re: Re: Fourth Statement: Trade arrows are money Support Apolyton buy from Amazon

quote: Originally posted by rjmatsleepers But until you reach democracy you cannot get 10 gold from 10 arrows, unless the roundings are working in your favour. And with a market (bank, etc) you get more than 10 gold from 10 arrows. My conclusion is that the "value" of a trade arrow depends on the form of government and the infrastructure that you have built, but it is very rarely 1 arrow = 1 gold. RJM at Sleeper's

I tried to remark that I was talking about cost and not about value yet.

The fact that you cannot get 10 gold from 10 arrows in most governments alters the "value" of trade arrows, but not its cost.

A slide restriction increases the value of trade arrows over the 1a = 1g. But the cost remains the same, just becouse cost depends on the elements used to get production.

	21-05-2005 23:55									#20
	The Difference Between Cost and Value: Support Apolyton buy from Amazon

I have to explain these economic concepts before continue explaining my theory for not becoming misunderstood.

Let there be a producer.
Let there be a customer.

The producer, produce output, for example chairs.

To build a chair, producer basicly needs:

wood
tools
time
...

These elements mean a cost for the producer.

Let's assume our customer needs a chair, this implies that a chair has some value for the customer.

Let C be producer's cost.
Let V be customer's value.
Let P be the price.

Producer will never ask for a price which P Customer will never pay P>V. He wants a chair but not at any price, in that way, V is the maximum price the customer will pay.

We can say

P-C >0 is producer's profit
V-P >0 is some kind of "customer's profit" as it buys at a lower prize under the maximum he wants to pay.

So, only when V>P>C, we have negotiation between producer and customer.

Producer wants P=V becouse that is the highest price he could ask and that maximizes his profit (P=V maximizes P-C).

Customer wants P=C becouse that maximizes his "profit" V-P.

Then, producer and customer start to bargain until they come to an agreement wich determines final price.

-----------------------------------------------------------------
My theory tries to study "value", so I need to determine costs first. Then I will estudy value, and finally we can study how can a "virtual" market will work and how prices are set up.

	22-05-2005 00:02									#21
	Increase the size of your Attachments

quote: Originally posted by rah That's why these types of forumlae are mental masturbations. There will always be turns where an adjustment will have to be made to maximize the city. I.E. in any perfect formula let's say it's kicking out 7 shields. after 7 turns you have 49 shields. that's seventh turn you could have adjusted to 8 to finish that caravan and not wasted the 6 shields the next turn. Despite the less then optimal use of food or trade. That turn your going to be one beaker short of making monarchy in an odeo year. That turn you need to finish the wonder before someone else does. The turn you crank down all science and trade to delay getting a tech that you plan to steal from a neighbor when he develops it so you can leap frog. The turn you crank your money so you can bribe that barb before it destroys a key city. The turns you maximize food to the city will be size two prior to an attack. The turns you minimize food to keep the city from growing and going into revolt. The turn were you maximize trade for celebrating or delivering caravans. There are hundreds of situations where your not going to be using that perfect combination. It depends on whats going on in the game around you. So you can all waste your time argueing over theoritical things (especially the vague nature of this one). I'll spend my time playing MP games by the seat of my pants. And I bet my results will be better than yours. It's always about what is most important to you for that turn. And you don't need a complicated formula to figure out.

Perhaps I cannot state a formula for players to play perfectly, but I can state a formula to play better.

But, one of the aims for this analysis is to find a way to program a better AI. If the AI were able to use a mathematical model to maximize the effects of its decissions, it could rid of cheats and become another amazing challenge for humans to play.

	22-05-2005 00:04									#22
	Browse Apolyton AD-FREE

quote: Originally posted by rjmatsleepers If I'm the I'm the person you're betting against, you'll win your bet easily. But thanks to Solo investigating "theoretical things" we now know about which trade goods a city will supply and how to keep it supplying them. There are a lot of other examples I could choose. You yourself mentioned an Oedo year - another example of investigating "theoretical things". Progress comes from a combination of good practical play and good theoretical analysis. RJM at Sleeper's

Totally agree with you

	23-05-2005 00:05									#23
	Support Apolyton, buy Galactic Civilizations: Deluxe Edition

Yes, this kind of analysis is what would make a competent AI.

We can dream, ya know.

Any prospect of another Civ2 Progresivo?

	23-05-2005 19:54									#24
	Full PM-box? Change here!

The two examples you guys quote are Oedo years and Solo's trade thread. There are actually many others. Xin's science and his square conversion tricks. The extensive attack manuals and barb guides. And most of these have contributed to strat, BUT, for solo's thread, and others there are only a couple of features that are used in fast paced MP games. Oedo years is easy to incorporate since it adds no time. Most of Xin's tricks aren't used because they're so time consuming and you'd never find a game if you played that slow every game. Calculating attack success % during a game are usually just approximated to the point of good/bad attack type thinking not taking the time to calc the exact percentage on every attack. Rough guidelines and not mind numbing calculations are the things that end up being used in MP games. For SP games you need not worry about anything since the AI is so easy to beat and almost any strat will work.

I agree that it could help the AI since anything would have to work better than the "MORE FOOD IS GOOD" type programming. But since we never play with an AI, it's still all mental masturbation.

	24-05-2005 00:41									#25
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Rah - I take your point, but I think you go too far with it. There are other ways to play Civ2 besides MP, most of which allow some time for thought -

1) GOTM's: The goal is not just to defeat the AI, but to do it quickly, or with maximal score, or etc.
2) PBEM's and PBEM duels.
3) Playing Scenarios
4) Those of us who are just curious about the best Civ2 strategies, and play SP games as experiments.

I think most (non-MP) players don't do calculations very often, but you are probably at a disadvantage if you NEVER do them.

	24-05-2005 02:05									#26
	Lose 30 kilos (of popups)

When I talk about AI, I am not thinking about AI as an enemy but also as an assesor, imagine how fluid your MP games will be if you can trust on your automatized citys because they are performing an optimal micromanagement for you.

	25-05-2005 02:41									#27
	Support Apolyton, buy Civilization 2

Don't get me wrong, I do use the calculations. Thanks to Solo I know when a demand can change so I plan better. I calc rough attack percentages. I know when a caravan delivery is on the optimal path. I squeeze every beaker to get monarchy on an oedo year as early as possible.
But as I said, they're usually quick approximations. That's all you have time for. What we're doing here is way to vague and would not have many applications. As I stated earlier, there are too many times when you would want to go against the formula to maximize what you're attempting to accomplish in a turn.

As for playing SP, if you check back in the archives you'll see that I participated in earlier SP challanges. I was the third person (i think) to win at OCC. I participated in some of the early landing and highest score contests. I have also played many of the scenarios. But guess what, they still got boring and I no longer participate. I don't begrudge the people that haven't done those things completely and are still having fun doing it. I no longer do. Trying to win the scoring record is probably the most boring thing anyone could ever do. Doing it more than a couple times is enough to make you never want to play the game again. I only tried 3 time because my brother was also doing it so it became a macho thing. I finally gave up when he topped my most recent record because I couldn't face doing it again even though I knew I could top it. That was years ago.

And you're right, I am slightly MP biased since it's the only thing that provides a challange. The AI will never be as challanging as a human opponents, even bad ones.

No matter how good they programmed the AI, I would NEVER let it manage my cities in an MP game without oversight. At least early in the game where a difference of one beaker, shield or food could make a BIG difference. Later in the game it might be nice, but most of your opponents are dead by then.

	27-05-2005 10:35									#28
	Browse Apolyton AD-FREE

So the answer then is while we're reprogramming the AI we reprogram things like making advance costs to be probabilistic, somewhat like MoO2.

I don't know if food and growth could be handled that way... Oh, what they heck, we're dreaming here. We'll reprogram the growth algorithm, and the production box to boot. Don't ask me the nit-picky details.

Then your precious beaker/food/shield squeezing won't matter so much.

	27-05-2005 20:54									#29
	Support Apolyton buy from Amazon

Yes, you are correct.
But I really do like reading the different theories. Any new trick that your opponent is not familiar with yet is an advantage to be exploited. I don't know how many times I've figured we've sucked new knowledge dry on this game only to be surprised. But I just don't see enough potential in this one. Of course, after saying that, prove me wrong. I've been married for almost 20 years, so I'm used to it.