30-09-2004 21:52									#31
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quote: Originally posted by Scouse Gits IIRC this is not the case - Capitalisation yields Gold, not trade arrows to be converted to gold - I am pretty sure that I ran a recent test and got a strict 1:1 ratio Stu

SG is correct. Capitalization converts shields directly to gold. Marketplace/Bank/Stock Exchange have no effect on the amount of gold produced, however because Factories and ___ Plants increase shield output, they also correspondingly increase gold output under Capitalization.

	30-09-2004 23:25									#32
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The basic thought of “production” (allocation of citizens on spaces yielding sheaves, arrows and shields) is a step, followed by the allocation of that production towards infra/units, beakers, coins, cups, and sheaves towards the food box.

The “price” during the production phase is the opportunity cost of alternative production choices; the “price” during the allocation phase is the alternative results of that production. However, since all of this is done ‘simultaneously’ one can transfer the allocation values to the production choices. Thus during any given turn, the “price” (shields) towards completion of a unit can be compared to the “price” (beakers) towards the completion of the next tech. However, should the next tech require more than one turn, then one needs to have an awareness of an interest rate (another complicating factor.)

	03-10-2004 04:09									#33
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1) Hello, Kramsib
Glad to see that there is an economist ready to keep this forum alive (I retired a year ago...but fortunately not from civ2).

2) IMO the concept of Net Present Value can be a great help when trying to solve the problems you deal with (but I started a thread about 3 years ago and most people found it a bit complicated for game purpose - decision making).

3) I had a long and thorough discussion with DaveV about the value of shields/gold, and we finally agreed that making use of 2 gold = 1 shield (price of rushbuilding improvements), or 2.5 gold = 1 shield (price of buying one row = 25/10, when rushbuilding units) was well enough for rough decision making (which is in fact what we all do when playing this wonderful game).

	04-10-2004 03:29									#34
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Kramsib, thx for a detailed explanation. Nevertheless it persuaded me your thinking in this case is wrong.

I will concentrate on the 2nd a)-d) example now:

quote: Originally posted by Kramsib Now, let's assume that we can always exchange shields for arrows at a constant rate, 1 shield for 1 arrow. That is to say, we have a wide range of alternatives like the following: a) 4A + 6S b) 5A + 5S c) 6A + 4S d) 7A + 3S In case a), each shield costs 4/6 = 0.66 gold. passing from a) to b) means changing a 0.66 gold shield for 1 gold (1 > 0.66, we earn money ). Shield cost raises to 1 gold. Passing from b) to c) means changing a 1 gold shield for 1 gold (1 = 1, we are indiferent ). Shield cost raises to 1.5 Passing from c) to d) means changing a 1.5 shield for 1 gold (1 < 1.5, we are losing money ). Passing from c) to d) is not worthwhile. This analysis is using prices in the margin, the marginal cost of exchanging 1 shield for a determined quantity of arrows.

You say passing from b) to c) is indiferent and passing from c) to d) is loss making. In the aggregate your theory says
1. passing from b) to d) is loss making

Now I will apply the following reasoning

quote: Originally posted by Kramsib Passing from b) to c) means changing a 1 gold shield for 1 gold (1 = 1, we are indiferent ).

Similarly we may say
Passing from b) to d) means changing a 1 gold shield for 1 gold (1 = 1, we are indiferent ).
So your theory claims also
2. passing from b) to d) is indiferent

1. and 2. are clearly in contradiction.

___________________
Flow/stock
Thx for your nice picture, it is exactly how I supposed.

	04-10-2004 03:31									#35
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Kramsib, now I will point out another contradiction of your theory.

quote: Originally posted by Kramsib quote: Originally posted by SlowThinker But in Kramsib's theory it is different: In other words if Kramsib sets 90% science + 10% taxes then price of 1 beaker is 0.11 gold. If he sets 10% science + 90% taxes then price of 1 beaker is 9 gold. But such a conception of price is completely useless IMHO. Kramsib, IMO you are thinking about one situation and speaking about a diferent one: If you can choose between 90% of science (and no taxes) or 10% taxes (and no science) then the price of 1 beaker is 0.11 gold. But in our case you can have both science and taxes. That is not correct. Asuming there is no marketplaces nor libraries, 1 beaker is equal to one gold, as the beaker is obtained from only 1 trade arrow. Prices are not altered with a different distribution of trade arrows, as the quantity of arrows stays the same. You can expend your trade arrows wherever you want, science, luxuries or "cash" in your treasure, prices remain the same...

...so you're saying a choice among science, luxuries or gold doesn't affect the price...

quote: ...Only changes in production (more/less arrows, food or shields) can alter prices.

...so you're saying a choice among food, shields or arrows affects the price...

But both situations are equal! In both examples a player makes a decision that reallocates the output among resources:
science, luxuries or gold
or
food, shields or arrows

Especially your example

quote: a) 4A + 6S b) 5A + 5S c) 6A + 4S d) 7A + 3S

is suspiciously similar to

quote: a) 40% tax + 60% science b) 50% tax + 50% science c) 60% tax + 40% science d) 70% tax + 60% science

isn't it?

	04-10-2004 03:59									#36
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Both posts were edited.

Excuse me for subverting economic theories... you know, a horse sense always wins.

	04-10-2004 14:06									#37
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First of all I want to say hello to LaFayette and thank him his presence in this thread.

Secondly, lets answer SlowThinker's questions:

quote: Originally posted by SlowThinker Kramsib, thx for a detailed explanation. Nevertheless it persuaded me your thinking in this case is wrong. I will concentrate on the 2nd a)-d) example now: You say passing from b) to c) is indiferent and passing from c) to d) is loss making. In the aggregate your theory says 1. passing from b) to d) is loss making Now I will apply the following reasoning Similarly we may say Passing from b) to d) means changing a 1 gold shield for 1 gold (1 = 1, we are indiferent ). So your theory claims also 2. passing from b) to d) is indiferent 1. and 2. are clearly in contradiction. ___________________ Flow/stock Thx for your nice picture, it is exactly how I supposed.

The economic theories I based my reasoning on, uses derivatives so they use continuous functions. But in Civ we are working with integer quantities and if we are not careful we can get incongruous results as you have noticed.

But, there is an easy solution.

What you have discovered is a known problem called "lack of transivity".

As you have said, if b) and c) is indifferent, and c) is better than d), b) should be better than d), but b) and d) are indifferent too. So there is no "transitivity" because of an incongruent result.

But when working with integers we must consider the inverse movements.

You will see

Changing b) for c) is indifferent, but changing c) for b) means a profit. Changing d) for b) means a profit too. (I hope you can manage with the numbers).

Consequently and considering all the movements we finally get an optimum choosing b).

	04-10-2004 14:24									#38
	Re: worker reallocation vs. taxes reallocation Support Apolyton buy from Amazon

quote: Originally posted by SlowThinker Kramsib, now I will point out another contradiction of your theory. That is not correct. Asuming there is no marketplaces nor libraries, 1 beaker is equal to one gold, as the beaker is obtained from only 1 trade arrow. Prices are not altered with a different distribution of trade arrows, as the quantity of arrows stays the same. You can expend your trade arrows wherever you want, science, luxuries or "cash" in your treasure, prices remain the same...

...so you're saying a choice among science, luxuries or gold doesn't affect the price...


...so you're saying a choice among food, shields or arrows affects the price...

But both situations are equal! In both examples a player makes a decision that reallocates the output among resources:
science, luxuries or gold
or
food, shields or arrows

Especially your example

is suspiciously similar to

isn't it? [/QUOTE]

Food, shields and arrows are the real resources, obtained by the work of the citizens from the terrain.

Beakers, luxuries and gold are different uses of the arrows. I do not consider them a real output but expenses ("money expended in").

Although your numbers are suspiciously similar they are not the same.

First group of three (food, shields, arrows) are production. Second group of three (beakers, luxuries and gold) are uses of one of the resources (arrows) in the same way food is split into food consumed and excedent, and shields are split into maintenance, waste and excedent (accumulated in the production box).

The reallocation of science, luxuries and taxes cannot affect the price as they cannot altere the quantities of food, shields or arrows.

Once again, food, shields and arrows are phisical production, but science, luxuries and taxes are accountancy.

Now I can anticipate the effects of some buildings like marketplaces or libraries. They work as there were an increase in the number of "arrows" used in a specific area (science, taxes and luxuries).

	04-10-2004 16:38									#39
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Kramsib, it looks your way of quoting quotes doesn't work well. (I edited my quotes externally).

	04-10-2004 16:38									#40
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quote: Originally posted by Kramsib Changing b) for c) is indifferent, but changing c) for b) means a profit.

How can you say such a sentence?? We call it lack of reflexivity .
You are saying you will strengthen your civ if you sit on your computer and change b) for c) and back repeatedly. I am starting to think you are laughing at me!

Yes, a)-d) is an ordered set. But in your theory it isn't, because of lack of transitivity, symetry and reflexivity.

**************************************************
**************

quote: Food, shields and arrows are the real resources, obtained by the work of the citizens from the terrain. Beakers, luxuries and gold are different uses of the arrows. I do not consider them a real output but expenses ("money expended in"). Although your numbers are suspiciously similar they are not the same. First group of three (food, shields, arrows) are production. Second group of three (beakers, luxuries and gold) are uses of one of the resources (arrows) in the same way food is split into food consumed and excedent, and shields are split into maintenance, waste and excedent (accumulated in the production box). The reallocation of science, luxuries and taxes cannot affect the price as they cannot altere the quantities of food, shields or arrows. Once again, food, shields and arrows are phisical production, but science, luxuries and taxes are accountancy.

There are many possible views how you can consider citizens, food, shields, beakers, gold etc.
A view where arrows are divided in the production phase (to be more concrete: a player makes some decisions by allocating workers and setting taxes. Then he gets food, shields, beakers, gold and luxuries as a physical production) is perfectly legal and your theory must work also with this view, but it doesn't.

quote: Once again, food, shields and arrows are phisical production, but science, luxuries and taxes are accountancy.

You have citizens. Citizens are transformed in workers and beakers, gold and luxuries (specialists). Workers are transformed in shield, food, arrows. Arrows are transformed in beakers, gold and luxuries.
There is not a significant difference between these transformations. So you could put a boundary production/accountancy to any point: for example workers is a physical production, but shields, food and arrows is accountancy.

	04-10-2004 18:56									#41
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quote: Originally posted by SlowThinker How can you say such a sentence?? We call it lack of reflexivity . You are saying you will strengthen your civ if you sit on your computer and change b) for c) and back repeatedly. I am starting to think you are laughing at me! Yes, a)-d) is an ordered set. But in your theory it isn't, because of lack of transitivity, symetry and reflexivity.

Unfortunately this does not work like this.

When analysing where to produce, you have to study every alternative of production. Once you have determined the best square (after analysing every movement), this is fixed.

I am not laughing at you, I know it is difficult to understand, it is also difficult for me to explain.

In the SCS I have made a "on play" explanation (it is in Spanish), and I found cases where both, x to y and y to x movement were profitable. That does not mean that changing every turn the production you are earning money, that means that there is an optimal "in the middle", (just imagine a quantity of 3.8 S and 5.5 A)

I explained this is the problem when working with integer quantities.

The fact that, b and c are indifferent it is true in the margin (infinitesimally speaking), there are growing loses when moving infinitesimal units from b to c. When moving a entire integer unit we lose infinitesimal analysis and we get some surprises.

But once you understand how it works, the theory is consistent.

quote: ************************************************** ************** There are many possible views how you can consider citizens, food, shields, beakers, gold etc. A view where arrows are divided in the production phase (to be more concrete: a player makes some decisions by allocating workers and setting taxes. Then he gets food, shields, beakers, gold and luxuries as a physical production) is perfectly legal and your theory must work also with this view, but it doesn't.

But, beakers, gold and luxuries have their origin on arrows, so it is easy to maximize arrows production and then split them, better than trying to maximize beakers, gold and luxuries before maximizing the quantity of arrows.

quote: You have citizens. Citizens are transformed in workers and beakers, gold and luxuries (specialists). Workers are transformed in shield, food, arrows. Arrows are transformed in beakers, gold and luxuries. There is not a significant difference between these transformations. So you could put a boundary production/accountancy to any point: for example workers is a physical production, but shields, food and arrows is accountancy.

There is a difference. Terrain types give f/s/a but not workers.

Ok my theory is one theory, you can create thousands of theories with different definitions. But under mine, f/s/a is production from earth, cityzens is "labour force" and gold/beakers/luxuries is accountancy. Making these assumtions the theory works.

Do you need something else?

	04-10-2004 21:37									#42
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Perhaps some examples would help us folk of dimminished capacity understand the usefulness of this "theory." Or does actually playing the game not matter??

Or put another way, how does this exhaustive "theory" advance one's playing ability beyond the already established general rule constants that we have been plugging in, namely, 1 shield = 2g (improvements) or 1 shield = 2.5g (units)??

I say this with respect because I recognize there is probably a language problem with this, but how will any theory be useful if it is incomprehensible to everyone else?? Two things might be helpful at this point: simplify the theory and give some examples, preferrably with saves.

Monk

	18-10-2004 23:23									#43
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I realized somebody could think I agree with Kramsib... I want to pronounce I disagree and I will disagree in the future unless I expressly say I agree.

quote: I know it is difficult to understand

Up to this point I understood well, but I found severe contradictions in your system.

quote: Originally posted by Kramsib quote: Originally posted by SlowThinker You are saying you will strengthen your civ if you sit on your computer and change b) for c) and back repeatedly. ... That does not mean that changing every turn the production you are earning money

No, I didn't speak about several turns, but about 1 turn. I suppose in your system a player's decision must be done within one turn, and so also comparison between a),b),c),d) refers to one given turn.
So your theory says that you open a city window, you replace workers from b) to c) and from c) to b) alternately, and after 10 minutes of 'hard work' you gain a big profit.

quote: The fact that, b and c are indifferent it is true in the margin (infinitesimally speaking), there are growing loses when moving infinitesimal units from b to c. When moving a entire integer unit we lose infinitesimal analysis and we get some surprises.

Why do you use infinitesimal analysis on integer-based numbers, especially when it leads to contradictions only?
BTW in your reasoning I found no infinitesimal analysis...

quote: There is a difference. Terrain types give f/s/a but not workers. Ok my theory is one theory, you can create thousands of theories with different definitions. But under mine, f/s/a is production from earth, cityzens is "labour force" and gold/beakers/luxuries is accountancy. Making these assumtions the theory works.

Under any theory the situation is following: a player manages his cities, makes decisions. These decisions determine additional food, shields, beakers, gold (nothing else) that will fill 'stocks' (production boxes, food boxes, tresure, beaker collection).
A system that sets relative price of food vs. shields in a different fashion than beaker must be wrong.

	19-10-2004 01:45									#44
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Thank you, SlowThinker, for that clarification. The following remark from you brings this into greater focus for me...

quote: So your theory says that you open a city window, you replace workers from b) to c) and from c) to b) alternately, and after 10 minutes of 'hard work' you gain a big profit.

That is what I thought he was saying. It is nonsense to claim that dithering between settings makes a profit--or anything. Nothing in the game changes until you hit "enter" and then it is only the final setting that changes things. The rest is daydreaming and means nothing.

In the end it is actually playing the game that is important. Theories and Strategies that do not further that are not helpful.

Monk

	25-10-2004 03:43									#45
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Kramsib,

I like this kind of question! I just discovered this thread and haven't been able to make sense of it yet. But here is my value system, which I posted in another recent thread:

1 Shield = 1.2 Beakers = 2 gold = 1.4 arrow = 0.4 turns (by 1 settler).

I will not claim it is "right", but I have used it to make decisions in the opening of ICS/conquest games, without regrets. It does not apply to EL/MP games or to the endgame.

	06-04-2005 16:41									#46
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quote: Originally posted by DaveV In a nutshell, where N is the number of shields left: Wonders and spaceship parts cost 4N to complete. Other buildings cost 2N to complete. Units cost N*N/20 + 2N. In all cases, it costs twice as much if the box is completely empty. Edit: added spaceship parts.

I have to make an addition here. It's not really interesting for those playing with the standard rules, but it can be of interest for scenario makers etc.

In the conversion from shields to gold, the N caps at 999.

E.g. if you make a building that costs 1200 shields, buying it will "only" cost 3996 gold (when the box is empty) instead of 4800. That also obviously means that from 1199 shields to 999 shields, the rushbuying cost doesn't change. It will be constant at 1998 gold, in this example.

	07-04-2005 08:00									#47
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Maybe I understand the Kramsib - ST debate a little better after a few readings, but I really sympathize with Bloody Monk's comment that a real game situation would help clear things up. And it might be fun to see some differing theories in action.

I propose to create a 4000BC save on a very simple map (grass + a few forests, no huts, no specials, no barbs, no AI nearby). You each get 2 settlers, monarchy and 100 gold. You have to state your theory of the position as simply as possible, and then act on it.

I will play "Banker" and sell shields and/or food to the highest bidder before play begins. Then everyone plays to 1000BC. We determine a winner based on some previously-agreed criterion, such as Mfg (shields per turn) or population.

I'm interested to see if anyone can find an optimal strategy for this simplified game. To make it simpler, let's remove beakers from the game by requiring that all science bars be kept at zero. Also, let's disallow all civ2 "tricks" except maybe rush-buying. Alternative ideas are welcome, of course.

	11-04-2005 22:52									#48
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A nice idea.
Maybe more players could participate, not only me and Kramsib.

	12-04-2005 00:07									#49
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If it means playing, count me in

	12-04-2005 05:12									#50
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quote: Originally posted by SlowThinker A nice idea. Maybe more players could participate, not only me and Kramsib.

Everybody is welcome. I don't know if Kramsib will participate or not, but I hope we can still learn something from the experiment anyway. I will work on the starting position and make a new thread when it is ready.

	18-04-2005 08:49									#51
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quote: Originally posted by La Fayette If it means playing, count me in

I have posted a thread "A Theory Contest" in this forum, and hope anyone interested in the subject will participate. It does mean playing, BUT

* it also includes having a theory and explaining it.

* the play might be much simpler than normal - at least that is my intention.