30-04-2005 20:26									#61
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quote: Originally posted by Grigor The optimal result for the practice position should be 48 cities.

Grigor - Your idea is tantalizing. I guess you are splitting the 60 turns into 4 cycles involving movement and production: m-p-m-p-m-p-m-p-m. Each "m" takes at least 2 turns of movement plus 1 turn to build a city, so there are 59-15 = 44 turns left for 4 p's, an average of 11t per cycle.

I estimate that a grass-city needs 33g for rushing 14s, to birth that fast. Cities produce 11-15g in taxes per cycle, so each new grass-city needs support from 2 neighbors. Maybe from its mother and a forest city, for example. But the mother and the forest city will need some gold, too, to maintain an 11t pace.

I don't think we have enough resources to make this all work perfectly, so unless someone has a new idea, I don't think 48 is possible. My max is 41. Have you done any more trials lately?

	30-04-2005 20:37									#62
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quote: Originally posted by Peaster Sorry, Kramsib, but I don't believe that. If you have time to develop a general theory of Civ2 and then refine it down to a set of practical playing formulas, then you have time for this simplified position.

Let me explain:

This weekend I have more time for posting, but only this weekend (because monday is holiday).

I started the other thread because I can follow it , from a weekend to other, and as it is only theory (by now) it is easier for me to follow.

After that, in june when I am on holiday I will start putting my theory in practise.

	30-04-2005 21:50									#63
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quote: Originally posted by Peaster I am thinking seriously about giving you Fundy at the start, to eliminate unhappiness completely. This would make warriors useless (except for disbanding purposes). Any objections? Here are my first thoughts about solving this position: 1) IMO the optimal growth strategy is to send a few Settlers from Berlin to the major nearby forests (no warriors, no roads). Then, the new cities mutliply in clusters around the forests. With Fundy, I got about 115 s/t in 1000BC this way. 2) A formula like "1 shield = 2 gold" means both sides of the equation are equally effective in pushing this strategy. It might be possible to deduce such a formula either from reasoning or from testing. 3) From reasoning, I figure these are about equally useful: 25 gold = 10 shields (2 NON-warriors) = 15 sheaves (1 food van) 4) I briefly playtested the effect of adding each of these 3 options into the 4000BC save. The 15 food seems a bit better than 10 shields, which is better than 20 gold (maybe because IRB'ing is hard to do). So, I do not have a final answer yet, but feel I am getting closer. Disagreement is encouraged, of course.

I do not think we will get the correct shield value in such a simplificated game, nor in a game where the goal is maximising shields. In fact, by maximising shields, the value of shields will decrease as they become abundant against gold.

In such a map, where bonus grasslands is preferred than simple grasslands, food is abundant so its value is reduced, shields are quite abundant so its value is also reduced, but gold is dificult to obtain without roads.

In a well developed country, average tile will have, 2 food / 1 shield / 1 trade arrow, so values will be aproximatelly.

1 food = 0,5 gold
1 shield = 1 gold
1 trade arrow = 1 gold.

As there are some forests these values will be distorted.

Let's see a better aproximation:

Cities won't develop more than 3 citizens as in ICS we are continuosly building settlers. So production in each city woul be

1 forest, 3 bonus grassland,

so production by city would be

7 food / 5 shield / 3 trade arrows maximum

So values are:

1 food = 0,43 gold
1 shield = 0,6 gold
1 trade arrow = 1 gold.

The less roads, the cheaper shields.

	30-04-2005 22:05									#64
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According to these values:

Irrigation, has no sense.
Mining grasslands changes 1 food for 1 shield, so we are changing a 0,43 gold unit for 0,6 gold units (food by shields), so we are increasing our value. Mining grasslands is profitable.
Building roads is even more profitable, as they give 1 extra gold per tile (except on forests).

Consequently, the tile improvement strategy implies mining simple grasslands and building roads on bonuss grasslands.

	01-05-2005 01:34									#65
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Kramsib - I don't think anyone has a complete answer to how much gold a shield is worth in Civ2. If there is a meaningful answer at all, it must depend on whether the player is going for conquest or OCC, which city the shield is in, etc.

This contest is not intended to directly answer that question. But as part of your theory, you should tell us how much a shield in 4000BC Berlin is worth. That is, how much would you pay for one shield? If someone can find a clear and correct answer to that, maybe we can talk about shields in other cities and settings.

I do not believe your reasoning about values posted above is correct. When you wrote "1 shield = 0,6 gold" do you mean that you would only pay 0.6 gold for one shield? In other words, you would never rush-buy ? I also think your conclusions about mining (etc) are wrong, but if you can do more with this position than I can, I will have to change my mind.
--------------------------------------------------------------

@ Grigor - I tried for 48, but gave up. I don't see how the average new city can produce a settler in just 11 turns. Maybe if every city had its own forest square, or if we could play to 950BC....

BTW - When I estimated that doubling occurs every 14t, I meant it in an average sense (some cities may take 16t, some 12t, etc). Also, the actual average might be more like 13.9 or 14.2. For your hope of 48 cities, it seems we need 14.0 uniformly and exactly. I don't see how to do that.

	01-05-2005 09:07									#66
	48 Cities and 141 shields/turn Support Apolyton, buy Call to Power 2

A very productive evening. By focusing on making sure I got a complete doubling each round, I achieved 48 Cities and 141 shields per turn in 1000BC starting with 100g. In 4000BC, i rushed the first row, then waited one turn before disbanding the warrior and buying the third settler. Both the second (NONE) and third settler walked an extra turn to get to a forest square. The second settler from Berlin walked two extra turns to get closer to the SE forest.

I can probably do even better with some careful thinking - I could have squeezed a fifth doubling out of both Berlin and Leipzig, and there was no reason for any of the fourth round cities to found between 1400 and 1000BC. It seems that rushing the first row whenever possible saves enough turns and enough money to finish the last doubling in 1150 BC.

I apologize for the crummy numbering in the E-class cities.

Attachment: 48c 141 sh.sav.zip
This has been downloaded 2 time(s).

	01-05-2005 09:34									#67
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Grigor - Congratulations!! I also found a way to get 48 cities tonight, but you did it first, and I only got 136 points from mine. Our openings were very similar. I think I waited one extra turn to RB in Berlin. When one settler appeared a little earlier than needed, I used it to build two road squares (for the trade arrows). I also felt afterwards that I could have squeezed out one more city if I had tried.

Sorry for doubting your idea. I am still kind of surprised that 48 is possible.

Attachment: d_b1000.sav
This has been downloaded 2 time(s).

	01-05-2005 11:27									#68
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quote: Originally posted by Peaster So, my theory hasn't really changed much since I posted it. When I say "2.3g = 1s", this refers to a shield in row 1 of a typical new city. I think value formulas like this will almost always need such qualifications. Algorithms seem easier to work with than value formulas. But we have seen that values can help us find algorithms (ex how far to walk for a forest). ---------------------------------------------- I am still wondering whether my theory will hold up. Has anyone found an improvement or a major flaw ? Has anyone beaten 134 s/t in 1000BC? (I only got 132 in a 2nd try). And what's happened to ST and Kramsib and LaF ?

My my, what a lot of posts in the last 24 hours. It will take me some time to absorb them.

The value theory I'm trying to articulate has a number of elements.

The "intrinsic" value of a shield is low - perhaps 0.5 geu (the geu is an accounting unit arbitarily set to equal 1 gold).
food is slightly more valuable than shields - perhaps 0.8 geu.
shields (and perhaps food) may have an additional value based on their ability to buy time. This is perhaps 3 - 6 geu per extra turn. (I separate the intrinsic value of a shield from the time enhancement value because the extra turns bought per shield can vary from 1 downwards. Combining the two would require using an average that wouldn't apply in some of the interesting cases.)
The value of trade arrows depends on the type of government and the city development. In despotism and without a market, a trade arrow is 0.6 geu.

I would like to use these values to "justify" some of the decisions I feel are "correct". For example in a size 1 city placing your worker on a shielded grass tile, but in a size 2 city placing both your workers on forest tiles.

At the moment, it feels like a theory with some interesting implications, but which doesn't quite work.

RJM at Sleeper's

	01-05-2005 20:23									#69
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quote: Originally posted by Peaster Kramsib - I don't think anyone has a complete answer to how much gold a shield is worth in Civ2. If there is a meaningful answer at all, it must depend on whether the player is going for conquest or OCC, which city the shield is in, etc.

I think my theory can give a complete answer to that question.

quote: This contest is not intended to directly answer that question. But as part of your theory, you should tell us how much a shield in 4000BC Berlin is worth. That is, how much would you pay for one shield? If someone can find a clear and correct answer to that, maybe we can talk about shields in other cities and settings.

According to my theroy, shield value has not a constant value in the game, it varies depending on its abundance during the play.

A little example, when you produce less shields, they become more scarce, and more "expensive", they have a great value for you and you will pay more for them, in such a situation you would rushbuy more often (change more abundant/cheap gold for scarce/expensive shields). When shields become abundant, they become cheaper and rushbuying is less worthwhile (less worthwhile but it can still be useful depending on the interest rate, intrinsec gold value).

quote: I do not believe your reasoning about values posted above is correct. When you wrote "1 shield = 0,6 gold" do you mean that you would only pay 0.6 gold for one shield? In other words, you would never rush-buy ? I also think your conclusions about mining (etc) are wrong, but if you can do more with this position than I can, I will have to change my mind.

1 shield = 0,6 gold, does not necessarily mean that rushbuying is not worthwhile. It depends on intrinsec gold value, in fact, in this simple position, stock of gold has no value at all (except for rushbuying).

This game is a competition against time, and time affects on gold value.

Let me explain it more clearly.

First of all, we need to discern between "flood of gold" and "stock of gold".

Flood of gold can be identified with the amount of trade arrows, as they "flood" every turn.
Stock of gold are gold accumulated in your treasure.

Flood of gold is employed on science investigation, return it to population in luxuries form, or keep it in your treasure.

Treasure is employed for paying maintenance, rushbuying or international transfers.

In your simple savegame, flood gold cannot be expended on science, so it can only be used for treasure or luxuries. In fact, in the first turns, when luxuries aren't needed to keep population happy, the best distribution is asign the maximum percentage on taxes, making your treasure grow.

As there is no rivals, there is no need to employ gold for international transactions, and as there is no buildings to build (only barracks but they are useless without enemies) treasure is only useful for rushbuying.

In other words, liquid gold (stock gold / treasure ) has no further use, and it is only useful for rushbuying, that is to say, bringing today, future production.

Changing, stock gold, which is gold with low "value of use", for shields which have a greater "value of use" is "profitable".

This reasoning is perfectly compatible with Adam Smith's thoughts who discovered that countries' wealth depends more on a great "flood" of gold than on a great "stock" of gold.

-------------------------------------------------------------------------------
I have prepared a practical example.

Let's assume a city with 4 shield production per turn which is building a Settler (40 shields - 10 turns). And let's assume there is no change in production during the following 10 turns. Let's assume there shield value is constand during this period too and equal to 0,6 gold per turn.

Remember that Rushbuying cost for units is:

N*N/20 + 2N

And twice when the box is empty.

Here is the meaning of the Columns in this excel file.

A: Here is the shield production of the city, 4 shields per turn.
B: The turns left until the settler is finished.
C: Shields left until the settler is finished (A * B)
D: Cost of rushbuying according to the formula mentioned before.
(C*C/20 + 2 * C). Twice for the first cell of the column.
E: Real shield value in gold terms using my theory, assuming it keeps constant during the 10 turns to simplify the analysis.
F: Simple interest rate for the period remaining.

C1 = ( 1+i*t ) * C0

Considering rushbuying as a way to bring today future production.

That is to say, if production remaining has a real value of C0 (E column) and rushbuy cost C1, what is the aditional cost in terms of an interest rate?

G: Simple interest rate in turn terms. By dividing by the remaining turns, we obtain the interest turn "payed" per one turn.

OBSERVATIONS.

When shields are cheap (0,6 gold per shield), rushbuying is less worthwhile, as we are paying more gold for rushbought shields. In fact the interest rate is positive. But you can notice that, as turns go by the interest rate is growing. Rushbuying at the second turn is cheaper than any other turn.

Interest rate is also a measure of how much value your stock gold is losing and reflects the cost of opportunity of not rushbuying.

But on the other hand, the second case where shields are expensive (3 gold per shield) there is a point when rushbuying become worthwhile (interest rates become 0 in the 6th turn = 5 turns remaining) and interest rates become negative.

CONCLUSIONS.

In your savegame, rushbuying is the only way to make stock gold useful, and the sooner you expend it the less value it loses.

When shields are cheap, rushbuying is less worthwhile except we have better uses for our money (science, international transfers, maintenance).

When shields are expensive, there is a point when rushbuying is always profitable.

	01-05-2005 21:56									#70
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RJM - That looks like a good start. I am not sure what you mean by the "intrinsic" value of a shield. To me, a shield has value only for making the next settler faster, which (I think) is what you mean by "an additional value".

Kramsib - If your theory can give a complete answer to shield values, we would all be grateful. But so far I have not learned anything from it. I have almost no idea what you are talking about, and judging from readers' responses in the other threads, they do not get it either. I urge you to focus on the specific questions at hand -

1) How to play this position correctly ?

2) How much would you pay for an extra shield in 4000BC Berlin? (also similar trade-offs with food, etc)

I suspect that part of the confusion is over what you mean by formulas like "1s = 0.6g". To me, it means 1s and 0.6g are equally useful in achieving my goal (which means your numbers are horribly wrong). Apparently, you have a different meaning in mind ?? Can you explain this clearly, please?

And if it does have a different meaning, how do you use it to make decisions?

	02-05-2005 01:02									#71
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I think I see where Kramsib is going, and I look forward to the rest of it.

So far, it seems to not be of practical use. We all know (from OCC among other practical trials) that rushing in the second turn is the cheapest strategy, but we usually do not have that option. In Civ II the most powerful practical tool for the human player is partial rushbuying, (which I think is perilously close to cheating but that's a different thread) and I look forward to any discussion of when and what kind is optimal.

In Peaster's current test position, there is only one partial rushbuying option, and after much playtesting the intuitive wisdom is to rush the first row as soon as the gold is available. I hope Kramsib's full theory will shed some light on this eminently practical situation.

	02-05-2005 01:26									#72
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quote: Originally posted by Peaster Kramsib - If your theory can give a complete answer to shield values, we would all be grateful. But so far I have not learned anything from it. I have almost no idea what you are talking about, and judging from readers' responses in the other threads, they do not get it either.

That's why I started the other thread to show the whole theory from the beginning to the end, statement by statement, discussing them separately and with quite time between them. It is quite revolutionary as it is based on different ideas from Economics, but I believe it applies perfectly to the game. If all of you are patient I will be able to explain it completely.

In "Hurry Production Thread" I stated it very quickly, so I was missunderstood quite often.

quote: I urge you to focus on the specific questions at hand - 1) How to play this position correctly ? 2) How much would you pay for an extra shield in 4000BC Berlin? (also similar trade-offs with food, etc)

Unfortunately, my theory does not apply for city placement or unit moving, but it is useful to determine which squares work in a specific city (it determines the more efficient tiles), it also helps to determine when rushbuying is worthwhile, as I have said on my previous post. And the most important application, it allows to give value to every item in civilization, in gold terms obviously. Units, buildings or even techs can be translated into gold thanks to my theory.

quote: I suspect that part of the confusion is over what you mean by formulas like "1s = 0.6g". To me, it means 1s and 0.6g are equally useful in achieving my goal (which means your numbers are horribly wrong). Apparently, you have a different meaning in mind ?? Can you explain this clearly, please? And if it does have a different meaning, how do you use it to make decisions?

When I say, 1s=0,6g I mean a exchange ratio, like 1 $ = 1,3 €, that is to say, If there were a shield market, I could buy 1 shield for 0,6 gold.

Of course, there is no such a market in civ (excepting rushbuying), but in a standard game, I can exchange techs, gold, or units.

This theory is specially useful in Multiplayer games, moreover when using Civ2Dip by Yaroslav (a great friend of mine), where human players are really interested in the real value of things.

How much gold does a settler cost?, a settler cost 40 shields, but how much gold does a shield cost?, this is the question.

My theory states that the whole shield production in a city has the same value as the whole food production and the trade arrows. That is to say.

food production value = shield production value = trade arrows production value

As trade arrows are directly convertible in gold (gold returned into luxuries, gold invested on science or gold in your stock of treasury), we have the following expression.

trade arrows = flood of gold = shield production value = food production value.

The ratio, trade arrows / shields, give me the value of 1 shield in gold terms.

Using your savegame as an example.

Berlin in 4000 BC, produces:

7 food / 3 shields / 1 trade arrow = 1 gold

So, 1 shield = 0,33 gold (1trade arrow / 3 shields = 0,33)

Now, if you ask me, how much gold I will pay for an aditional shield as a stock in my production box?, my answer will be 0,33 gold per shield.

	02-05-2005 03:31									#73
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quote: Originally posted by Kramsib Berlin in 4000 BC, produces: 7 food / 3 shields / 1 trade arrow = 1 gold So, 1 shield = 0,33 gold (1trade arrow / 3 shields = 0,33) Now, if you ask me, how much gold I will pay for an aditional shield as a stock in my production box?, my answer will be 0,33 gold per shield.

I am glad you cleared that up, because it is finally completely obvious to me that your theory doesn't work. I suggest that you play the position two ways (use cheat mode to make these changes, and govt = Fundy):

1) Start with 110 gold + 3 shields in the box.

2) Start with 100 gold + 13 shields in the box.

You will have much better results with 2).


@Grigor - You are a very nice man, but let's be honest. We both know Kramsib is off by at least 600%. I would not be so harsh with him except that he pretends to know divine secrets which are really just untested ideas.

@All - I probably will be ready to start in a few days. How are your theories coming along?

	02-05-2005 04:23									#74
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Peaster -

Yes, I am nice

But in our playtesting we cannot even decide whether the play is more efficient if we wait to rush the settler in Berlin 0, 1, or 2 turns. Having enough gold to rush the first row early in the 2nd gneration settler builds can take off significant turns.

I will try tonight, but I expect that waiting 2 turns with 110 gold will give enough gold left over to rush all 3 first rows on the first available turn.

	02-05-2005 05:27									#75
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Grigor - I was suggesting the exercise with the 110g to Kramsib as a way to test his theory. You already know that 10s is worth much more than 10g.

I hope you will write up your understanding of this position, including a statement about values to use in the auction. Your idea of four doubling cycles is wonderful IMO, but I am not sure it will work the same way from a slightly different starting position. So, I hope you will form a theory that doesn't assume exactly 4 cycles.

I will probably revise my theory a little in the next few days and put some more thought into how to run the auction. I have been thinking it might be easier and fairer to create a few different starts and let each player choose one. Any opinions on this?

	02-05-2005 06:05									#76
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quote: Originally posted by Peaster I am glad you cleared that up, because it is finally completely obvious to me that your theory doesn't work. I suggest that you play the position two ways (use cheat mode to make these changes, and govt = Fundy): 1) Start with 110 gold + 3 shields in the box. 2) Start with 100 gold + 13 shields in the box. You will have much better results with 2).

I cannot understand how can you refuse my theory so quickly.

It is totally clear that, 1s = 0,33g , implies that shields are cheaper than gold.

But I think that I explained that stock gold loses value in high speed so its better invest on shields.

Of course 2nd position is better than the first, but it doesn't in a standard game with scientific research.

I am talking about nominal value, and you are talking about value of "use".

Oh, oh, the marginalist revolution is near, as Estilpón said.


In other words, you are talking about the subjective shield value. As far as gold don't produce settlers, shields are more valuable. Of course.

But I am talking about objective shield value, shield value based on its cost of production.

I insist, I must end the theoretical concepts for all of you to understand the theory.

You should be patient with it.

	02-05-2005 08:31									#77
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quote: I cannot understand how can you refuse my theory so quickly.

Easy. I judge a tree by its fruit. I asked you a specific question which seems easy to understand - How much would you pay for a shield in Berlin ? [This is clearly about "value of use" as you call it]. Your answer was 0.33g !? If you didn't understand the question, feel free to revise your answer.

	03-05-2005 03:16									#78
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Ok, then we missunderstood each other.
In fact, you are making me think a lot, and my theory is growing in complexity and power.

If we are talking about "value of use", we are talking about how desired shields are. In that case, the highest price I would pay for a shield would be the rushbuy cost.

That's it , In Berlin on 4000 BC with 3 shields in box and producing a settler I would pay:

37 / 20 + 2 = 3,85 gold for the first additional shield.
36 / 20 + 2 = 3,8 gold for the second additional shield.

and so on, descending on 1/20 for each additional shield.

This is why, as rushbuying is the only way of obtaining more shields, it acts just like a blind monopolist stablishing a high price for shields.

An imaginary shield seller who offers shields on a higher price than the "rushbuy monopolist" would be refused from the market, as rushbuying is more efficient.

But if there was an imaginary shield seller who offers a lower price I would rather buy him his shields instead of rushbuying.

Now, let's imagine, there were several imaginary shield sellers who compete against them. Would they compete lowing shield price to nearly 0 ?.

Of course not, shields have an internal cost of production. That cost is my 0,33 gold per shield. In fact, when I produce 3 shields per turn I am employing 2 citizens, the same labour force as my trade arrows, If the imaginary shield seller were in the same situation, selling shields for a lower price than 0,33 is unneficient as he would rather employ his citizens to produce other more valuable goods. My 0,33 gold per shield is the value which makes equally worht producing trade arrows or shields. That means that, internally in my civ, I have an internal exchange rate between shields and gold of 0,33 gold per shield. This is an internal value.

In an imaginary shield market I would earn money if I sell shields over 0,33 gold (my internal cost).

Now, let's imagine, that there were more players with different internal costs.

Player 1 has 0,33 gold per shield internal rate.
Player 2 has 0,5 gold per shield.
Player 3 has 1 gold per shield.

Assuming rushbuy cost is the same in this turn and equal to 3,85, for every player, player 1 could sell shields to player 3 for 0,9 gold in exchange and buy shields to player 2 for 0,6 gold per shield, gaining a spread of 0,3 gold per shield traded without losing production.

Reproducing this behaviour, with all players competing among them, we would have a shield market with an equilibrium shield price which can be considered the real value of a shield in the civ play.

To sum up:

We have a range of shield value, where it can fluctuate:

from 0,33 gold to 3,85 gold per shield.

I will never buy shields over rushbuying price.
I will never sell shields lower than my internal exchange rate.

The shield trade, the number of shield buyers and shield offerers, their interanl exchange rates and the rushbuy cost, would determine the exchanged price.

In this simple position, I only trade with the IA at a fixed price, the rushbuy cost which varies depending on how full my production box is, and the kind of item I am producing.

Last edited by Kramsib on 04-05-2005 at 04:47

	03-05-2005 04:40									#79
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I think we are talking about the same thing now.

IMO, when most Civ2 players wonder about the "value" of something, they want to know how much it will help them win. So, that's what I want to focus on in this contest.

I don't see how you got "37 / 20 + 0,5 = 2,35" for the cost of the first shield, but this is much more reasonable than 0.33. I think the true cost is more like 6g, but that ignores the option of rush-buying just the first row, or disbanding the warrior (both are legal in this game). There is also the option to save your gold for the next city.

So, I don't think it is that simple. I expect my value will be about 3g, based on the best known playing/spending strategy.

Anyway, thanks for your patience.

	03-05-2005 10:48									#80
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@Grigor - I think we are both interested in the question of when to rush the first setter from Berlin. I think we both start by rushing row 1 for 16g (84g left) and disbanding the warrior (delaying this has no benefit). So, we have 15 shields in the box. We can rush the settler in 4000BC, 3950BC or later on. Let's compare the first two options.

4000BC "pros": We build city #3 a turn earlier, gaining an extra 2 food + 3 shields +1 gold. Also "Mom" (Berlin) gets back to work a turn earlier, gaining 2 shields.

The "cons": We spend an extra 81g - 68g = 13g for this, worth about 6 shields (in city #3 for example).

IMO the pro's exceed the con's, so we should RB in 4000BC rather than 3950BC. The same reasoning shows that waiting for 3900BC is worse than 3950BC, so we can ignore that option. [In fact, the cons generally decrease each turn you wait].

I was careful with the pro's and con's, to only discuss shields in the "second generation cities" (city #3 and Berlin after her first birth). It is misleading to compare these shields with the 3 extra shields purchased in 4000BC Berlin. This is another example of the time-value of money (and shields) principle.

As usual, I must qualify my calculations a little. The 6 shields mentioned in the "cons" might be worth more than they seem, because you have some choice in where they go (eg, maybe you need them in city #2).

It is very easy to miss something in this kind of comparison. What do you think?

	03-05-2005 11:26									#81
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quote: Originally posted by Peaster RJM - That looks like a good start. I am not sure what you mean by the "intrinsic" value of a shield. To me, a shield has value only for making the next settler faster, which (I think) is what you mean by "an additional value".

If a shield "has value only for making the next settler faster" then its intrinsic value is 0; I wouldn't rule this out, but for the time being I prefer to use a small but positive figure.

The computational difficulty with the "value for making the next settler faster" is that it does not directly relate to the value of a shield. You have to know how many shields will make the next settler faster, and how much faster. Once you know how many shields are required and how many turns you save, you can multiply the value of making a settler 1 turn faster by the number of turns saved and then divide by the number of shields to get a value per shield. It's all horribly complicated, which gets us back to your idea of using turns as the accounting unit. The part that makes me uncomfortable is that the value extra turns is apparently relative. I would like to be able to establish a fixed point so that I could always do the same comparison - how many extra turns does x give you compared with the standard?

At the moment I'm concentrating on a theory that can cope with an even simpler situation than your game - that is where do I place my workers in typical size 1 and size 2 cities? For example, I can usually choose between a shielded grassland tile and a forest. If I know that 1 food is more valuable than 1 shield, I put my worker on the grassland. But if I don't have a shielded grassland and the value of a shield is more than half the value of 1 food, I assume I would choose a forest rather than an unshielded grassland.

BTW I'm following the exchanges between you and Kramsib with interest, but a high degree of incomprehension.

RJM at Sleeper's

	03-05-2005 12:03									#82
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quote: Originally posted by Kramsib In an imaginary shield market I would earn money if I sell shields over 0,33 gold (my internal cost).

After 1 turn in Peaster's game you can have 3 shields in the box. You could use the cheat function to remove those shields and increase your gold by 2. (That seems to be the equivalent of selling the shields for 0.66 gold which you say would earn you money.)

I don't think that there are many of us that would prefer 3 less shields and 2 more gold.

So let's restate Peaster's question: Assume you can start the game with 10 shields and 100 gold or with 0 shields, but more gold. Which is it to be? Your theory seem to be saying that it is better to start with 0 shields and 105 gold. That's the only only construction I can put on the above quote.

Assuming you wouldn't really settle for 5 extra gold, how much would you settle for? My answer by the way is anything over 50 - the cost of rushing the first row from scratch. If I start with no shields and 151 gold and rush that first row straight away, I'm better off than starting with 10 shields and 100 gold. (I might settle for something less than 50, but more than 50 is certainly worth taking.)

RJM at Sleeper's

	03-05-2005 19:01									#83
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quote: Originally posted by rjmatsleepers It's all horribly complicated, which gets us back to your idea of using turns as the accounting unit. The part that makes me uncomfortable is that the value extra turns is apparently relative. I would like to be able to establish a fixed point so that I could always do the same comparison - how many extra turns does x give you compared with the standard?

The ultimate value is your final score. Each turn adds about 7 points to that, so we know 1 turn = 7 points. If you have 14 cities, then each city-turn is worth about 7/14 = 0.5 points at that time. And so on - in principle, we can evaluate any commodity at any time in terms of points (though it is usually easier to compare 2 other commodities directly).

But IMO evaluation has to be done in the context of a strategy for maximizing your score. Whenever Grigor finds an improvement in strategy, I have to re-think my values. Fortunately, they don't seem to change too much, which gives me some hope that we don't need to know the absolutely best-possible strategy before claiming to know the approx values of things.

quote: For example, I can usually choose between a shielded grassland tile and a forest. If I know that 1 food is more valuable than 1 shield, I put my worker on the grassland. But if I don't have a shielded grassland and the value of a shield is more than half the value of 1 food, I assume I would choose a forest rather than an unshielded grassland.

Yes. The hope is that a theory of value will answer that question for you. But I think some questions, like this one, can be answered more simply with a rule than with values. For this contest, my current rule is:

Keep the worker on forest, unless this leads to obvious problems, such as disbanding the city.

This is part of my strategy, that each city should make a settler ASAP (rather than build up its food box, etc). It is a little different from what I said in my first draft of values, so will have to revise that statement.

quote: BTW I'm following the exchanges between you and Kramsib with interest, but a high degree of incomprehension. RJM at Sleeper's

I think Kramsib was writing formulas, and using the word "value", with some odd economic meaning, which I still don't follow. Maybe he will explain it more in his other thread. His latest post here seems fairly clear, and I regard that as a good starting point for more discussion. He needs to include the objective of the contest into his theory though.

It is hard to believe that I would say anything incomprehensible, but if I did, please tell me, and I'll try to explain.

	04-05-2005 04:52									#84
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quote: Originally posted by Peaster I think we are talking about the same thing now. I don't see how you got "37 / 20 + 0,5 = 2,35" for the cost of the first shield, but this is much more reasonable than 0.33. I think the true cost is more like 6g, but that ignores the option of rush-buying just the first row, or disbanding the warrior (both are legal in this game). There is also the option to save your gold for the next city. So, I don't think it is that simple. I expect my value will be about 3g, based on the best known playing/spending strategy. Anyway, thanks for your patience.

I was wrong, the correct expresion is:

37 / 20 + 2 = 3,85

That is to say, the rushbuying cost of a unit is:

N*N/20 + 2N

Where N are the left shields (remember that if the production box is empty it doubles).

Dividing by N we have the rushbuy gold per shield:

N/20 + 2

As a Settler costs 40 shields, and we have 3 shields, there are 37 shields remaining:

Finally we have

37/20 + 2 = 3,85 gold per shield.

	04-05-2005 08:01									#85
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Kramsib, that looks better. You have computed the average cost of a shield when you buy 37 at a time.
But I remind you, it is legal to rush the first row, disband the warrior, and then buy the other 25 shields. That's a better spending strategy, so I don't think I'd pay 3.85 g/s for that group.

Also, in my view, the shields do not all cost the same, but I won't go into that unless someone is interested.

At the moment I am working on food vs shields and hope to offer a fairly complete answer by tomorrow.

	04-05-2005 10:49									#86
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Here's a fairly complete theory of food -vs- shield values for this contest. IMO strategy comes before values. So, finding the correct values is not for placing city workers (which we have to understand first). Instead it is intended for comparing two similar positions in play-testing or in a thought experiment, for example. IMO a 10 percent error is acceptable, though I will try for better.

I am going to focus mainly on values in a new city, or in one that just gave birth, assuming the goal is to produce a settler asap, without regard to increasing city size or keeping the food box full, etc. If there is a forest tile nearby, this means the city will only stay at size 2 for one turn.

EDIT: I wrote this assuming there was only one forest tile nearby. The case of two forest tiles comes up later in other posts. Sorry for not stating this clearly.

I am convinced that every commodity (food, shields, gold) decreases 50 per cent in value every generation, and I will use that idea here. Some of this is debatable, I guess, but it is based on a lot of thinking, posting and testing. As I said, you usually have to decide on some aspects of your strategy before you can compute values.

Case 1: Suppose the city has a forest tile nearby. The fastest way to make a settler [with normal rush buying] is to set the worker on forest for 10 turns, so the food box is full. Assuming we rushed 7 shields on the second turn, we have 37s at that point, and we get a settler on the 11th turn. [Rushing 6 shields would be slightly better, but it isn't possible]. Let's assume this is the best approach - but the following calculation is probably OK for most other strategies, too.

Suppose your city is given +2 food. This gift causes the city to grow a turn earlier than before, which means it gets one extra shield this cycle. And the +2f is still there for the next cycle, but this benefit should be reduced in value by 50 per cent to +1f. So,

Value of +2f gift = 1s + 1f. So, 1f = 1s.


Case 2: Suppose the city has NO forest tile nearby. There is no choice about where to place workers, but the reasoning is similar.

Suppose your city is given +3f, which causes the city to grow a turn earlier than before. We get

Value of +3f gift = 1s + 1.5f. So, 1.5f = 1s in this case.


Adjustment to Case 2: In such a grass-city, food sometimes gets "lost" when the city shrinks. For example, consider a size 2, about to give birth. It doesn't matter whether it has 20 food or 30 food in the box - the results are the same. So, there is a good chance (about 33 per cent IMO) that the +3f gift only has an effect ONCE. In that case, the formula should be 3f = 1s. I prefer to use an "expected value" approach and say

Case 2 revised: 2f = 1s.

Case 3 (maybe not relevant to this contest): Suppose that in case 1, the food box and shield box sizes are changed to 30 each. It is no longer necessary to keep the workers on forests all the time. It will take (30+30)/5 = 12 turns to give birth (assuming a very small rush buy, to compensate for the annoying need to fill the food box before the shield box). With this flexibility in placing workers, 1f=1s.

I mention this case because I once thought we had this flexibility in our contest. It is curious (probably just a coincidence) that the value formula is the same for Case 1 and Case 3. It does offer some hope that value formulas are fairly stable when we must adjust them to fit improved strategies.

Case 4: Berlin in 4000BC. This one is tougher, because rush-buying strategy will have a big effect, and the size of the gift may affect the relative values, too. So, I am less sure about this case, but I think we should assume the player rushes a settler on turn 1. Then a gift of +3f has an effect similar to that in Case 2, but I think the +3f will be lost with the second settler. So, 3f = 1s seems about right.

I play tested the position with a food van replacing the warrior. The results in 3000BC were approx as before, which tends to confirm the theory (15f = 5s). But if I buy a van in this contest, I might use it in a different city, more in need of food than Berlin.

Fine print: IMO these formulas are useful in an average value sense, but there will be exceptional situations where they don't apply. For example, the size 2 city with 20 food [discussed in the adjustment to Case 2] has no need at all for +10f, so the marginal value of food is zero in that case. Likewise, a new city in Case 2 can use +2f, +3f, or +4f equally well [full box in 6 turns].

Last edited by Peaster on 05-05-2005 at 20:27

	04-05-2005 11:42									#87
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I've just realised why we are coming to different conclusions about some aspects of this. I was looking at the position at the start of the game (when we are in despotism and some tiles give a reduced value for food). I will need to rethink my approach for forms of government where we get 3 food from the irrigated grassland. (But I'm not sure when )

Presumably, no-one doubts that the city should be founded on a grassland tile?

RJM at Sleeper's

	04-05-2005 17:50									#88
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Peaster -

in your 4000BC analysis (fundy, 100g), I would suggest that the point of comparison is that at which all 3 cities have a complete first row. That reflects the time cost of using all your money on th first turn.

I haven't done that analysis yet.

	04-05-2005 18:10									#89
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Peaster - regarding your elaborate case analysis: I have lookd at one of th crucial points of the test game - the end - and found an interesting point in a common situation - a city with access to two forests:

After rushing the first row, worker placement does not change the result

That is not precisely true, but there are three strategies. I begin at 1550BC with 3 food in the box and 10 shields. In the next 8 turns I can do the following:

Strategy 1 - Build at maximum speed
This means 1 turn at 3 food and 2 shields (avoiding food waste) and 7 turns at 2 food and 3 shields. I end up with a full food box and 33 shields.

Strategy 2 - grow at maximum speed
This means 5 turns at 3 food and 2 shields plus 1 turn at 2 food and 3 shields filling the food box, plus 2 turns at 1 food and 5 shields, working both forests. I end up with the same 33 shields! but with 2 extra food in the box.

Strategy 3 - mix and match
This would be 3 turns at 3 food and 2 shields plus 4 turns at 2 food and 3 shields filling the food box, plus 1 turn at 1 food and 5 shields working both forests. I end up with 1 extra food in the box but the same 33 shields!

The implications for the earlier portion of the game are unclear except that in 2-forest cities, 10-turn settler building is possible for 35g. (19g for the first row and 16 for the last row)

	04-05-2005 20:05									#90
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@RJM - Despotism? The posted save starts you off in monarchy, but I suggest you change that to fundy. Yes, I build all cities on grass until the endgame.

@Grigor 1: Not sure what you meant... Is this about playtesting from 4000BC? [I have been playing to 3000BC, when there are usually 6 cities]

@Grigor 2: First, 2 minor questions:

Did you really mean 1550BC ? If the city takes 10 turns to make a settler, there is not enough time left for the settler to make a city. I guess this is not relevant to your main point - just curious.

In Strategy 2, you state that after filling the box, you can get two turns at 1 food and 5 shields (which I call 2<1,5> ). But in the growth year, the AI always places one of my workers on grass, so I get a turn at <2,4>. Do you know a way to prevent that?

I was mainly interested in the 3500-1800BC period, and didn't really consider cities with 2 forests, or the possibility of having 35g per city to spend. These cities are different because they can still produce 5 useful stock at size 2 [with one forest you can get <2,4>, but the food is not useful for the current cycle]. So, Strategy 2, to reach size 2 quickly, is probably the best option (especially if you are right about the 2<1,5> )

Assuming this is best, my food-shield analysis for such cities is

+3f = +3s + 0.5f, so that 0.84f = 1s.

[But if you apply this after about 1800BC, it should be 1f=1s]

Finally, I am curious about your 4-cycle strategy. If the game ended in 1200BC or 800BC instead, could you adapt the strategy to that?