A Theory Contest

[Grigor]

Yes, the balance between walking, roading, and rushbuying is quite interesting even in this restricted setting. In your posted save I have gotten to 93 shields with 25 cities. My latest strategy was to keep the number of cities at 12 (thus controllable by martial law) until the last turn, when 13 carefully located setlers founded nw cities, many on forest working a second forest.

Of course, Berlin is in a far less than optimal location. Also, my second city remained a low shield producer despite a forest square; it may be that walking 5 squares is optimal at first because of the possibility of filling in from otherwise mediocre Berlin later. The idea is to maximize size 2 cities working 2 forest squares.

Without happiness concerns, the strategy changes.

I will try again tonight. There is still some life in this position - it is like a chess problem: King Ludwig to play and produce 100 shields on the date of 1000 BC

[Peaster]

It is like chess because there is no luck involved, and it is still hard to fathom completely.

I have not decided about ICS vs Go-For-Forest (GFF). I played a GFF game today that would have paid big in 500BC, but it was still a bit lame in 1000BC. [I started with Fundy and 130 gold, and scored 120s/t. I forgot to found the final cities on forests - this might have added 5-10 points].

I hope success in this game is not too much about tricks played near 1000BC. It is supposed to be mainly about the 4000BC position. But here are some observations about the endgame (which Grigor has surely noticed already):

* The last turn that gold has any value is 1150BC [unless you have roads]. In 1150BC you can rush a Settler, and it still has time to move twice and build.

* The last turn to build a city which can grow naturally to size 2 is 1400BC. Hence, the last turn to RB that Settler is 1550BC.

*IMO the best long-term use of gold is to RB from 4 or 6 shields up to 10 (warrior) at every opportunity. Then switch to Settler and wait. This advice may not apply in the very early game or the late game.

[Grigor]

In the Monarchy start, I discovered some value in the trick of disbanding one of the warriors to give an extra push to rushbuying. I tried that on turn 1 in Berlin, and again in the endgame when I was too short of cash to finish the last few settlers. I still cannot evaluate that outcome properly, although disbanding in the second row of a settler build makes those 5 shields worth somewhat more than 2.5 gold.

I think the optimal plan must be to rushbuy the first row at the first oppportunity once the city hits size 2 and is a production center. Here are three options for efficient settler production:

(1) New Settler in 9 turns. For my cities with at least one forest square, I was rushbuying 7 or 8 shields in the first row, then working grassland two rounds (3 shields/Turn), then switching to one forest (4 sh/T) until the end. That was to keep the population at size 2. It pumps a city out in 9 turns and puts 21 shields in the food box.

(2) New settler in 7 turns. The fastest is to rush 7 or 8 shields at the beginning, then work both forests (5 sh/T). That pumps a city out in 7 turns, but puts only 10 sheaves in the food box.

(3) New settler in 8 turns. An intermediate plan is to rush the first row, work both forests for 2 turns, then work 1 forest for 5 turns. That makes a new city in 8 turns and replaces 15 sheaves in the food box.

Are you going to post your Fundy start?

[Peaster]

The real contest will be Fundy, but you can change the prcatice game in any way you want. Click on Cheat Mode and then Force Government, Germans, Fundy. You can also change the amount of gold or shields you start with, or you can create a food van.

I guess I haven't thought enough yet about efficient settler production. So far, I have used the old "greedy algorithm" of maxing food while size 1, and maxing shields while size 2 (with RBs on first row).

I hope to decide the ICS vs GFF question mathematically as soon as I can estimate growth rates with/without forests. Probably, deciding your question should come first. And, if it is too hard to decide from math or testing, a third option is to write a short spreadsheet program to simulate growth.

[Grigor]

OK, I tried a practice game at Fundy. With no special effort on a modified checkerboard plan I got 37 cities and 128 shield.

The 2-food penalty for settlers makes food more valuable, and perhaps gives some value to roads. It also adds value to the strategy of the NONE settler moving a greater distance early, though the benefit of compounding will be reduced and needs to be calculated. On the opening turns, for instance, I am contemplating the following two strategies:

Strategy 1: maximizing compounding speed
4000 RB Warrior; disband warrior; RB settler.
3950 move NONE settler one square. Move settler
3900 Leipzig founded. Move settler
3850 Hamburg founded

Strategy 2: Make some plans for the future
4000 RB warrior
3950 NONE settler builds road. disband warrior. RB settler
3900 settler moves 2 squares
3850 Leipzig; NONE settler moves 2 squares.

I don't know what happens next yet. Options include: (1) making a second road both for settler speed and an extra gold in Berlin when it hits size 2. (2) founding 3rd city near the closest forest (3) heading for the large northern forest to found the 3rd city in a 2-forest square.

I think a challenging goal would be either 45 cities or 150 shields.

[SlowThinker]

Since the aim is to develop an evaluating theory I think

1) there should be the shield/food ratio only so that the evaluation theory can be simple.
I think this might be achieved if you add techs to allow one-row rushbuys: This way the ratio shield/arrow is close to be constant (supposing beakers and luxuries must be set to 0).
But still I would prefer to put the gold out from the game completely.

2) there should be more ways of development for a choice. In other words I agree with Grigor there is not enough of space for decisions.
The problem is the standard Civ2 is ICS-based and more decisions would require some changes to rules.txt:

2a) I think the most natural decision would be 'build a settler' or 'let a city grow'. This requires to make the food box smaller or the settler more expensive. Also cost of granary and factory (it could be allowed) could be lowered.

2b) to allow more 'deals' shield-food you could add more terrain types that would be spread on all the map - like 3food - 0shield, 2F-1S, 1F-2S, 0F-3S. This allow simple deals between food and shields in a 1:1 ratio.

2c) Another interesting decision is placement of cities. To preserve an option of this kind of decision you could add some 'specials' in a bit distant positions (like forest on the testing map).

More notes:
I suppose the map will be revealed(?)
I think fundy is a good idea. Chieftain doesn't get you rid of corruption.
I agree the evaluating by shields is a best idea. Shields are what you finally want (to build army and destroy your oppoments). Population is rather a means to get shields.

[SlowThinker]

I posted a PM to Kramsib...

[Peaster]

Grigor - It sounds like you are doing a little better with ICS growth than I am with GFF. Do you have a 1000BC save I could look at ? I am interested in the percentage of size 1 cities, and the percentage of cities near forests at the end (see below).

SlowThinker - Welcome! In general, I agree that gold is a complicating factor, but am not sure how you'd get rid of it. Would you require taxes = 0, or just make a rule that it cant' be spent...? Also, I am not sure how the bidding phase would work without it.

Regarding (2), I am finding the decisions hard enough already. But your ideas are interesting, and I don't object. Maybe you could experiment with them a little and let us know which seem best.


Here are the results of my math approach to "ICS vs GFF". I think the results are not very practical yet, and maybe that says math is not the best approach to such problems.

Estimates of birth rates , assuming no rush-buying, and ignoring support costs of new Settlers:

Grass only: Starting from scratch with no rush-buying, a city reaches size 2 on the 8th turn, and has 17 shields. It needs 8 more turns at 3s/t to make its first Settler, so 16 turns. But after that it will usually be size 2 and make Settlers approx every 13 turns.

Grass with forests: The city can make a Settler in 13-14 turns, with about 8-14 food in the box. Future Settlers will take approx 11 turns.

Estimate of city values , measured in shields per turn, assuming that 2/3 of the cities are size 1, and the rest are size 2.

Grass only: (2/3)(2s/t) + (1/3)(3s/t) = 7/3 s/t. This means an average city on grass will be worth 7/3 points at the end. If all the cities are size 2, this figure should be 9/3.

Grass + forest: (2/3)(3s/t) + (1/3)(5s/t) = 11/3 s/t. If half the size ones are built directly on forests, this should be 12/3 s/t instead.

Application: This predicts that GFF (move the Settler to the forest before starting ICS) should pay off better than ICS on grass, especially in a long game. I will omit the math unless someone wants to see it. The basic idea is that city values near a forest are so much higher, that you can afford to delay building a city for 10 turns or more. The improved growth rates near forest are a fairly small factor.

Warning: This reasoning ignores the fact that ICS growth on grass will eventually spread to forest areas. It also ignores support costs, rush-buying, etc. I will probably try to include those ideas soon, and would not be too surprised if ICS wins.

[rjmatsleepers]

I think this is a really interesting exercise which could provide some fascinating results.

At the moment however, I'm not sure how a conclusion about values will be reached. The tentative conclusion from the trial phase seems to be that an ICS strategy produces lots of shields. How do we get from that to say a shield is worth 2, 2.5 or 3 gold?

In other words, are we testing a value theory or the ICS strategy?

Grigor's achievement in getting 37 cities and 128 shield was magnificent, but how did a theory of value enter in to it?

I am not trying to discourage anyone from entering - I'll probably have a go myself when the rules are established. I'm just not sure how I would apply the results to a non-fundy, non-ICS situation.

RJM at Sleeper's

[Grigor]

My Theory of Value is not mathematically statable yet, but it essentially goes like this:

The value of compounding is so great that earlier city building is vastly more important than elegant city placement except in extreme cases.

I think that similar to ST when he says that Civ II is ICS based.

I don't consider my 37 city result very impressive. I actually lost several settlers by placing a city near a forest (at a one-move extra time cost) in the 2nd build cycle. I would be impressed by 45 cities and 150 shields, which would require careful timing of food growth and settler builds.

The practical question remains: How much food should remain in the food box when a settler is built to maximize total shields in a 60-turn game? To restate in ST's language, when does the choice tip from Let City Grow to Build a Settler?

Perhaps the way to eliminate gold from the equation is to have so much of it (like 20,000g) that one can make choices independent of gold availability. This would put the issue of when to pump out the next settler on a more strategic level and give a nice comparison of food versus shields.

[Peaster]

@Grigor - Thanks for the save.

With 20,000g, the only value left is food. The only reasonable production strategy is to rush-buy as soon as the city reaches size 2 (no?). There is no advantage to staying at size 2 because there is no increase in food production, and shields don't matter.

If I understand ST's idea correctly, he suggests (as I did) including BW and Writing to make rushbuying easier. This would make the relation between gold and shields so simple (1s = 2.5g) that those two variables can be treated like one.

I am neutral on this idea. After you said you could easily spend 200g, I thought it would be interesting to leave things as is.

@RJM - I am not sure a simple value system is possible. For example, (IMO) a city at size 1 needs food more than shields, but at size 2 it needs shields more. So, a formula like "1.5 food = 1 shield" cannot apply exactly to both situations. Maybe we need different formulas for different cases, or some other modification. Maybe algorithms are more useful than formulas. I hope this contest will help us decide.

The challenge in this contest is to find values (or etc) that apply to Berlin at size 2 in 4000BC. I want to know the best playing strategy before I try to assign values, so I haven't said much about them yet. I know this sounds a little backwards - the value formulas should help us find the best strategy, so maybe they should come first.

Will this help us play normal Civ2? I don't know. I hope it will help us learn how to think about Civ2. Some useful formulas or approaches might also come out of it.

[Grigor]

OK, my question is:

In Fundy, there is a 2-food penalty for settlers. I think that the time necessary to grow to size 2 is shortened by delaying the settler rushbuy because each turn of delay is 3 food towards growing to size 2. This means settler builds every 6 or 7 turns (I am not certain of the food growth in the turn the settler is rushbuilt.

Is the timing the same if the settler is rushbuilt at the first opportunity? My head hurts trying to figure it out.

[SlowThinker]

Originally posted by Peaster
If I understand ST's idea correctly, he suggests (as I did) including BW and Writing to make rushbuying easier. This would make the relation between gold and shields so simple (1s = 2.5g) that those two variables can be treated like one.

It is not so easy. Gold is more valuable because it is transferable. Therefore it may be used almost immediately. In opposite shields are freezed until the production is completed.
Imagine you can build DoubleSettlers for 80 shields and 40 food. A city from this DoubleSettler will yield a double net production. But still you will prefer to produce normal Settlers.

With 20,000g, the only value left is food. The only reasonable production strategy is to rush-buy as soon as the city reaches size 2 (no?). There is no advantage to staying at size 2 because there is no increase in food production, and shields don't matter.

I agree. And for simplicity I would forget the starting gold at all...
( Frankly said, I wonder how Grigor, a man with a mathematic thinking (and so a simlar thinking like me), could come with such a bad idea. This point was automately clear for me, without any thinking. But maybe this is because in past I did more thinking about Civ2, in other words my brain is more experienced? )

BTW I propose Peaster waits with his original idea to begin the main conquest one week after the thread was started. Or do you have your theories prepared already? Until now I see your tests are not based on any algorithms.

I will answer more points later, I will be out of the net now.

[Peaster]

No, I am still working on my theory. If nobody objects, let's postpone the start another week.

ST - Your ideas about the initial save are interesting, but I am not sure what to do with them. If there is no gold at the start, how do we bid ? If we are going to change the starting conditions much, we need to do it pretty soon, so the players can make plans. Also, I feel that anyone who has already put some effort into the position (eg Grigor) has a right to object to major changes.

If we want to make 1 shield = 2.5 gold in the starting position, with the BW/Writing idea, I suppose I can sell you warriors instead of shields (1 warrior = 5 shields). That way, shields are almost as fluid as gold. For myself, I expect to spend my gold quickly, so fluidity is not too important to me.

In Grigor's save, the average prod per city in 1000BC was about 3.5, which is much higher than one can get on grass (no pun intended). He had many size 2 cities, with a fair number near forests at the end. With GFF, I can get over 120 s/t, but not 128. I may give up on GFF for this map, though I think one large forest within 6 squares would make it worthy.

[Kramsib]

Hello everyone:

I am very proud of being requested for such an important investigation, in fact I started a strange theory about "shield value" some months ago. But unfortunately I had to focus all my efforts in my Master studies, so I am quite busy at the moment.

I am really interested on finding a "gold rule" to give value to every Civ - item, and this thread seems the best way to put my theory in practice, so if you are patient I will manage to play the save.

Thank you all for thinking of me for this project.