A Theory Contest

[Peaster]

Welcome, Kramsib! The save above is intended mainly for practice. I will post another one in a week or so, probably with Fundy replacing Monarchy and maybe some other changes suggested by Grigor or ST.

Grigor - After many attempts, I have an approximate value system in mind, and used it to reach 134 (from Fundy + 100g). I struck a balance between ICS and GFF, and avoided size 2 as much as possible.

[Grigor]

I have a more careful checkerboard game working and I will let you know how it turns out. Avoiding size 2 - !!! That seems counterintuitive to me at first blush but as I consider it, the irrigated base square is more of an advantage at size 1. Hmmm...

[Peaster]

Two size one cities get 4 tiles, but a size two gets only 3 tiles. IMO you should make a Settler ASAP. Every turn you delay costs about 4 prod-units (food+shields). I figure that a forest square cuts about 3 turns from this delay, so it is worth walking an extra 3 turns for the forest. I am not sure I have this exactly right yet, but the approach makes sense to me.

[DaveV]

Interesting discussion, but it seems like you're trying to turn Civ into SimCity. I like building horses and warriors, dealing with barbarians and rival civs, etc. "No plan survives contact with the enemy", or something like that.

Has anyone tried mining some grassland to forest? Five settler turns for an extra shield seems like a good trade in a resource-poor environment (as this one appears to be). Or is it not allowed under the rules?

[Peaster]

Dave - In the previous post, I estimated that a forest tile is worth about 3 settler-turns. So, IMO mining would be a waste of time. I will allow mining, irrigation, etc to give people a chance to prove me wrong.

Edit: However, I do not want to allow the mining of hidden specials - which presents a problem. I guess you have to avoid the specials (if you know how) or save your game and replay if you get one by accident.

BTW - I am planning how the auction will work. I think I will list about 4-5 items, such as

20 shields (in Berlin)
20 food (in Berlin)
A food caravan
3 warriors (=15 mobile shields)
A forest tile near Berlin
5 extra turns in your game

Let me know if you have any better ideas. Then, I will ask you to make a (public? private?) bid from 0 to 100 gold on each item, consistent with your theory/value statement. I will sell each item to the highest bidder. A player may get two items, but can't spend more than 100g total.

You are not allowed to disband the van for shields, nor to produce warriors in order to disband them later [not sure these are even good ideas, but they seem like "tricks" to me]

[Elephant]

Isn't mining Grass to Forest 10 settler turns? Irrigating is 5.

[Peaster]

Here is my theory of this position. When I say "23g = 10s" I mean that having 23 more gold or 10 more shields would be equally effective in boosting my expected final score.

1) The period after 1800BC is fairly simple. You can make decisions to maximize your final score without considering other values.

2) The period from 3500BC to 1800BC is mainly for growth. IMO: 23 gold = 10 shield = 10 food = 2 city-turns = 3 settler-turns. A forest is worth about 3-4 settler-turns (increasing in value to over 6 settler-turns by 1800BC), so most cities will be built near a forest. A road is a waste of time except in a few rare cases.

Support costs should be added into the value of a "settler-turn" for some applications, like road or forest work, but not when considering whether to rush-build.

3) In 4000BC Berlin, you need shields more than food, and cannot spend gold effectively. Roughly, 6g = 2s = 3f depending on the amounts involved, etc. For example, I would not pay 3g for a shield in the first row of the box (because rush-buying is cheaper than that) but I would pay 75g for 25s. I would pay 15g for a warrior (with value = 5 shields) because those 5 shields are portable. Conversely, I'd prefer not to buy a large amount of food (eg a food caravan), but would spend 10 g for 5 food, for example.

I will probably bid only 90 per cent of the value for an item (because at 100 per cent, there is no profit, there is only a risk of error).

I will try to explain any formula above upon request. I don't consider this theory final until the deadline for Part A.

If anyone wants to change the rules or any aspects of the starting postion, please post your suggestions here within 2-3 days. Please look over ST's ideas too, and share any opinions you have on those.

[SlowThinker]

Very likely I won't be able to post suggestion to rule changes within 3 days. But we may try another conquest with changed rules later.

Originally posted by Peaster
The period from 3500BC to 1800BC is mainly for growth. IMO: 23 gold = 10 shield = 10 food = 2 city-turns = 3 settler-turns.

Are you able to explain how did you find it out?
Are you able to fabricate a formula for changed rules, for example smaller food box? In other words do you have a general algorithm for a simple Civ2?

[Peaster]

I am not sure how many players are actively working on the position. If there are a few people ready to start in a few days, we will start. I am open to doing something like this repeatedly, as long as people are interested.

The formula is based mainly on my playing strategy. Most of my cities have a forest square, which they use 90 per cent of the time, and shielded grass otherwise. Because of this flexibility, 1 shield = 1 food.

Each city generates about 13 gold in taxes, per cycle, and I can typically afford 16 gold for 7 shields in the first row, in the cities closer to forests. Since this seems the optimal use of gold, I set 16g = 7s (or 23g = 10s).

Each size 1 city produces 5 stock per turn (food+shields). Size 2's are rare in my strategy, and only produce 6 stock anyway, so I ignore this difference. So, the value of a city for one turn = 5 stock = 5 shields.

A settler cannot produce stock until it changes into a city, so I devalue it's turn, assuming a 5 per cent interest rate until it becomes a city of average age [IIRC I assumed about 7 turns for this].

BTW - I found that assigning values in 4000BC was much harder than doing it in 3500BC-1800BC.

I have not thought much about a general algorithm for simple Civ2. This theory took me over a week, and I expect that each new factor (eg size of food box) could take another week to figure out, especially if it changed the overall playing strategy. But who knows? This is all new to me, and there are probably better methods still to be found.

[Grigor]

Very interesting, Peaster.

My theory is not incompatible with yours but is about differnt things:

The best result must be by continuous doubling, and with enough cash to buy a settler on turn 1 and have 3 cities by turn 4, one should strive for 48 cities by doubling 4 times. (3,6,12,24,48) There only remains insuring that the last doubling happens on or before turn 57. With 54 turns, that becomes 13 per turn including travel time which can be 2 at least, or 11 turns per build.

With the city having a forest square, this will work fine. Furthermore, upon thinking, it seems that there is no difference between 7 shields in the first row or 7 shields in the last row, except: (1) there will be more money by the last turn, and (2) once the city grows to size 2 there will be an extra shield each turn. So my strategy would be to never rush the warrior in a city with a forest square.

Starting on grass is the crucial part, since the first two doublings will not necessarily have a forest square. With no rushbuying, the city grows to size 2 in 7 turns, producing 14 shields, then 3 shields/turn for 9 more turns. 16 turns is not acceptable. By rushbuying 8 shields the first turn the build is reduced to 13 turns. By rushing the last 9 shields it is further reduced to 11. So I want 19g for the first row and 22g for the last, or 41g. And I want it for the first 2 builds, or 9 cities. Berlin will be less becaus of the extra 2 turns of growth.

To get the 4th doubling, there are only 2 turns total of wiggle room. The last doubling will have many forest squares, but all will have some cities without forst squares, requiring 41g.

It is faster for me to get to the end of this problem empirically by trying it out, so more after another trial.

[Peaster]

Grigor - At the risk of teaching grandmother (as RJM would say) there is a hidden cost in rushing the last row, because it stops shield production for one turn. It might still be a good idea in many cases. And, it might be interesting to find a general rule for when to do it.

[Grigor]

Ah. Grandma understands.

Grandma also notices that rushing during 2-shield production is more valuable than during 3-shield production.

There often is not enough gold to rush the first row in this game.

We all agree that rushing in the last row is a good idea when it saves a turn.

Is the issue in this contest when to wait and when to rush?
The last row would be worth rushing in general if it saves one more turn than the equivalent in the first row.

[Peaster]

After some more thought, I realize there is also a hidden cost for buying shields in the first row. You have to wait about 10 turns before they are used. So, shields in the last row are worth almost twice as much as ones in the first row! It is not easy to decide which hidden cost is greater, but for now, I expect the best strategy will involve buying in the last row as you suggested.

Also, I agree that it is useful to think in terms of turns saved rather than shields added.

[rjmatsleepers]

Originally posted by Peaster
After some more thought, I realize there is also a hidden cost for buying shields in the first row. You have to wait about 10 turns before they are used. So, shields in the last row are worth almost twice as much as ones in the first row! It is not easy to decide which hidden cost is greater, but for now, I expect the best strategy will involve buying in the last row as you suggested.

Also, I agree that it is useful to think in terms of turns saved rather than shields added.

There is only a hidden cost of buying shields in the first row if there is a "time value of money" - ie if 1 gold now is worth more than 1 gold in 10 turns. AFAIK, it has always been difficult to establish this in Civ II. The best argument seems to be about the opportunity cost of spending the money - ie if you spend it on shields in the first row, you can't spend it on anything else. In this case, I'm not sure there is an anything else worth spending it on. (There are certainly cases in Civ II where there is a negative time value of money - eg if one of your cities is under threat from a barbarian.)

The benefit from buying the first row is most clearly illustrated if the city produces 5 shields. Buying 5 shields in the first row reduces the time to build a settler whereas buying 5 in the last row does not change the time required. I believe this advantage from buying a particular number of shields in the first row rather than the last is true whatever the number of shields the city produces, it is just more difficult to see.

I believe the question as to whether you should rush buy the final row is different. If the city produces 1, 2, 3 or 4 shields, then the next settler will be produced anything from 8 turns to 1 turn earlier by rushing. The question is one of cost and benefit.

The actual cost (in gold) of buying the final row is clear and depends on the number of shields already there. However there is an issue (in contest terms) about the underlying theory. If you rush the final row, you are only buying shields that you would not otherwise have produced. For example if your city produces 4 shields and you have 4 in the final row, rushing only buys 2 shields. The underlying theory has to place a very high value on shields to make that worth while - a lot more than your 2.3 gold per shield.

The analysis of cost is complicated by considering micro-management of the city during that turn. If you could switch 2 workers from forest to spice, the net cost of buying the extra shields would be reduced from the tax value of the extra arrows. In this case the choice is (I believe) simply between food and shields which makes things easier to understand.

As far as the benefit of rushing the final row is concerned, this depends on what you can do with the settler. I find it difficult to believe that any benefit from having a settler 1 turn earlier will be greater than the cost of rushing. The apparent benefit in this case seems to arise because of the "artificial" time horizon set by the contest rules. If you were making the comparison when the civ reached a specific population, or a particular number of cities (or completed researching a specific technology) the answer would be different.

So, it seems to me that the value of thinking in terms of turns rather than money is a result of the underlying ICS strategy. The quicker you can build a settler the sooner you can establish a new city. When you have finished the current test, it may be worth repeating the exercise, but with a different terminal condition - perhaps one that favoured an OCC strategy.

Sorry to post at such length, but I believe this exercise is sufficiently important that it is worth exploring all the nooks and crannies that surround it.

RJM at Sleeper's

[Grigor]

RJM - nice post. Even such an artificially restricted game has surprising complications.

In all of our discussions on these forums the underlying goal is fastest time to a certain goal. Noting your caveats, that will usually make settler building very important.