A Theory Contest

[Grigor]

(1) Regarding my late game situation analysis: You are right, I forgot about the AI placing workers on grass in the growth year. So that means that strategy 1 is the optimal endgame strategy, as you suggested. (optimal means having the most shields at the end) I was indeed talking about 1550BC, but with 3 food already in the box. I was planning to buy whatever shields are necessary in 1150BC. This way I can found a city in 1600BC and still have it make a settler.

(2) In the 4000BC position, you suggested stopping to compare strategies at 3000BC, but I was suggesting that a more pertinent comparison point is the date when the first rows are full in all the first three cities. The earlier that point comes the more efficient the early strategy.

(3) Different dates:
(a) 1200BC (56 turns) - I am not sure that a complete 4th doubling would be possible, but certainly a partial double could occur. 1800BC would be the earliest practical date to found a city and have it build a settler. It looks like a real tossup between the two strategies of getting more forest squares or building more cities.

800 BC (68 turns) would challnge me to try for 5 doublings (96 cities), which might actually be possible. That could imply that spending turns walking for forest access in the early stages might be less important, because normal expansion will get to the big forest areas by the 5th doubling.

(4) In the growth stage, there is usually a shortage of money, and one must decide which cities need help and which can build sttlers normally. Traditional civII wisdom is to prioritize food at size 1 and place workers to maximize shields at size 2. (DaveV) I think there is value if the city has access to one forest to maximize shields at size 1 before and after rushing the first row, which will give an 11-turn settler at a cost of 11g. I would like to see a case analysis of that growth period, to help with those decisions.

[rjmatsleepers]

Originally posted by Peaster

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.

My experimentation in fundamentalism with a city site that includes at least 2 grassland and at least 2 forest makes me conclude that at size 1 the worker should be on grassland.

After 2 turns with the worker on grassland, it is possible to rush 6 shields in the first row for 13 gold. Continue for 4 more turns. There are now 18 food in the food box, so switch the worker to forest. At turn 8 put your second worker on forest. The settler is built on turn 11. Compared with putting the size 1 worker on forest, you spend 3 less gold (because you can buy 6 shields) and you have 2 extra food in the food box. This is not a dramatic improvement, but it is consistent with food being slightly more valuable than shields, even if the benefit of rushing 6 rather than 7 shields is ignored.

[Note 1: this analysis was not done on the Berlin game start, but with a random start where 50 gold was obtained from a hut and the cheat menu used to change the government to fundamentalism.

Note 2: I assume that for the final turn for the case where the worker is on forest the worker is switched to grassland in order to avoid wasting the extra shield.]

RJM at Sleeper's

[Peaster]

@RJM - I agree with you about cities that have two forest squares. It is better to reach size 2 ASAP, to take advantage of the two forests. The quote above was written badly. I just edited it, to clarify that I was thinking of a city with just one forest. Summary of food vs shields, for new cities during the growth period:

With no forest tile: 2f = 1s
With 1 forest tile: 1f=1s (set workers mainly on forest)
With 2 forest tiles: 0.84f = 1s (set workers mainly on grass)

I expect that shields in City A have approx the same value as those in City B [but I haven't thought about this much]. Apparently, having food in the City A box is not equivalent to having it in City B.

@Grigor - I haven't thought very hard about the post-1800BC period, mainly because it doesn't model real Civ2 very well. When I started the contest, I expected that period wouldn't be too important. Then I was shocked by your 4-cycle plan. Anyway, I think you might want to stick with Strategy 2 (growth) for these 2-forest cities, because in Strategy 1, you can't rush the final row without disbanding the city. You get to <20,33> in 9 turns, but then what?

[Grigor]

OK, we are on to something. I reached

50 Cities, 143 shields/turn

by following the following strategy:

(a) aim for forested areas, including the NE clump
(b) use RJM's and Peaster's valuation to determine worker placement strategy to save gold and time
(c) make 2 roads near Berlin, Hamburg, and Leipzig in case there is enough money to buy settlers in those towns in 1050BC. I got two of them, but perhaps was not optimal in gold use in the earlier game, so I think 3 are possible. I also used the strategy of disbanding warriors from nearby cities.

[Peaster]

Sounds like you have almost perfected your strategy for this position. I also played around with short roads near Berlin, mainly for the extra arrows. I have gotten 1-2 cities near the NE clump a few times, but was usually more attracted by the larger NW clump.

I thought very briefly about making warriors for disbanding, and decided to just call it a "trick" (see some earlier post) rather than pursue the idea. But if nobody objects, we can make it legal. Is this something that makes sense mainly in the last 10 turns ?

I am more-or-less ready to start the contest, if a few people want to play. Or, we can continue the discussion
a while longer - or we can summarize the thread and move on to something else.

BTW - ST and I have started a PBEM duel. By coincidence, I suppose, we started with approx the same goodies as in this contest (100g + 2 Settlers + 2 warriors, but not Fundy). I don't want to say too much about it yet, though.

[Peaster]

I hope I'm wrong, but this thread seems to be slowing down. It seems unlikely we will actually play the contest. Maybe it didn't interest enough people, or the goal was too difficult. Before it dies, I would like to summarize it.


Conclusions from the Theory Contest

Do Civ2 theoreticians have anything useful to say to Civ2 players?

Probably no (or not yet). I found some formulas that seem useful to me, but no other players are using them. So, I cannot claim success. Grigor found a great approach to the practice position, but he has not stated a general theory which we can test in a contest. I assume RJM has quit working on his. Kramsib and Slowthinker did not offer much insight into the practice position.

One recurring issue is communication and trust. Kramsib talked about "values" a long time before we understood that he meant something very different than we expected. I have offered a lot of formulas, but nobody seems convinced by them. Results speak for themselves, but almost nobody is ready to play the proposed contest, so we are rather short on results. [Grigor's results with the practice position are impressive, but I'd like to see his ideas tested in similar positions].

Is it meaningful to talk about the value of a shield (etc)?

I think we will continue to make most of our decisions with time-tested playing algorithms, rather than formulas. An equation like 1s = 2.3g might be useful in certain contexts (such as evaluating a position for comparison purposes). It does not often seem very useful for making specific decisions in a real game, partly because the value of a shield depends on the situation. Maybe Civ2 is just too complicated to be reduced this way.

On the other hand, I learned that the value of a settler's time (for example) can be measured pretty accurately. This is useful in deciding about rushing production, about how far to walk for better terrain, whether to make roads, etc.

IMO we learned a lot - eg, how to make a settler ASAP in cities with varied terrains (but not too varied). We agreed that the warrior should be disbanded and the first settler rushed very very soon. I used this idea in my current PBEM duel with ST to get an early growth lead (I think).

I am gradually using values more and more in my thinking. They will probably never replace common sense, but I think they have a role, which has not been explored very well yet.

[rjmatsleepers]

Originally posted by Peaster

Conclusions from the Theory Contest

Do Civ2 theoreticians have anything useful to say to Civ2 players?

Probably no (or not yet). I found some formulas that seem useful to me, but no other players are using them. So, I cannot claim success. Grigor found a great approach to the practice position, but he has not stated a general theory which we can test in a contest. I assume RJM has quit working on his. Kramsib and Slowthinker did not offer much insight into the practice position.

...

Maybe Civ2 is just too complicated to be reduced this way.

I haven't stopped working on the question, but at the moment I can't get anything useful to emerge. I'm sure that Civ2 theoreticians do have useful things to say. I don't believe the question addressed in this contest is too complicated to be analysed, but we haven't yet found a good key. The problem I can't find a way round at the moment is the game's "time values". Deciding how to get that settler built 1 turn earlier is a matter of trial and error - for me at least. And I still don't have a clear idea how much I would pay for the 1 turn gain.

To take an example from the OCC game. I'm very comfortable with spending 75 to rush rows 2, 3 and 4 of a van. However I'm less comfortable about spending 125 to rush the van in a single turn. (Partly the problem is how to value the beakers!) If I'm sure of getting more than 125 gold per van I'd rush it in 1 turn, but if I'm only getting about 100 per van I hesitate. If I'm getting less than 75 per van, I'd probably not even rush 3 rows.

At least 2 things have emerged from your game - the warrior as a portable shield holder and building a road to get money to rush a settler faster. I haven't looked enough at either to see how they fit into a value theory.

RJM at Sleeper's