Key Civ Ideas

The Key Civ

It has been known for a while that giving away techs can reduce your beaker cost.
Also, there always seems to be one Key Civ to whom tech-gifting triggers the beaker reduction.
What has been unclear is the relationship between the Key Civ and the Human Civ.
How do you know which civ to give techs to in order to effect beaker reduction?
I think I have found the answer to this.

I hestitate to post my conclusions for two reasons. First, early announcements of "findings"
often turn out false. And secondly my answer is pretty ridiculous, in my own opinion.
Nevertheless, here it is.

The relationship between the Key Civ and the Human Player
involves the Power ratings and Turn positions.
Each civ's Turn Position is determined by its color:

1 White
2 Green
3 Dark Blue
4 Yellow
5 Light Blue
6 Orange
7 Purple

Power Ratings are reported by the Foreign Minister:

1 Pathetic
2 Weak
3 Inadequate
4 Moderate
5 Strong
6 Mighty
7 Supreme

The Key Civ for tech-gifting can always be found occupying the Turn Position
which corresponds to your Power Rating using the above numbers.
For example, if your Power is 'Inadequate', the Key Civ will be Dark Blue.

Science beaker cost is the product of two things: the number of Acquired Techs (+1) that you have
and a Tech Multiplier. One of the determinants of the Tech Multiplier is your relationship
to the Key Civ as found by the above method. If you have the same number
of Acquired Techs as your Key Civ, you get the nominal Tech Multiplier and pay an average cost.
If you have fewer Acquired Techs, you pay less. If you have more, you pay more.
By giving a sufficient number of techs to the Key Civ you can reduce your beaker cost.

If your Power rating corresponds to your own Turn Postion, you will always have
exactly the same number of techs as yourself and therefore will always pay the average cost.
You can give away techs till you're blue, it won't help. Well, it might.
Power ratings are in part determined by how many techs you have. So giving away techs
may lower your PR and get you out of the 'dead spot'.

If you're planning to spend a lot of time being 'Pathetic', don't choose White!
Same for 'Supreme' and Purple.
I know, this seems like a ludicrous design.
Maybe that's why it has proven so illusive.

Let me know if you have questions or if you can show this to be wrong.

samson

P.S.

My testing was with V2.42, deity, 7 civs. I haven't tried fewer civs yet.

Also, this finding may explain the 'destroyed civ' phenomenon.
When a civ is destroyed, your Power Rating may change. If the destroyed civ
occupies the Turn Position corresponding to your new PR, you will be much higher
in techs (since they now have none) and would have to pay the highest possible beaker cost.
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OEDO YEARS

-3850___-925___460__1580__1836__1903
-3650___-825___540__1620__1844__1907
-3450___-725___620__1660__1851__1911
-3250___-625___700__1700__1855__1915
-3050___-525___780__1740__1859__1919
-2850___-425___860__1756__1863__1923
-2650___-325___940__1764__1867__1927
-2450___-225__1020__1772__1871__'31
-2250___-125__1100__1780__1875__'35
-2050____-25__1180__1788__1879__'39
-1850_____60__1260__1796__1883__'43
-1650____140__1340__1804__1887__'47
-1450____220__1420__1812__1891__'51
-1250____300__1500__1820__1895__'55
-1050____380__1540__1828__1899__'59...

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The Cost of Research Explained

Hi all.

The Key Civ discovery allowed me to run some controlled tests on the numbers of beakers
required for researching new technology. I think I understand how the cost is calcuated now.
Some of this stuff is already known, but I will repeat it here just to have
the whole mechanism described in one place.

The cost of researching a new technology (the beaker count) is the product of two factors.
The first is the Tech Number which you are researching. This is the number
of Acquired Techs you have +1. Acquired Techs are all techs you have received
in gameplay from research, huts, trades, gifts, or steals.
It does not include your starting techs.

The second factor is a Base Tech Multiplier to which either a bonus or penalty
can be added. The formula would look like this:

Cost of Research = TechNumber X (Base + Penalty/Bonus)

The Penalty/Bonus is based on how far ahead or behind your research is
compared to your current Key Civ. That relationship is quantified by
comparing your TechNumber to your Key Civ's TechNumber. If you are the same
you receive the Base Tech Multiplier with no Penalty or Bonus.

If you on a lower TechNumber than your Key Civ, then you receive the Bonus.
The Bonus is the same no matter how far behind you are. On a medium map
it is either a -1 or -2 depending on the TechNumber (see chart below).

If your TechNumber is higher than your Key Civ's, you are penalized a +1
to the Base Tech Multiplier for every 3 techs which you are ahead of him.
In other words, if you are even or ahead by one or two, your penalty is 0.
If you are ahead by 3,4, or 5 techs then your penalty is +1.
Thus, the higher the TechNumber which you are researching the farther
ahead it is possible to be. If your Key Civ is stuck in the Bronze Age
while you are researching Space Flight, you will be paying an enormous
penalty in beaker costs.

Here is a chart of TechNumbers, Base Multipliers, and Bonuses for the first 20 techs.

Tech# Base Bonus

01 10 0    --10
02 11 -2   --18
03 11 -1   --30           Based on Mid size map.( Convert 4/5, 5/4 for other maps)
04 12 -2   --40
05 12 -1   --55
06 12 -1   --66
07 12 0    --84
08 13 -1   --96
09 13 -1   -111
10 14 -2   -120
11 14 -2
12 15 -2
13 15 -2
14 15 -1
15 15 -1
16 16 -1
17 16 -1
18 17 -2
19 17 -2
20 26 -2

All TechNumbers above 20 have a Base of 26 and a Bonus of -2.
The Minimum Beaker Cost for a given TechNumber can be calculated from this chart
and that Minimum can be achieved in gameplay by lowering your TechNumber
relative to your Key Civ through tech-gifting.

One important consequence of the fact that the Penalty/Bonus is based on TechNumber,
rather than total techs, is that Starting Techs are critical in determining how much
you will pay for research in a game. If you have fewer Starting Techs than
your Key Civ, then you can only get the Bonus when that Key Civ actually
is ahead of you in researching. You can never reach the Bonus through tech-gifting alone.

On the other hand, if you have more Starting Techs than your Key Civ,
you can easily get the Bonus without even giving away all of your techs.
Starting Techs are an enormous advantage not just at the start,
but throughout the whole game as they determine your ability to reduce your science cost.

If you start with NO techs, and the other civs all have them, you may be
paying research penalties the entire game, even with aggressive tech-gifting.

samson

[This message has been edited by samson (edited April 23, 2001).]
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How Supply and Demand Lists Are Determined

Overview

The key to understanding Supply and Demand lists in cities is recognizing that each commodity has its own formula and set of determining factors which govern its appearance and disappearance. Each of these commodity formulae derive what I call a Supply Quotient and a Demand Quotient. When a trigger event occurs, such as the 16-turn "solo" cycle, the SQ and DQ are calculated for each of the sixteen commodities.

If a particular commodity's Demand Quotient is higher than its Supply Quotient, it goes on a roster of demanded commodities. If not, it goes on the supplied commodities roster. (This prevents a commodity from being both supplied and demanded by the same city, as a rule.) The top three commodities on each roster become the city's supply and demand list.

If either the supply or demand roster does not have enough commodities to fill its list, then the commodity with the highest ID number that is enabled and not already on the list is used.

Wildcard Commodities

There are also two Wildcard commodities, one for supply and one for demand. These are based solely on the city's map coordinates. The wildcard formulae are:

Supply Wildcard = RemainderOf ( (Horizontal x 13 + Vertical x 7) / 14)

Demand Wildcard = RemainderOf ( ( Horizontal x 3 + Vertical x 5) / 14)

Because coordinate pairs on Civ2 maps are always either both even or both odd, the remainder from this division by 14 is an even number between 0 and 12. This number is used as an index into the commodity list to choose the Wildcard. The commodity list is:

0 Hides
1 Wool
2 Beads
3 Cloth
4 Salt
5 Coal
6 Copper
7 Dye
8 Wine
9 Silk
10 Silver
11 Spice
12 Gems
13 Gold
14 Oil
15 Uranium

Each Wildcard is then checked against the six commodities on the Supply and Demand lists and against the other wildcard to prevent duplicates. If the Wildcard is not present on either list, it replaces the middle commodity on its respective list.

After a civilization has acquired 32 Techs, the wildcard formulae for its cities changes slightly. The divisor is now 9 instead of 14, and 5 is added to the remainder, as follows:

Supply Wildcard = RemainderOf ( (Horizontal x 13 + Vertical x 7) / 9) + 5

Demand Wildcard = RemainderOf ( ( Horizontal x 3 + Vertical x 5) / 9) + 5

This eliminates commodities 0-4 (Hides to Salt) from the Wildcard spot in the middle and late game and allows odd numbered commodities to appear. Again, if the wildcard commodity is already present on either list, it is not used and the originally determined 3 commodities remain.

If the supply and demand Wildcards are the same commodity, it is used only on the demand list.

After the discovery of Industrialization, Oil becomes available as a secondary wildcard, used to substitute the middle commodity when the primary wildcard was eliminated as a duplicate. It is because of its role as a secondary wildcard that Oil sometimes appears on both the Supply and Demand lists of a city.

Wildcard commodities, when present, always appear in the middle position on the list.

Determinants of Supply and Demand

The formulae for calculating each commodity's Supply and Demand Quotients involve a number of factors.

Terrain. Terrain is probably the most important factor in determining supply and demand. The terrain of all 21 squares in the city radius are counted by type to create a city's Terrain Profile. Resource specials count as 4 of their base type. Thus, Fish and Whale count as 4 Ocean; Wine counts as 4 Hills; Wheat counts as 4 Plains, etc. Rivers are counted as a separate terrain type, making for a total of 11 terrain counts. Each commodity's selection and weighting of terrain types will be unique.

Location. In addition to the Wildcard calculation, location affects a number of commodity SQs and DQs. Location's role includes use of the city map coordinates in calculating proximity to the poles or equator for a simulation of historical distribution patterns of commodities.

Continent. Continent number and continent size(?) are important determinants for some commodities.

City Size. The population of a city affects many commodity SQs and DQs, but in different ways. There is no one city size algorithm, although a pattern of 3, 8, 13, etc. (increments of 5) occurs in a number of instances.

Tech Acquisition. The number of techs acquired is used as a measure of progress and time passage, reducing or increasing demand and supply of certain commodities in simulation of their historical importance to civilization. Specific technological advances have profound affects on certain commodities, many of these are well known, such as Industrialization and Automobile's impact on Oil. Tech acquisition applies to all cities in a civilization. In a few rare cases, a tech discovery may have global impact.

City Improvements. Some city improvements affect the SQs and DQs of commodities for that specific city.

Nationality. Occasionally, a civ's historical association with a specific commodity is reflected in its supply and demand. French cities are more likely to be suppliers of Wine, while Silk is often common in Chinese cities.

Some of these determining factors are static, unchanging throughout the game, or change only rarely (like terrain). Others change rapidly over time. It is the changing factors alone, City Size and Tech Acquistion, that are responsible for the changes in supply and demand lists that occur over the course of the game. Once all of the commodity SQ and DQ formulae are known and well-tested, it will be possible to determine not only the initial commodities of a newly founded city, but to chart all future changes to these lists based on city growth, terrain modification, and the strategic acquistion of technologies.

Last edited by samson on 06-12-2002 at 15:27
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OEDO--NEXT AVAILABLE TECH CHOICE

Another brilliant insight, oedo! Thanks for sharing it.

I think Sequoya is probably right, that the formula is just based on position in rules.txt. Here's a list of the techs, each marked with the turn when it's not available. Take the number of techs you've discovered (STARTING TECHS ARE NOT COUNTED), divide by 3, and take the remainder (modulus, for fellow programmer types). Any tech marked with that number in the following table is not available for research.

	2 Advanced Flight,		0 Alphabet,
1 Amphibious Warfare,	2 Astronomy,		0 Atomic Theory,
1 Automobile,	2 Banking,			0 Bridge Building,
1 Bronze Working,	2 Ceremonial Burial,		0 Chemistry,
1 Chivalry,	2 Code of Laws,		0 Combined Arms,
1 Combustion,	2 Communism	0 Computers,
1 Conscription,	2 Construction,	0 The Corporation,
1 Currency,	2 Democracy,	0 Economics,
1 Electricity,	2 Electronics,	0 Engineering,
1 Environmentalism	2 Espionage,	0 Explosives,
1 Feudalism,	2 Flight,	0 Fundamentalism,
1 Fusion Power,	2 Genetic Engineering,	0 Guerrilla Warfare,
1 Gunpowder,	 2 Horseback Riding,	0 Industrialization,
1 Invention,	2 Iron Working,	0 Labor Union,
1 The Laser,	2 Leadership,	0 Literacy,
1 Machine Tools,	2 Magnetism,	0 Map Making,
1 Masonry,	2 Mass Production,	0 Mathematics,
1 Medicine,	2 Metallurgy,	0 Miniaturization,
1 Mobile Warfare,	2 Monarchy,	0 Monotheism,
1 Mysticism,	2 Navigation,	0 Nuclear Fission,
1 Nuclear Power,	2 Philosophy,	0 Physics,
1 Plastics,	2 Plumbing,			0 Polytheism,
1 Pottery,	2 Radio,			0 Railroad,
1 Recycling,	2 Refining,	0 Refrigeration,
1 The Republic,	2 Robotics,	0 Rocketry,
1 Sanitation,	2 Seafaring,	0 Space Flight,
1 Stealth,	2 Steam Engine,	0 Steel,
1 Superconductor,	2 Tactics,	0 Theology,
1 Theory of Gravity,	2 Trade,	0 University,
1 Warrior Code,	2 The Wheel,	0 Writing,

 A very easy way to use this info, if you do not mind marking up your tech tree chart, is to write the number from DaveV's list for each tech on the chart. Then when a new list is presented, just see what groups are represented (omit the first tech, of course, since it is the joker). If tech choices belong to groups 0 and 1, the next list will omit the "0" techs since "2's" are not on this one. On the following list, it will be the "1" techs that are missing. This makes it easy to chart an optimal path and to know when to make trades to skip over unwanted lists.

 In 720 AD you wonder why you can not research Steam Engine. The answer to this question is that at that time you had acquired 31 techs, and Steam Engine would have been 32nd. However, this tech is in Oedo group #2, which is omitted from tech lists when the remainder of total techs/3 = 2, which it is in this case (32/3=10 with a remainder of 2). Are you aware you can predict any list of tech choices by using Oedo’s discoveries detailed in the “Techs – Next Available” entry of SG’s Great Library?
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2) For understanding the second rule take a look at the rules.txt. You can see that all techs are listed in alphabetical order there. The highest ranked tech is Advanced Flight, followed by Alphabet, then Amphibious Warfare etc.  The highest ranked available tech in the rules.txt acts as a joker tech. It is always available and doesn´t follow the xxo pattern. Since Advanced Flight isn´t available in the beginning,  Alphabet will be the first joker tech. When you discover Alphabet, another tech will become a joker tech (for example Bronze).
When you have the prerequisites for a tech which is ranked higher in the rules.txt than the current joker tech, the new tech will take its place. The former joker tech will follow the xxo pattern as described above. (example: Bronze is joker tech, after detecting Mysticism and Mathmatics, Astronomy will become available as new joker tech.  From now on Bronze will follow the usual xxo pattern).
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OPTIMAL SPACESHIP CONFIGURATION

 While looking around the web, I found the following table, listing flight times for various configurations. The first number is the number of components, the second is the number of structurals, and the third number is flight time. One of each module and Fusion power was included for these table results:

2-15-36.1
4-15-21.0
6-15-15.7
8-17-13.2
10-21-10.0
12-25-8.3
14-29-6.7
16-33-5.7

Adding more of anything to these configurations will just slow down a ship. For earliest dates, it's most important to build in as few turns as is possible to take advantage of the switch to 1 year increments.
TO GET THE MOST POINTS:  39-8-8-444   11.7? yrs
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TERRAIN TRANSFORMATIONS

Thanks Father Beast
Of the two kinds, never will you get something on one list to turn into one of the other. the last three types are what you can make (with enough engineers and time) out of any land terrain, using default rules.

TERRAIN SPECIAL 1 SPECIAL 2
Ocean Fish Whales
Swamp Peat Spice
Jungle Gems Fruit
Glacier Seals Oil
Tundra Musk Ox Furs
Desert Oasis Oil
Mountains Gold Iron
Hills Coal Wine
Plains Buffalo Wheat
Forest Game Silk

What this means, is that If I have Peat, I can turn it into Coal, or Glacier oil into wine, wheat, or silk at my leisure.
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THE TWIN CITIES STRAT    (La Fayette 10-29-01)

Dear friends Apolytoners.
Today is the last day without civ3.
It is also the day for me to publish my last strategical proposal for civ2.

The name is 'twin cities',
...and here is the reason why:

The special ability of a SSC is the ability to transform 1 trade arrow into 6 beakers with help of the following multipliers (before SETI):
Library: +50%
University: +50%
Isaac: +100%
Cope: *2
Hence: (1 + 0.5 + 0.5 + 1) * 2 = 6
(SETI or Research Center would make it 7.5)

If there are Einsteins in the SSC, 1 Einstein provides 3 arrows (or 18 beakers, as you like).
The trade arrows are provided either by the squares worked in the city radius ( 3 arrows for 1 ocean square in Rep or Demo) or by the 3 trade routes allowed.
There are 21 squares.
Therefore, what you can get after having grown the city to size 21 is approximately:
21*1 = 21 trade if Monarchy, no river, no ocean, no trade special
21*2 = 42 trade if Republic, no river, no ocean, no trade special
21*3 = 63 trade if Rep (or Demo) + Colossus
21*4 = 84 trade if Demo (or Rep) + Colossus + Motorways

Mountains,... and other kinds of rough terrain make it lower.
Rivers, oceans and trade specials make it higher.
But we can keep in mind that a SSC without trade routes would provide about 84*6 = 504 beakers/turn in the endgame (less if rough terrain, more if many rivers or trade specials, ...ocean squares don't benefit of motorways)

WHAT ABOUT THE TRADE ROUTES ?

Their value is Zero if you don't have any (that would be silly!).
Their value can very easily be over 60 arrows (which means 360 beakers/turn) if you follow my proposal of twin cities.

WHAT ARE THE TWIN CITIES ?

You build a SSC as usual (nice site, preferably grassland, trade specials and rivers...).
VERY close to the SSC (let us say 4 squares away), you build the twin city (preferably nice site, grassland, trade specials...). ASAP you send 3 caravans from the SSC to the Twin (or from the Twin to the SSC). ASAP you road the direct path between the SSC and the Twin. ASAP you build a railroad. You grow the Twin to size 21 or so, and THAT IS ALL (of course Temple + Colloseum, probably Harbor + Market Place + Courthouse, why not Bank + SE + Library + University, in the Twin).

WHAT DO YOU GET THEN ?

The value of a trade route is (HTA + DTA + 4) /8, where HTA is Home Trade Arrows and DTA is Destination Trade Arrows. This is halved if both cities are yours, +50% if direct road, +50% (on top of that) if direct railroad.

Therefore, with a SSC providing 84 arrows (Demo, Colossus, Motorways) and a Twin providing 63 arrows (Demo, Motorways), one trade route is worth (84 + 63 + 4)/16 = 9, ...
9, ... +50% = 14
14 +50% = 21
3 trade routes provide 21*3 = 63 arrows (in the SSC and also in the Twin)

WHAT ELSE ?

The standard SSC I have described (size 21, no Einsteins) provides (84 + 63) *6= 882 beakers/turn (settings 100% science). The standard Twin (size 21, no Einsteins) provides
(63 + 63) *2 = 252 beakers/turn
With 10 Einsteins in the SSC (providing 180 beakers) and 4 Einsteins in the Twin (providing 24 beakers), you get VERY EASILY a total of 882 + 252 + 180 + 24 = 1338 beakers/turn as soon as you build Motorways.

CONCLUSION

With about 1000 beakers/turn after Railroad and over 1300 b/t after Automobile, the 'Twin Cities Research Center' is the easy way to high speed research (1 tech/turn without caravans).

(La Fayette, ready to go to bed before D Day)
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