24-04-2001 03:25									#1
	The Cost of Research Explained Remove this text

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
02 11 -2
03 11 -1
04 12 -2
05 12 -1
06 12 -1
07 12 0
08 13 -1
09 13 -1
10 14 -2
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).]

	24-04-2001 07:33									#2
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Fabulous! Be sure to have Scouse Gits 2 enter a link to your work in the Great Library Index thread. This will be helpful material to have on hand. Keep the lab working on new discoveries...

------------------
"There is no fortress impregnable to an ass laden with gold."
-Philip of Macedon

	24-04-2001 10:37									#3
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Congrats Samson. I guess I don't have to finish my research anymore since you have a working formula along with the way to figure out the key civ. Now I can get back to playing and maybe try my hand at OCC

	24-04-2001 18:54									#4
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My lab is closed and I had told myself I wouldn't post here before being back from vacation.
But I feel compelled to say 'WoW'.
Congrats Samson: beakers + choosing the right civ when giving techs; this is perhaps one small step for you, but IMO quite a gift to all players.
Also thank you to you Mixam. I am fairly convinced that what you did and found out was helpful.


------------------
aux bords mystérieux du monde occidental

	24-04-2001 20:06									#5
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Mixam

I missed a thanks to you for the work you put into resaerching this.


samson

Can you do all of us a favor and put off meeting Delilah until you have finished making all the remaining important discoveries about the game?

	24-04-2001 20:14									#6
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Thanks, Marquis and La Fayette.
I'm quite happy to give something back after all I've learned here.

Mixam,

There's still some unexplored questions, if you're interested.
Like what happens if you start with less than 7 civs? Does the missing Power rating
always correspond to the absent color? Or will there be deadzones where
you are unable to gift the missing Key Civ?
This could be especially troubling for those who play on a small map when the 7th civ
will sometimes fail to start. In gameplay, Minimum beaker tables are easier to use
than the formula, so I wouldn't throw out your work. By creating a test case,
where the human civ is locked into its own Key Civ position, you can augment
your MIN and MAX data with the NOMINAL beaker cost data.

samson

	24-04-2001 23:01									#7
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Great and brilliant work!!! Serious patience was unquestionably required to extract 14 vs 15 vs 16 as well as -1 and -2. Programming note: How did the Microprose folks decide 4 @ 12, 2 @ 13, 2 @ 14, 4 @ 15, etc.?

Of course other questions remain. For example, how is the table affected by the choice of a large map or a level other than Deity?

	28-04-2001 02:13									#8
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Now in GL - thanks samson
_______________
The SGs in red ...

	29-04-2001 02:53									#9
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Samson: Excellent work by both you and Mr. Firefly.

(Seems unfair that the rotton Mongols can get Future Techs at average cost while my Romans wound up paying the maximum 32,000! And I'm the Greeks my current game)

One clarification on "Power Rankings" versus the "PowerGraph." The Power Rankings that your formula relies upon (i.e., those that may be accessed via F3,send emissary) appear to be recalibrated every other year; the "PowerGraph" represents changes every fourth year, the oedo year. This may explain some inconsistencies in terms of the timing of changes in the amount of research required.

(Since my original experiments were designed to determine what the power graph measures as opposed to what it did not, I was already thinking of the PowerGraph in terms of "snapshots" taken of the game every four years. Your formula, however, required rechecking my assumption; and thus, apparently, Power Rankings are recalibrated every other year, but illustrated on the PowerGraph every fourth year.)

Once again. Congratulations on some great work done.
(I'm post a link on the other forum.)
Once again, very good work!

	01-05-2001 04:16									#10
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{advances}
{beakers count}
{}{SlowThinker}

------------------------------
This is a post with keywords. See The Great Library: a hierarchical structure" thread.

	27-04-2002 08:16									#11
	Re: The Cost of Research Explained Support Apolyton, buy Civilization III: Complete

quote: Originally posted by samson Here is a chart of TechNumbers, Base Multipliers, and Bonuses for the first 20 techs. Tech# Base Bonus 01 10 0 02 11 -2 03 11 -1 04 12 -2 05 12 -1

If I understand well, then the minimums are
10, 18, 30, 40, 55

But in my "Campo" game I have
10, 18, 27, 36, 45...

	28-04-2002 02:08									#12
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Are you playing a small map? Map size matters (if you read carefully you'll notice that Samson's numbers were for mid size maps).

	28-04-2002 04:58									#13
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quote: Originally posted by Xin Yu Are you playing a small map? Map size matters (if you read carefully you'll notice that Samson's numbers were for mid size maps).

not carefully ... yes, small map...
Thank you

	09-03-2003 00:32									#14
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It looks there are many basic questions unanswered (or did I miss answers?):

quote: Originally posted by samson There's still some unexplored questions, if you're interested. Like what happens if you start with less than 7 civs? Does the missing Power rating always correspond to the absent color? Or will there be deadzones where you are unable to gift the missing Key Civ?

quote: Originally posted by Posted by Bloody Monk on 27-02-2003 23:01 in Early Landing Comparison Game #1 2) Does Samson's formula in the thread "The Cost of Research Explained"--in the Great Library--apply to medium maps?? What about other map sizes??

quote: Originally posted by solo I believe small map tech costs are 4/5 that of medium maps and that large map tech costs are the reciprocal of that. Samson's "Cost of research ..." thread applies to medium maps...

And my question:
What happens if I destroy my key civ and the 'don't restart eliminated players' option is off?

	09-03-2003 02:39									#15
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ST ... this was a very good bump!

I don't know the answer to your question.

-----------------

SG(2)

	09-03-2003 08:00									#16
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ST,

If your key civ is destroyed, your research costs are maximized. If restarts are on, you will have to wait until the new key civ appears. The new key civ is apt to have fewer techs than the old one, so you will have to gift all techs again to lower your research costs. If restarts are off, you're in big trouble, since you no longer have a key civ unless your power rating changes.

If a civ other than your key civ is destroyed, your key civ remains the same, as do your tech costs.

I have not tested games starting with less than 7 civs, but would guess that missing colors also mean missing key civs, since in a game with 7 civs, destroying civs other than your key civ does not affect your own key civ relationship.

Samson's formulas apply to medium maps only.

	09-03-2003 08:55									#17
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quote: Originally posted by solo If your key civ is destroyed, your research costs are maximized.

What does this mean? I thought there is no maximum and that every three techs cause +1 penalty beyond any limit.

	09-03-2003 11:04									#18
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Bravo solo!

Combined with the base beaker numbers one will be able to calculate the total number of beakers required for all situations, provided you know the number of techs controlled by your key civ.

Awesome

	09-03-2003 21:17									#19
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Exactly obiwan18!

All of this can be figured out down to the last beaker, if one wants to make the effort. After all, it's a computer running things and computers are NOT good at being inaccurate.

ST,

When your key civ is destroyed, the game interprets this to mean they suddenly have zero techs, which gives you a tech lead equal to the number of techs you currently have. You will incur the maximum penalty, which is equal to your tech total divided by 3. (Of course, for every three techs you acquire afterwards, the "maximum" penalty will increase by 1.) Perhaps an example will help:

In my test game, I had 72 techs and currently had a 3 tech lead over my key civ, which gave me a +1 penalty (3/3=1), which when added to the base of 26 resulted in a beaker cost of 1944 (72 x 27).

Then I destroyed my key civ. After this my tech "lead" was 72, so the game assigned me a penalty of 24 (72/3=24), which when added to the base of 26 (26+24=50) resulted in a beaker increase to 3600 (72 x 50).

In this test my tech costs increased even more, because my SSC had three railed routes to key civ cities, and these routes vanished after the key civ was destroted, increasing my tech costs all the way up to 4032 beakers.

Since restarts were on, once I re-established contact with my new key civ and gifted them all of my techs, my research costs went back down quite a bit, but did not recover fully due to the missing SSC trade routes.

One reason why the restart option is on in our comparison games is to make it fairer for players who happen to have their key civ destroyed. When the new one appears they can recover. Without a new key civ, they would be paying the maximum penalty for the rest of the game.

Last edited by solo on 09-03-2003 at 21:23

	09-03-2003 21:58									#20
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@ Solo

Thank you for taking the time to explain the penalty consequences so fully. The more details, the better the concept anchors, at least for me. You are a great teacher and we all appreciate your contributions. It took a lot of patience, on a Sunday morning, to compose that lesson for us. Thanks.

I can't wait to read your forthcoming "Doctrine."

Monk

	09-03-2003 22:40									#21
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Thank you, solo. But I don't understand the following sentence:

quote: In this test my tech costs increased even more, because my SSC had three railed routes to key civ cities, and these routes vanished after the key civ was destroted, increasing my tech costs all the way up to 4032 beakers.

Does a trade route directly decrease the tech costs?

	09-03-2003 22:58									#22
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Monk,

Flattery will get you everywhere! The guide goes slowly, as I'd rather be playing.

ST,

Trade routes add many trade arrows from which beakers used for research are based. Losing my trade routes decreased the beaker capacity of my SSC, making techs seem more costly.

	09-03-2003 23:31									#23
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quote: Originally posted by solo Monk, Flattery will get you everywhere! The guide goes slowly, as I'd rather be playing. ST, Trade routes add many trade arrows from which beakers used for research are based. Losing my trade routes decreased the beaker capacity of my SSC, making techs seem more costly.

It's not so much flattery as appreciation for your willingness to teach.

The trade route problem happened in my game in a slightly different way. After Flight, the Karakorum routes no longer stuck when I delivered to the SSC. This drop from +27 to +9 for that slot was just enough to drop me out of one turn for the next advance. The 611g I received for the delivery of demanded spice was nice, but costly in terms of advances.

Lots of nuances to this game.

Monk

	09-03-2003 23:55									#24
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ST,

I should have thought this over a bit more. You are right that trade routes should not alter the number of beakers needed for the next tech, since this is a fixed cost.

After a few more tests, it's not clear to me where the additional +6 penalty came from that resulted in the 4032 cost instead of the expected 3600. This could be due to the starting techs given to the new key civ when it is created. If this is so, the penalties are still steep for players when their key civ is eliminated, even after contact is established with the new key civ and all techs are gifted.

	10-03-2003 02:09									#25
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Anyone have an algorithm for the first 19 techs?

Once you are researching your 20th tech, the beaker counts jump to (32)X where X = the technumber of the tech you are researching.

	10-03-2003 03:37									#26
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quote: Originally posted by obiwan18 Anyone have an algorithm for the first 19 techs? Once you are researching your 20th tech, the beaker counts jump to (32)X where X = the technumber of the tech you are researching.

obi,

I think you are mistaken. Everything you ask for is given in the first post of this thread. If, after reading it, you wish to delete your post, then, I will delete this one.

As noted elsewhere, the thread is about medium maps. If you are thinking of different map sizes, Solo suggests a 4/5 or 5/4 correction, IIRC.

Monk

	15-03-2003 22:50									#27
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Thank you for showing how to calculate beaker costs for advances.

There is one question I need to ask which is not directly related to the science cost. I did try to search for the answer but could not find it. So forgive my ignorance but how do you calculate the science bonus created by a caravan trade route?

Thank you for your time.

	15-03-2003 23:30									#28
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Thanks, BM.

Guess my head was hard. Reading over solo's post, I realised that his list of numbers 1-20 for the base count explains the differences.

I'll rephrase my request:

If Cost = Technumber * (Basefactor + penalty/bonus).

Let Cost = C, Technumber = T Basefactor = X penalty = p and bonus = b

Now C = T *(X- p/b)

X = ? All we have for X is a list of numbers, for techs
0-20.

Can we have a formula to calculate X?
This would make it much easier to remember the most obvious case without beaker penalties.

	16-03-2003 00:59									#29
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quote: Originally posted by goape forgive my ignorance but how do you calculate the science bonus created by a caravan trade route?

When you deliver a commodity caravan (freight) somewhere, you are granted a one time bonus in gold + the same amount in beakers.
The ongoing bonus (usually named trade route) is trade arrows.

	16-03-2003 01:18									#30
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obiwan18,

All techs totals of 20 or above have the same base, which is 26. Base numbers vary for the first 19 techs, so each one was listed. Base numbers are not calculated from any thing else, they are constants. Calculations involve adjustments (penalty or bonus) to the base number, after which the tech cost can be found by multiplying this adjusted base by the current number of techs.

goape,

Besides the delivery beaker bonus (exactly equal to the cash payoff in gold) mentioned by La Fayette, once a new route is established, it adds more trade arrows to the total, from which a city's total of science beakers is derived. You can check a city's beaker total before and after a delivery to see how many beakers you gain this way.