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.

------------------
Scouse Git[1] -- git1@scousers.net

For sure, though, your work will be quickly verified as people try it out in practice.

I guess that gifting to all will continue in OCC where improving the attitude of other civs is as important as beaker count. But in regular SP games this is a vital piece of information and I, for one, have printed off your post and it will be found sat beside my machine for a while.

As you point out choice of civ is affected. I like to play all colours but I have a predilection to play purple which may need reconsidering.

Rufus T.'s discovery that there is a key civ for tech gifting purposes seems to me to be work of Apolyton Nobel prize winning calibre but this work of yours builds on that discovery so substantially it must rank with it.

EST - The 'eureka' moment is recorded in the log of my 'size 1 OCC' game posted here also.
In playing that game I tracked all beaker counts to be sure I was paying the minimum cost.
Whenever the beaker cost went up, it was because the Key Civ shifted from Romans to Babs
or vice versa. After awhile I noticed that this happened at the same time
as my Power rating changed from Pathetic to Weak.
I used this 'tell' in the game but didn't understand the connection until late in the game
when I jumped to Inadequate and the Key Civ switched to the French whom I had been ignoring.
My beaker cost got clobbered. That's when the connection hit me. I left the game
for a couple hours and did some testing. When the theory proved true I couldn't stop grinning.

I've tracked this through two games now and found it explained all beaker count
increases and decreases. It also held up through a number of Cheat Mode test cases
I devised. Then I went back to some save games of odd beaker bumps I had. Bingo!
The topper was that it explained the 'destroyed civ' phenomenon neatly, too.
If this isn't the answer, it's damn close.

As to strategy, I think it will change my play even in OCC. Tech gifting does three things:
it lowers your beaker cost, it improves AI attitude and makes alliances possible,
and it slows down AI research. The last of these is not always desirable in OCC
because it means you have to do more of the basic research.

My future research strategy for all games, including OCC, will be based on three things:

1) Accurate beaker minimum cost tables
2) Tracking the Key Civ
3) Embassies with all AI

By knowing the beaker minimums and the Key Civ, I can control my research costs,
getting the maximum benefit with minimum impact on the AI's research ability.
I will still gift techs to AI to get alliances and maintain relations, but only
give the minimum needed, not every tech I acquire. By establishing embassies
I can see what tech each AI is working on. I can give that tech to that Civ
immediately if I have it. If they are researching something new to me,
I will leave them alone (suspending my tech gifting) to allow them to complete their research
as quickly as possible. In this way I can pay the minimum for my research
and utilize with maximum efficiency the AI's own research efforts.
In theory, I could effectively control seven lines of research simultaneously.
In practice, two or three or four perhaps.

samson

So thanks for sharing it with us.

Like many a breakthrough it may now seem a straightforward connection to have made. But this is always ex post facto thinking. Fact is, many folk have counted beakers in OCC but none of us previously ever guessed at this.

You had Rufus T's discovery to help and Mixam too has been making interesting posts around all this. But the actual discovery fell to you and a fine one it is.

Can't imagine what the developers were doing. Perhaps there is some programming reason it has convenience.

Absolutely brilliant discovery!

It's one more area (hut pattern, Oedo years, 3 tech groups, ...) where the developers used an unrealistic, illogical pattern where a purely random method would have served just as well and been less easy for humans to exploit. I hope Civ3 takes a different tact.

As you noted, it can still be worthwhile to gift techs to non-key tribes to improve their attitude and slow their research.

I've done more testing of this and I'm now convinced this is the explanation
for all changes in beaker counts occuring during a game. I went back
to Rufus T. Firefly's "Does Giving Away Tech Help Your Science" thread
and it explains both of the examples he posted there perfectly.
It also explains all of the counter examples I posted to refute his hypothesis.
The "delayed beaker reduction" phenomenon that I described occurs when you are your own Key Civ.
Since you can't give techs to yourself, giving them to everyone else has no immediate effect.
But on the next turn, the Power ratings may change and you might have a new Key Civ.
Since you gave away all your techs, he is now ahead of you and so your beakers reduce.
It even explains the extremely odd case I reported where the reduction of my city population
by one point caused my beaker count to go up on the next turn.
Obviously, my Power rating dropped, my Key Civ changed, and I now had more techs than this guy,
so I was charged more beakers for my current research.

In my 1056 landing game I was supreme and was playing the Indians, both in the #7 spot, and I noticed that gifting techs to everyone never changed my beaker requirements, and was wondering why not. Your theory supports exactly what happened to me in this game, at least, and also confirms my overall experience that there definitely is one key civ that triggers beaker changes.

The 'key civ' idea has been around for awhile in its earlier guise as the 'sixth civ' theory.
Rufus's work refuted that hypothesis, replacing it with one of his own,
which also proved to be false.
So far, this new one looks good.

samson

Well, done, samson! I wish I could have been the very first to congratulate you, but I've been away. But let me make it up to you with some data:

1) I went back to the saved games I had which failed to conform to my speculations about tech and the power graph, and tried your method out; worked every time!

2) "Every time" includes a game where a civ had been eliminated: I was Mighty in a game where the Indians had been wiped out, but giving tech to the English still lowered my count. I would imagine that eliminating a civ eliminates the possibility of gift reduction corresponding to that civ's position, but not for others.

3) I found a game where I occupied my own preferred "tech giveaway" slot -- I was the Babylonians, and Weak -- and found that when I gave tech to the Pathetic Germans, my tech count reduced on the next turn, and when I gave tech to the Inadequate Sioux my tech cont reduced two turns later. I haven't checked for sure, but it seems likely that when I gave the techs to the Germans, I helped them pass me on the Power Graph and thus got the reduction on the next turn, whereas when I gave to the Sioux I didn't get the reduction until the Germans passed me on their own.

4) I still haven't been able to get the multiplier down below 24 for 20+ techs, so I suspect you're right about that being the floor.

It would be interesting to know what happens when you occupy the privileged slot yourself, give away techs, and then go up the power graph rather than down. I think I'm playing a game know where I can make that happen; I'll let you know what I find.

Again, kudos. If my students were even half this imaginative or this diligent, I'd be a happy man indeed.

Now: any ideas on the second gunman in Dealy Plaza?

quote: I would imagine that eliminating a civ eliminates the possibility of gift reduction corresponding to that civ's position, but not for others.

That is correct. And tech-gifting can sometimes change your Power rating enough
to shift you into a different position. From the testing I've done, it would seem
that an eliminated Key Civ acts as if it has 0 techs, which means you pay the maximum penalty.
That is not a good situation.

quote: ) I found a game where I occupied my own preferred "tech giveaway" slot

Actually, you really aren't too bad off when this happens. You don't get the MINIMUM,
but you don't have to pay a penalty either, even if you're way ahead in techs.
If you're Purple and Supreme, you can arrogantly forge ahead with no tech-gifting at all
and never pay too much extra for your research. The penalties for the late game techs
are quite severe (more than 100%) whereas the Bonus is constant
and so actually becomes less as a percentage of your cost.

#4) Yes, 24 is the Bonus Multiplier for a medium map, 19 for the small.

samson

quote: Originally posted by samson on 04-24-2001 11:35 AM Yes, 24 is the Bonus Multiplier for a medium map, 19 for the small.

If we fit the numbers to an equation:
Bonus Multiplier=a+b*(map size), then from the above numbers (mdium map size 50x80=4000, small map size 40x50=2000) we get a=14, b=1/400.

Now 14= 10x1.4 = tech paradigm x deity modifier. Coincidence?

I just did some quick testing on a Large Map (75x120=9000) and the Bonus Multiplier is 30.

So if "14= 10x1.4 = tech paradigm x deity modifier" is correct then we have:

Map Size(in K) MapFactor

Small 2 5
Medium 4 10
Large 9 16

The progression seems roughly logarithmic instead of linear, i.e.:

MapFactor = 5 * Log(base2)(MapSize/1000)

samson

Sid and Brian want to make a science progression cost ladder. Already, the leader needs more beakers to next advance, simply because he has more techs, the tech*(tech+1) cost. But they also want to implement a way to make it even easier for a weak civ to catch up, for a strong civ to halt its growth. Sid proposes to link a science penalty to size of the tech gap between player and the player above (or below) him.
Brian sets to work. Adds a line in code, late in development, late at night.

tech_cost += tech_dynamic_constant * (player_tech_size - tech_size(player_power_position - 1));

Or something like that.
Meaning add a modifier based on difference between number of discovered techs for you and the player one step worse than you in power. A civ with a huge lead to #2 will have a huge modifier added. Pathetic civ will be compared with barbarians.

Mistake.

tech_size table is organized, not after power graph position, but after turn number (color). A player in power position 1 (pathetic) gets compared with the tech level of player 0 (white). Nobody gets compared to player 7, barbarians.
A subtle bug.

Brian should have made a simple power table for each round, fixing barbarians as position 0, and sorted in rank up to 7.

A likely explanation?

some quotes, but the whole article is excellent read:

The general idea:

quote: Getting ahead in the game should (properly) give the player a greater chance to win, but it should not make it easier for him to further increase his chance to win. Rather, just as the further we stretch a rubber band the more it resists, the farther ahead a player gets the harder it should be for him to increase his lead. Likewise, the more a player has fallen behind the easier it should be for him to begin catching up-again, our game system's "rubber band" pulls the player back toward the competition

what, according to Brian R., went wrong in civ1:

quote: Players ahead in the technology race had the first crack at building "wonders" and "improvements" which had the effect of further increasing their lead in the technology race-many wonders directly or indirectly increased research speed. Then, as the time scale proceeded from "B.C." to "A.D." the technology cost for all players suddenly doubled-again working to the advantage of players who had been able to research more technologies at the "cheap rate" and effectively locking out those players who were already behind by imposing a further penalty on top of their already bad situation. A winning player rapidly eclipsed the opposition and the rest of the game (often a considerable period of time) consisted simply of mopping up.

Actually, in civ1, game ended when human player got chariots
The fixed that in civ2 a bit, no more superchariot 4/1/2

Finally, the rationale behind tech design in civ2, abstract:

quote: With some care and tuning, a technology race can be changed from the "Rich get Richer" to a "Poor get Richer" situation. Moreover, this can even be done in a way which also pays homage to our common sense historical intuitions. We know from history that nuclear weapons were extremely difficult to develop and required a massive and unprecedented investment by the Americans who first developed them. But nuclear weapons having once been developed, a far lesser investment was required for their duplication and imitation by other powers.

In game terms:

quote: Translated into game terms, this means that technologies should be much more expensive for the first power to develop them, and then increasingly easy for other powers to copy. That way, players who are ahead in technology have to expend increasingly large efforts to maintain and increase their lead-they are paying the expensive first-research cost while the trailing players are paying the cheaper "catch up" prices. And the further behind a player falls, the longer a time period passes between the initial discovery of a technology and the player's attempt to research it-cumulatively reducing the cost to "catch up."

quote: When these sorts of changes were applied to Civ2, the result was a game which was much more likely to remain competitive into modern times. Now even experienced players were often challenged to deal with nuclear-armed opponents and participate in hotly contested space races.

yes, with size one cities on polar caps

quote: The rules of the game should work to keep the game competitive for as long as possible.

Acceptable. Tech thing is part of the rules to help the weak. If it has been more random it would work bettern then this though. Now that samson discovered The Key, it feels a bit unfair, at least to me.

Clearly, this logic does not give as good a result as counting all the techs that everyone has, and then comparing, but maybe it was simpler to code (I'm no programmer)

Game 1 (current game):
Deity, seven civs
Playing as Romans, 1250 bc (just built Marco Polo), power supreme
Gave six techs to Sioux
Beaker requirement for current tech declined from 128 to 120, even after gaining one tech through exchange of knowledge.
Beaker requirement for next tech declined from 153 to 135
This makes my favorite wonder, Marco Polo, even more valuable.

Game 2 (old game):
Deity, seven civs
Played as Romans, 1834 AD, power moderate
Gave 21 techs to Spanish
Beaker requirement for current tech declined from 860 to 640, a reduction of 25 percent!
This game had a SSC and several repeated commodity trade routes, making two discoveries per turn ridiculously easy, even with moderate power.