Research. It's the fundamental way of advancing in life and in Civ IV, and a necessary part of making your way up the food chain in Civ IV from doormat to winner (whether via space race, diplomacy, conquest, or culture). Unfortunately, it's also the way to figure out how research actually works in Civ IV.

Fortunately for you all, I've done all that. This article came about because I was interested in what the optimal start to the game was. However, upon working out that information, I was startled to discover that the amount of research differed from what my lone city was producing. I dug further in depth into the mechanisms of the game and figured out how research is priced, accumulated, and applied in the game.

This article will explain the ins and outs of how your beakers get put to work to research the technologies that make or break your game of Civ. To learn more, read on....

One important note.

FLOOR means rounding DOWN to the nearest integer AND it has higher precedence than all other operators EXCEPT FOR parentheses. You will see it used a lot in the article.

The basics (of generating beakers)

1) Each city generates a raw amount of commerce via the squares that are being worked and the trade routes in the cities.

2) This commerce is in turn translated into beakers (research), coins (gold), or notes (culture) via the technology and culture sliders. The actual amount of beakers and notes are gained by using the specified slider rate in the following equation:

FLOOR (total commerce * the specified slider rate).

The remainder is then given in gold.

So, yes, you WILL get AT LEAST one gold from each city that has a commerce that is not a multiple of 10, if your science or culture is not 100%.

3) Each city then takes each amount and adds in any additional sources of research, gold, or culture (via shrines, production processes, and specialists, mainly).

4) Each city then multiplies it by whatever modifiers it has depending on what buildings it has built (e.g., beakers are multiplied by 1.25 if it has a library, gold is multiplied by 1.5 if it has a bank, etc.). NOTE: multipliers are ADDITIVE (i.e., if you have a library and university, your beakers will be multiplied by 1.5 (1 + 0.25 + 0.25) NOT 1.5625 (1 * 1.25 * 1.25)).

5) The beaker totals are then added up across the cities and the sum is your base beaker total.

Technology Costs

To calculate the technology cost of a technology:

1) Take the base cost of the technology. (This can be found for each technology in Assets\XML\Technologies\CIV4TechInfo.xml).

2) Take the Difficulty Modifier and add 0.5 * the Number of teammates you have to it. (The difficulty modifier can be found in Assets\XML\GameInfo\CIV4HandicapInfo.xml.)

3) Multiply 1) by 2) and take the FLOOR of the product.

4) Multiply 3) by the Map Modifier and take the FLOOR of the product. (The map modifier can be found in Assets\XML\GameInfo\CIV4WorldInfo.xml.)

5) Multiply 4) by the Speed Modifier and take the FLOOR of the product. This generates the actual cost of the technology. (The speed modifier can be found in Assets\XML\GameInfo\CIV4GameSpeedInfo.xml.)

Thus the formula to calculate a Technology's cost is:

Technology Cost = FLOOR (FLOOR (FLOOR (Base Cost * (Difficulty Modifier + 0.5 * # of teammates)) * Map Modifier) * Speed Modifier)

Applying the Research to the Technology

The amount of beakers applied to the technology cost is dependant upon the number of civilizations which know the tech and the number of requirements you have fulfilled for the technology.

Calculating the Known Civilizations w/ Tech modifier

1) Multiply 0.30 by the number of KNOWN, LIVING civilizations, who have the tech.

2) Divide by the number of civilizations which STARTED on the map and ROUND DOWN to the hundredth place (0.01) of the quotient.

3) Add 2) to 1

Tech Known by Civilizations modifier = 1 + RDDW (0.30 * # known Civs who have the tech / # of Civs who started the game

Calculating the Prerequisites modifier

1) Start with 1. If the technology does NOT have a minimum requirement (i.e., the starting techs = Fishing, The Wheel, Agriculture, Hunting, Mysticism, Mining), then use 1 AS the modifier.

2) Add 0.2 to 1) if a Technology has a MINIMUM Requirement that the player has met. Note: Even if a tech has MANY MANDATORY PREREQUISITES, it will still only give you a boost of 1.2 because you MUST have all those prerequisites to research the tech. (IOW, the minimum requirement IS all of those prerequisites.)

3) Add 0.2 to 2) for EACH ADDITIONAL OPTIONAL Prerequisite that the player has met.

Requirements modifier = 1 + (0.2 * MINIMUM Req. met) + (0.2 * # of Optional Prereq. met)

Calculating the Actual Amount of Beakers Generated Toward a Tech

To calculate the amount of beakers which you generate toward the technology:

1) Take the total sum of beakers generated by all your cities (the result from the basics part).

2) Add 1 to it if you have a city.

3) Multiply 2) by the Known Civilizations w/ Tech modifier and take the FLOOR of the product.

4) Multiply 3) by Prerequisites modifier and take the FLOOR of the product.

The formula to calculate the amount of beakers applied to your technology is:

Beakers applied to Technology = FLOOR (FLOOR ((Total Base Beakers + 1) * KCwT modifer) * Prerequisites modifier)

An example

I always seem to understand better with an example, so here's a basic one.

Say you want to research Code of Laws which has a base cost of 350 beakers, the mandatory requirement of Writing and the optional (meaning you must research one of them) requirements of (Priesthood or Currency).

You know Writing and Priesthood

You produce 37 net beakers per turn and you have met 3 other civilizations who know it out of 7 who started the map.

You started on a standard map (1.4 modifier) at the monarch difficulty level (1.15 modifier) at epic game speed (1.5 modifier) and have 1 teammate.

Your cost would be:

FLOOR (FLOOR (FLOOR (350 * (1.15 + 0.5 * 1)) * 1.4) * 1.5)

FLOOR (350 * 1.65) = 577
FLOOR (577 * 1.4) = 807
FLOOR (807 * 1.5) = 1210

Total cost = 1210

The amount of beakers applied to code of laws would be:

FLOOR (FLOOR ((37 + 1) * (1 + RDDW (0.30 * 3 / 7))) * (1 + 0.2 + (0.2 * 0))

1 + RDDW (0.30 * 3 / 7) = 1.12
FLOOR (38 * 1.12) = 42
FLOOR (42 * 1.2) = 50

Beakers applied to Code of Laws/turn = 50

Note that having Writing AND Priesthood only gives you a bonus modifier of 1.2 because you must have at LEAST Writing PLUS one of the optional prerequisites to be able to research Code of Laws. If you also had Currency, then the modifier would be 1.4.

Overflow

The overflow is calculated by the modifiers from the PREVIOUS Technology. Therefore, if you finished researching Writing this turn, and you had all THREE optional requirements, the overflow beakers which applied to your next technology would be equal to however many you had left USING THE MODIFIERS FOR Writing after finishing Writing. So, your Requirements modifier would be 1.6 (1.2 * 3). So, you could conceivable get a significant boost toward your next tech OVER WHAT YOU SHOULD HAVE GOTTEN if you have a lot of overflow.

Req

Repercussions

1) It can be VERY important to establish contact with all the other civilizations in order to speed your beakers applied count. You could potentially be making 28% (17 known civs w/ tech/ 18 civs total) more beakers than you normally could on a tech. This is especially true on harder difficulties. If you just meet half of the other civs, your research on techs known by the others would improve by 14%. This is probably the biggest repercussion of the calculation.

2) If you're going to research several technologies and one is an optional requirement of another, research the optional one first as that will boost your research toward the other one unless you have a specific reason for researching the other one.

3) If you're researching the starting techs (no prerequisites modifier), try to reduce the amount of overflow you have, as you're multiplying it by the lowest amount possible. It would be better spent earning some gold which may be necessary to run a deficit research job.

4) If you're researching a tech which is known by a lot of people and which has many optional prerequisites which you already have, try to time it so that you end a turn with 1 beaker left to research that tech. The next turn INCREASE the amount of commerce you generate in order to increase the research overflow on the next turn to the max amount possible. You could potentially generate 104.8% ((1 + 17 known civs w/ tech/18 civs) * 1.6 [tech w/ 3 optional prerequisites]) more beakers of overflow than you normally would for that tech (assuming it's from Writing to a Starting Tech which no one knows. I know, it's unlikely. :lol:). However, for a realistic overflow difference getting almost 46% (1.25 * 1.4 / 1.2) more beakers in overflow is very feasible.

[First tech = 6 known civs w/ tech out of 7 civs and 1 additional optional prerequisite obtained]
[Second tech = no known civs with tech and no additional optional prerequisites obtained]

like Paper w/ Civil Service and Theology to Education.

5) Pre-Alphabet (and possibly in non-tech trading games), you will be able to determine the number of known players with a certain tech but not who has this specific tech unless all known or no known civs have it. (thx to DaviddesJ for pointing this out).

6) Similar to repercussion #5, if the AI is ahead of you in tech, you will be able to determine the number of known players with a technology which is BEYOND your research ability (i.e., those you do not have the prerequisite technologies for) but not who has this specific tech unless all known or no known civs have it. NOTE: there would also be times where you would NOT know whether another known civ has the tech as the civ modifier would be small enough that no difference could be detected. (thx to Roland Johanson for pointing this out.)

7) If you don't choose a tech as soon as you found your first city, you are probably losing a bonus (if you don't choose a starting tech). This might not be that significant, but when every beaker counts, losing two beakers in the beginning might mean the difference between getting that iron rush 1 turn faster.

8) If you have a neighbor who you're thinking of killing off who has techs which you have not researched yet, it might not be worth it to kill them off UNTIL you've researched the tech (1 neighbor who knows the tech in a 7 player game will provide a 1.04 boost).

Difficulty, Map Size, and Speed Modifiers

Difficulty Modifiers
Will wait until the patches are done before posting a full list

Map Size Modifiers
Will wait until the patches are done before posting a full list

Game Speed Modifiers
Will wait until the patches are done before posting a full list

Additional Modifier for knowing 1 more civilization who has the tech out of....
2 Starting Civilizations = 0.15
3 Starting Civilizations = 0.10
4 Starting Civilizations = 0.075
5 Starting Civilizations = 0.06
6 Starting Civilizations = 0.05
7 Starting Civilizations = 0.0428...
8 Starting Civilizations = 0.0375
9 Starting Civilizations = 0.0333...
10 Starting Civilizations = 0.03
11 Starting Civilizations = 0.02727...
12 Starting Civilizations = 0.025
13 Starting Civilizations = 0.0230769...
14 Starting Civilizations = 0.0214...
15 Starting Civilizations = 0.02
16 Starting Civilizations = 0.01875
17 Starting Civilizations = 0.017647...
18 Starting Civilizations = 0.01666....

Thanks to
-LordTerror for his work dealing with the teammate modifier
-Zombie69, Roland Johanson, kryszcztov, jesusin, and LordTerror for suggesting ways to improve and/or clarify the article
-DaviddesJ for suggesting repercussion #5.
-Roland Johanson for suggesting repercussion #6.
-Arthog for his idea about dead civilizations possibly contributing to the modifier which led to repercussion #8 and for providing a save file to test the idea on.

Req

Reserved for future use.

I see a glaring mistake in your post :

"4) Multiply 3) by (1.2 * the number of requirements you have fulfilled - the minimum requirements count as ONE requirement) and take the FLOOR of the product."

You either mean "1.2 ^ nbr req fulfilled" or "1 + 0.2 * nbr req fulfilled".

As it stands, according to your formula, having just one more requirement than needed DOUBLES your research speed, and having 2 more than needed TRIPLES it. I highly doubt that's the case.

Regardless, i didn't know there was such a factor involved at all. This makes horizontal research, rather than vertical research, more appealing, especially if for whatever reason, you can't trade higher techs for lots of lower techs to compensate for slower research.

I see a glaring mistake in your post :

"4) Multiply 3) by (1.2 * the number of requirements you have fulfilled - the minimum requirements count as ONE requirement) and take the FLOOR of the product."

You either mean "1.2 ^ nbr req fulfilled" or "1 + 0.2 * nbr req fulfilled".

As it stands, according to your formula, having just one more requirement than needed DOUBLES your research speed, and having 2 more than needed TRIPLES it. I highly doubt that's the case.

Regardless, i didn't know there was such a factor involved at all. This makes horizontal research, rather than vertical research, more appealing, especially if for whatever reason, you can't trade higher techs for lots of lower techs to compensate for slower research.

It's a typo. Trying to get too much data in on one line. I will break it apart.

Thanks,
Req

1) It can be VERY important to establish contact with all the other civilizations in order to speed your beakers applied count. If you don't, you're potentially making 21.8% (1/1.28) less beakers than you could on a tech. This is especially true on harder difficulties. This is probably the biggest repercussion of the calculation.

The first posting just says the number of civilizations with the technology; it doesn't say that it matters whether you have contact with them.

The first posting just says the number of civilizations with the technology; it doesn't say that it matters whether you have contact with them.

Oops. Nice catch.

Req

Thank you for this very well written and informative article. The modifier for number of prerequisites of a technology known is especially new to me. Also, I would have thought that the modifier for the number of opponents who know the technology would be bigger (it was bigger in civ3).

I really hate the repercussions 3 and 4, but that is not your fault. That is just lazy programming from Firaxis (the modifiers for the new technology should be applied to the overflow, not the modifiers for the previous technology). This will again mean that micromanaging the technological research is beneficial. :(

Still, I want to make a few critical remarks to try and make the article completely error free.

1) Zombie69's remark.
2) the 1.28 factor in repercussion 1 should be explained because otherwise people will ask why 1.28? It is probably the largest modifier you can get for other civilizations knowing the technology which is 1+ 17/18 * 0.3.
3) The modifier for 1 more civilization knowing the tech seems to depend on the number of starting opponents as seen in the formula that you posted:

1 + RDDW (0.30 * # Civs who know the tech / # of Civs who started the game)

If one civilization knows a technology in a 2 player game, then this results in a modifier of 1.15. If one civilization knows a technology in a 5 player game, then this results in a modifier of 1 + 0.3 * 1/5 = 1.06.
So the table in the repercussions section is wrong or the formula is wrong or I'm not reading your article the way I was meant to read it.

Thank you for a great article. :goodjob:

A few questions, not sure if I understand it well :
- For each city, how are partial results and final results for gold, beakers and culture handled ? Rounded down, up, to the closest integer (what happens to 0.5 then ?), or nada ?
- I still don't understand if you have to make contact with the civs which already know the tech you're researching in order to have a discount or not. In Civ3 you had to, what is it in Civ4 ?
- I don't understand the prerequisite part of your theory very well. There are some techs which only have one or more mandatory prerequisite(s), some other techs which only have optional prerequisites (not 1, since it would be mandatory then ;) ), some other techs which have both, and the starting techs. Care to explain for each case please ? :)
- I didn't catch your 3rd repercussion ; if you let science at max on the last turn, you'll get more overflow for the next tech, what's wrong with it ?

But all in all, I'm impressed to see such a complex theory already ! :goodjob: Thanks so much for the work done in so little time. Of course it needs to stand our own experimentation now, but in any case, you're surely very close to the truth (and probably ON the truth). I'll come back here if I find contradicting results.

What we'd need is a science calculator now ! :)

Also, though I like some features that are driven from your theory (discount for optional prerequisites is one of those), I dislike some other features (the +1 beaker that you get in any case, totally NOT needed and wrong IMHO).

Also, I would have thought that the modifier for the number of opponents who know the technology would be bigger (it was bigger in civ3).
I think it's fine that you don't get a fair discount, otherwise it leads you to wait for other civs to get it first, which shouldn't be the usual way to play a game and run a civ in RL. Also it is another counter-effect to Civ3's heavy tech trading (any AI would be pleased to sell you whatever techs they had).

I really hate the repercussions 3 and 4, but that is not your fault. That is just lazy programming from Firaxis (the modifiers for the new technology should be applied to the overflow, not the modifiers for the previous technology). This will again mean that micromanaging the technological research is beneficial. :(
Didn't understand #3. As for #4, I disagree with you for the moment. For once, it SHOULD be the same as for hammers in a city (and here it is the same, the overflow of hammers that you get on the next turn are kept with the former modifiers). I will be totally against a difference between hammers and beakers. Now, I also think this is better, since the hammers/beakers were produced on a turn when you were building/researching something with some modifiers. The overflow is just stored, you know it beforehand, and so, no surprise next turn. As for more MM, it depends on what you want : if you want to get more hammers/beakers, then you'll have to delay the thing by 1 turn, which often means 1 turn of not-profitting from the building/unit/tech. On hard levels I'm sure it can sometimes be critical. It's a trade-off, you choose. And when you can run science at 100%, there's a cost for delaying the discovery, since you won't be able to run science higher on the next turn to catch back the delay.

3) The modifier for 1 more civilization knowing the tech seems to depend on the number of starting opponents as seen in the formula that you posted:

1 + RDDW (0.30 * # Civs who know the tech / # of Civs who started the game)

If one civilization knows a technology in a 2 player game, then this results in a modifier of 1.15. If one civilization knows a technology in a 5 player game, then this results in a modifier of 1 + 0.3 * 1/5 = 1.06.
So the table in the repercussions section is wrong or the formula is wrong or I'm not reading your article the way I was meant to read it.
Yes, another thing I didn't understand very well. Also, your table goes from 2 civs to 18 civs. Shouldn't it be from 1 other civ knowing the tech to 17 civs ?
And regarding the number of civs which started the game, does it include our own civ as well ?

A few questions, not sure if I understand it well :
- For each city, how are partial results and final results for gold, beakers and culture handled ? Rounded down, up, to the closest integer (what happens to 0.5 then ?), or nada ?

Darn you, I was hoping someone wouldn't notice this :blush:. I just thought up that part when I was posting the article, but since I was more than halfway through it, I just decided to finish posting it. OTOH, I just checked, and actually, it's very simple. So, I'll just add it now.

- I still don't understand if you have to make contact with the civs which already know the tech you're researching in order to have a discount or not. In Civ3 you had to, what is it in Civ4 ?

The updated article clarifies this.


- I don't understand the prerequisite part of your theory very well. There are some techs which only have one or more mandatory prerequisite(s), some other techs which only have optional prerequisites (not 1, since it would be mandatory then ;) ), some other techs which have both, and the starting techs. Care to explain for each case please ? :)

Hmmm, perhaps I should have better examples.... The techs with one or more mandatory prerequisites and NO optional prerequisites = 1.2. Techs with only optional prerequisites = 1.2 * # of optional prereqs you have. Techs with one or more mandatory prerequisites and optional prerequisites = 1.2 * OPTIONAL prereqs you have.

It really is more a question of what is the MINIMUM requirements to research a technology. Whatever that is gives you a 1.2 modifier. Each additional optional requirement gives you another 0.2 added on to that modifier.... Hmmm, perhaps, I should explain it that way.

- I didn't catch your 3rd repercussion ; if you let science at max on the last turn, you'll get more overflow for the next tech, what's wrong with it ?

The problem is that you're likely getting NO or very little bonus with the starting techs (Mining, Hunting, Fishing, etc.) since they have NO MINIMUM requirements.

But all in all, I'm impressed to see such a complex theory already ! :goodjob: Thanks so much for the work done in so little time. Of course it needs to stand our own experimentation now, but in any case, you're surely very close to the truth (and probably ON the truth). I'll come back here if I find contradicting results.

You're very welcome. And don't worry about posting contradicting results. I'm pretty sure I got everything nailed (that's what took me the better part of half a month :mad:), but peer review is always helpful.

What we'd need is a science calculator now ! :)

Errrm, hmmm, that doesn't sound like something someone would mod, perhaps? Maybe, in an advisor or something? :lol:

Also, though I like some features that are driven from your theory (discount for optional prerequisites is one of those), I dislike some other features (the +1 beaker that you get in any case, totally NOT needed and wrong IMHO).

Yeah, I like the optional prerequisites, but I DON'T like the way overflow is calculated for the reason Roland points out. And I really don't understand why they put in the +1 beaker when THEY DON'T USE IT IF YOU HAVEN'T FOUNDED A CITY.

Req

Another repercussion is that you can try to figure out whether the players you've met have a particular technology by looking at the turns to research it on the Science Advisor screen. This would be a lot of effort for not much benefit, but it could be useful once in a while. Of course, it doesn't work for techs that you already have.

Thank you for this very well written and informative article. The modifier for number of prerequisites of a technology known is especially new to me. Also, I would have thought that the modifier for the number of opponents who know the technology would be bigger (it was bigger in civ3).

I really hate the repercussions 3 and 4, but that is not your fault. That is just lazy programming from Firaxis (the modifiers for the new technology should be applied to the overflow, not the modifiers for the previous technology). This will again mean that micromanaging the technological research is beneficial. :(

I concur. It just sucks that micromanaging becomes somewhat important again.

Still, I want to make a few critical remarks to try and make the article completely error free.

1) Zombie69's remark.

Fixed.

2) the 1.28 factor in repercussion 1 should be explained because otherwise people will ask why 1.28? It is probably the largest modifier you can get for other civilizations knowing the technology which is 1+ 17/18 * 0.3.

Good point. Fixed.

3) The modifier for 1 more civilization knowing the tech seems to depend on the number of starting opponents as seen in the formula that you posted:

1 + RDDW (0.30 * # Civs who know the tech / # of Civs who started the game)

If one civilization knows a technology in a 2 player game, then this results in a modifier of 1.15. If one civilization knows a technology in a 5 player game, then this results in a modifier of 1 + 0.3 * 1/5 = 1.06.
So the table in the repercussions section is wrong or the formula is wrong or I'm not reading your article the way I was meant to read it.

Clarified hopefully. Please let me know if this makes it clearer.

Thank you for a great article. :goodjob:

You're welcome and thank you for the great feedback.

Req

Another repercussion is that you can try to figure out whether the players you've met have a particular technology by looking at the turns to research it on the Science Advisor screen. This would be a lot of effort for not much benefit, but it could be useful once in a while. Of course, it doesn't work for techs that you already have.

Isn't this already done in the Foreign Advisor? Or is that different somehow?

Req

Isn't this already done in the Foreign Advisor? Or is that different somehow?

I don't think the Foreign Advisor gives you any information about the techs of opposing civilizations until tech trading is enabled via Alphabet.

(Also, it may not give you any information in games with tech trading turned off---but I haven't played that variant, so I don't know.)

I don't think the Foreign Advisor gives you any information about the techs of opposing civilizations until tech trading is enabled via Alphabet.

(Also, it may not give you any information in games with tech trading turned off---but I haven't played that variant, so I don't know.)

Ah, I see. So, you mean pre-Alphabet tech info or non-tech trading tech info.

Ok, I'll add in that to the Repercussions section.

Req

Hi,

thanks for putting some beakers into researching this! ;)

It helped explain a lot of things I was confused about. Great work! :goodjob:

-Kylearan

Calculating the Known Civilizations w/ Tech modifier

1) Multiply 0.30 by the number of KNOWN civilizations, who have the tech.

2) Divide by the number of civilizations which STARTED on the map and ROUND DOWN to the hundredth place (0.01) of the quotient.

3) Add 2) to 1


Are you sure this applies to all difficulty levels? In the xml for the difficulty levels there is a field with "TechKnownModifier" or something like that in it. This value is 0 for all difficulties above Warlord.

Are you sure this applies to all difficulty levels? In the xml for the difficulty levels there is a field with "TechKnownModifier" or something like that in it. This value is 0 for all difficulties above Warlord.

I'm not completely positive about this, but the actual field is called "iTechTradeKnownModifier" which I believe is related to tech trading. I could be wrong about this, but someone else can test it out and let me know :mischief:.

Req

Well that's kind of what I'm interested in most is the value of the tech when trading. I'd like to know if the techs devalue as I trade them around to other AI's. But I guess someone else will have to figure that one out. I'm not tech savvy enough myself.

Well that's kind of what I'm interested in most is the value of the tech when trading. I'd like to know if the techs devalue as I trade them around to other AI's. But I guess someone else will have to figure that one out. I'm not tech savvy enough myself.

Ah, well, that's a WHOLE other subject. Which I might sometime tackle, if I have the time.

This thread is only devoted to Technology Research :scan: !

Req

Clarified hopefully. Please let me know if this makes it clearer.
Req

The modifications to the article have made it a lot better (and it was already good). If you write an article, then there are always things that are totally clear to yourself, but less clear to the readers that haven't thought about it that extensively. Good job!

I don't think the Foreign Advisor gives you any information about the techs of opposing civilizations until tech trading is enabled via Alphabet.

(Also, it may not give you any information in games with tech trading turned off---but I haven't played that variant, so I don't know.)

And maybe it also helps to see if there are other civilizations that are far ahead of you. In the Foreign Advisor, you can only trade for those technologies that you can research at the moment. If the research bonus (caused by civilizations that know the technology) is already applied to technologies that are further down the tech tree, then you can see if someone has already researched it. I must remark that this can be a lot of calculations for something that is not that interesting to know.


Didn't understand #3. As for #4, I disagree with you for the moment. For once, it SHOULD be the same as for hammers in a city (and here it is the same, the overflow of hammers that you get on the next turn are kept with the former modifiers). I will be totally against a difference between hammers and beakers. Now, I also think this is better, since the hammers/beakers were produced on a turn when you were building/researching something with some modifiers. The overflow is just stored, you know it beforehand, and so, no surprise next turn. As for more MM, it depends on what you want : if you want to get more hammers/beakers, then you'll have to delay the thing by 1 turn, which often means 1 turn of not-profitting from the building/unit/tech. On hard levels I'm sure it can sometimes be critical. It's a trade-off, you choose. And when you can run science at 100%, there's a cost for delaying the discovery, since you won't be able to run science higher on the next turn to catch back the delay.

I also know about the production overflow and it's micromanagement repercussions and I also don't like it. (I agree that both production and research should be treated in the same way.) It has to do a bit at how you look at the game. I think of it as a continuous game, where the ruler can make some changes at some moments in time. So if the year counter moves from 1510 to 1520 and the research produced is twice the amount that is needed to finish a technology then the technology is finished in 1515 and you give orders to research a new technology with new bonusses for that new technology.
I can see that you see this differently and that's ok.
What I really don't like about it is that it offers advantages to micromanage. This can be valuable when you're not running 100% research but something like 70% research (because you need the money for city maintenance or upgrading units). In that case fluctuating the research between say 20%, 60% and 100% at the moments this is advantageous as described by Requies in his article (repercussions 3 and 4) will still allow you to invest the maximum amount in research while taking optimal advantage of the research bonusses. This is a kind of micromanagement that I don't like. It's not smart or something, it's just micromanagement.

Awesome article! I will now be looking for prequisite techs when trading for techs because they give me an advantage in researching.

Again fantastic job. Most usefull article ive read so far.

Well, the overflow really is like with hammers though... all screwy but it seems screwy in a new way. For the sake of Firaxis fixing with a patch, the way to avoid ANY MM encouraged/rewarded with the hammer/beaker overflow is

Overflow-Overflow*(ALL output bonuses)/(All output Bonuses+1)=Base added to next 'thing' (that should then get its own bonuses)


PS I think there is a way you can simplify the prerequisites formula
Prereq bonus=1+0.2 * number of 'OR' Tech requirements that you have

The way to check this would be with techs like Divine Right which have no 'OR' options, do they get the *1.2 for having those minimum no 'OR' requirements fulfilled or not? If not, then the above simplification is the actual system.

Well, the overflow really is like with hammers though... all screwy but it seems screwy in a new way. For the sake of Firaxis fixing with a patch, the way to avoid ANY MM encouraged/rewarded with the hammer/beaker overflow is

Overflow-Overflow*(ALL output bonuses)/(All output Bonuses+1)=Base added to next 'thing' (that should then get its own bonuses)


PS I think there is a way you can simplify the prerequisites formula
Prereq bonus=1+0.2 * number of 'OR' Tech requirements that you have

The way to check this would be with techs like Divine Right which have no 'OR' options, do they get the *1.2 for having those minimum no 'OR' requirements fulfilled or not? If not, then the above simplification is the actual system.

ALL techs except the starting ones give at least a 1.2 boost to research. This includes those techs with NO 'OR' requirements.

Req

awesome article here :goodjob:

I have to say I am a little overwhelmed by all those equations. But, at least i get a better grasp of what's going on.
So, getting optional techs from the AI will be very useful. Problem is, that the tech tree at the moment is too confusing to actually help much in this respect at the middle stages of the tech tree.

And if I understand this correctly, it will hurt to beeline for an advanced tech. If that's true, I think it should be modified. Wasn't the claim that the tech tree is now very flexible?

awesome article here :goodjob:

I have to say I am a little overwhelmed by all those equations. But, at least i get a better grasp of what's going on.
So, getting optional techs from the AI will be very useful. Problem is, that the tech tree at the moment is too confusing to actually help much in this respect at the middle stages of the tech tree.

And if I understand this correctly, it will hurt to beeline for an advanced tech. If that's true, I think it should be modified. Wasn't the claim that the tech tree is now very flexible?

Like almost all other aspects of the game, it's a tradeoff. If you beeline for a tech, it means that your research will have the least bonuses possible. However, you DO get the benefit of that tech quicker as well as the advantage of having that tech when others do not.

Req

Excellent article. Some of the repercussions are ... weird. I agree with Krikkitone's suggestion on a good fix. But it also helps clarify some questions/issues about how beakers are counted. And adds some strategy layers to the tech order questions, which was already pretty convoluted.

Knowledge is always good, though. Great work!

Arathorn

ALL techs except the starting ones give at least a 1.2 boost to research. This includes those techs with NO 'OR' requirements.

Req

Too bad, that seemed like it might have been an easier way for them to do it. O well, so basically its 1.2 +0.2* 'extra prerequisites' for all non-starting techs.

So, tech MM in civ4 is still needed and actually more difficult. :)

Excellent article. Some of the repercussions are ... weird. I agree with Krikkitone's suggestion on a good fix. But it also helps clarify some questions/issues about how beakers are counted. And adds some strategy layers to the tech order questions, which was already pretty convoluted.

Knowledge is always good, though. Great work!

Arathorn

Thanks for the kind words Arathorn, Willburn, and ThERat.

Oh, yes, and I came up with a 7th (ED: so that Roland's repercussion matches with 5th), kind of small, repercussion related to the early game.

Req

The modifications to the article have made it a lot better (and it was already good). If you write an article, then there are always things that are totally clear to yourself, but less clear to the readers that haven't thought about it that extensively. Good job!

Thank you, and thank you for the contributions you made to it!


And maybe it also helps to see if there are other civilizations that are far ahead of you. In the Foreign Advisor, you can only trade for those technologies that you can research at the moment. If the research bonus (caused by civilizations that know the technology) is already applied to technologies that are further down the tech tree, then you can see if someone has already researched it. I must remark that this can be a lot of calculations for something that is not that interesting to know.

Note: this will only occur if your turn count actually CHANGES (but, actually now that I think about it, it probably will, considering 1.2 is not an inconsiderate amount of multiplier to add). I think I'll update repercussion #5. ED: Hmmm, I was mixing my modifiers. It would be at min 1.01, so it might not be noticeable.... You would need to get to 1.05 AND have a research time more than 20 turns to make it show up....

I also know about the production overflow and it's micromanagement repercussions and I also don't like it. (I agree that both production and research should be treated in the same way.) It has to do a bit at how you look at the game. I think of it as a continuous game, where the ruler can make some changes at some moments in time. So if the year counter moves from 1510 to 1520 and the research produced is twice the amount that is needed to finish a technology then the technology is finished in 1515 and you give orders to research a new technology with new bonusses for that new technology.
I can see that you see this differently and that's ok.
What I really don't like about it is that it offers advantages to micromanage. This can be valuable when you're not running 100% research but something like 70% research (because you need the money for city maintenance or upgrading units). In that case fluctuating the research between say 20%, 60% and 100% at the moments this is advantageous as described by Requies in his article (repercussions 3 and 4) will still allow you to invest the maximum amount in research while taking optimal advantage of the research bonusses. This is a kind of micromanagement that I don't like. It's not smart or something, it's just micromanagement.

I concur with this opinion. I'd rather handle the "big picture" things of Civ IV rather than the trivial, mundane ones which creep up just because a programmer got lazy :p.

Req

Note: this will only occur if your turn count actually CHANGES (but, actually now that I think about it, it probably will, considering 1.2 is not an inconsiderate amount of multiplier to add). I think I'll update repercussion #5. ED: Hmmm, I was mixing my modifiers. It would be at min 1.01, so it might not be noticeable.... You would need to get to 1.05 AND have a research time more than 20 turns to make it show up....

To estimate the actual ingame research cost of a technology, you could do the following:
1) Reduce the science slider to 0% and acquire 1 scientist in your empire.
2) Note how many turns of research it takes to acquire the technology
3) If it takes 350 turns to research a technology, then the research costs are between 349*3+1=1048 and 350*3=1050.
4) Now you can look at the basic cost of the technology (say 1200) and see that your research bonus is between 1200/1050=1.143 and 1200/1148=1.145.
5) Comparing this with the research bonus that you should get from prerequisite technologies and other stuff, allows you to get a pretty accurate picture of the number of opponents that know the technology. Comparing that with the opponents that actually have the prerequisites of the technology, maybe even allow you to make an educated guess about which opponents have this technology.
6) The science slider was only lowered to estimate the actual cost of a technology. It can be moved back to its original setting.

The fact that I know how to find this information doesn't mean that I'm actually going to do it. It's by far too much work for my taste. But it can be done.
The programmers of Firaxis could remove the possibility of acquiring this information by not allowing the 'known by other civilizations modifier' to effect a technology that you can't research yet.

We Civfanatics will probably always find ways to micromanage this game, but the most rewarding ways of micromanagement should be removed from the game and replaced by actual strategic decisions. Civ4 has done a good job in removing some of the micromanagement, but some of it is still there.

To estimate the actual ingame research cost of a technology, you could do the following:
1) Reduce the science slider to 0% and acquire 1 scientist in your empire.
2) Note how many turns of research it takes to acquire the technology
3) If it takes 350 turns to research a technology, then the research costs are between 349*3+1=1048 and 350*3=1050.
4) Now you can look at the basic cost of the technology (say 1200) and see that your research bonus is between 1200/1050=1.143 and 1200/1148=1.145.
5) Comparing this with the research bonus that you should get from prerequisite technologies and other stuff, allows you to get a pretty accurate picture of the number of opponents that know the technology. Comparing that with the opponents that actually have the prerequisites of the technology, maybe even allow you to make an educated guess about which opponents have this technology.
6) The science slider was only lowered to estimate the actual cost of a technology. It can be moved back to its original setting.

The fact that I know how to find this information doesn't mean that I'm actually going to do it. It's by far too much work for my taste. But it can be done.
The programmers of Firaxis could remove the possibility of acquiring this information by not allowing the 'known by other civilizations modifier' to effect a technology that you can't research yet.

We Civfanatics will probably always find ways to micromanage this game, but the most rewarding ways of micromanagement should be removed from the game and replaced by actual strategic decisions. Civ4 has done a good job in removing some of the micromanagement, but some of it is still there.

Ah, good point.... Heh, wasn't thinking too hard on that, I guess :scan:.

Req

I think one must be careful with any change/fix.A great game,such as this,must never have a single,sure,best strategy.
Best regards,

So, tech MM in civ4 is still needed and actually more difficult. :)

Well to be fair to Firaxis, their carryover still decreases the reward for MM over no Carryover, but you are correct in that it is still there. (and ridiculously complex) and being fair to Firaxis also means being critical of the fact that they seem to not have a grasp of basic math.

Rep, great article! I still have a question. I remember Sirian said that to avoid an isolated civ becoming too backwards, a civ will receive the "other civ knowing this tech" bonus no matter whether it knows the knowledagable civ or not. But you say that a civ must meet others for the bonus. Are you absolutely sure about this? If you are correct, I feel a bit disappointed, because it means another so-called new feature is gone ...

Rep, great article! I still have a question. I remember Sirian said that to avoid an isolated civ becoming too backwards, a civ will receive the "other civ knowing this tech" bonus no matter whether it knows the knowledagable civ or not. But you say that a civ must meet others for the bonus. Are you absolutely sure about this? If you are correct, I feel a bit disappointed, because it means another so-called new feature is gone ...

Well, I'm not 100% sure about this (but then, who is in life about anything? ;)), but ALL the testing I've done, shows this effect.

If you or someone else has a save where someone is isolated, I could check to see if this effect exists.

Req

Spectacular article Requies. Thank you for spending what I am sure was a considerable amount of time figuring this out...and thanks even more for taking the time to document your findings so well. :hatsoff:

The appreciation I feel toward you is even greater than the frustration I feel toward Firaxis for not mentioning these factors in the manual. And that means my appreciation is very, very high.

I would never expect Firaxis to give us the actual numbers, but they could have at least mentioned that knowing optional tech requirements affected research rate! [pissed]

If you or someone else has a save where someone is isolated, I could check to see if this effect exists.


I just looked at such a save, where i am in 1270AD, after a long war while isolated on a small island with one other civ. That civ is destroyed, and i met Victoria recently. Setting is Monarch, standard size, normal speed, 7 civs.

Everything seems to go as Requies said: for exemple, i skipped researching Meditation...which at such a late date, i expect more than one AI to have. However, the "number of civ" modifier is clearly 1.04, as should be expected from "1 known civ out of 7 starting civs knows the tech".

As a side note: i wonder if dead civs count or not? My destroyed neighbour was even more backwards than me, so i can't check on this save...but what would happen if he had researched Meditation before his death? Would the modifier be 1.04 or 1.08?


1) Reduce the science slider to 0% and acquire 1 scientist in your empire.
2) Note how many turns of research it takes to acquire the technology
3) If it takes 350 turns to research a technology, then the research costs are between 349*3+1=1048 and 350*3=1050.
4) Now you can look at the basic cost of the technology (say 1200) and see that your research bonus is between 1200/1050=1.143 and 1200/1148=1.145.
5) Comparing this with the research bonus that you should get from prerequisite technologies and other stuff, allows you to get a pretty accurate picture of the number of opponents that know the technology. Comparing that with the opponents that actually have the prerequisites of the technology, maybe even allow you to make an educated guess about which opponents have this technology.
6) The science slider was only lowered to estimate the actual cost of a technology. It can be moved back to its original setting.


I'm not sure i understand that. From Req's article, i understood that the "number of civs" modifier was applied to the generated beakers, not the cost of the tech (and that is indeed the result i get in my saves).
If we use 1 scientist, we generate 3 beakers, then multiply by the number of civs modifier (between 1 and 1.3), and take the floor...which still gives 3. So the number of turns should not change, whatever the number of civs who knows the tech.

Thanks though for the idea...for the test described above, i set the research slider to 0, and then used from 1 to 8 scientist specialists to get a controlled amount of beakers.

I'm not sure i understand that. From Req's article, i understood that the "number of civs" modifier was applied to the generated beakers, not the cost of the tech (and that is indeed the result i get in my saves).
If we use 1 scientist, we generate 3 beakers, then multiply by the number of civs modifier (between 1 and 1.3), and take the floor...which still gives 3. So the number of turns should not change, whatever the number of civs who knows the tech.

Thanks though for the idea...for the test described above, i set the research slider to 0, and then used from 1 to 8 scientist specialists to get a controlled amount of beakers.

Oh, yes, you're right. I forgot about the rounding down (floor) in the formula (stupid me). If you're actually researching a tech, then it is easier to attain the factor because you can look at the quotient of the number of beakers that are actually added in a turn and the number of beakers that were invested in a technology.

If you aren't researching a technology than using multiple scientist (or artists who produce 1 beaker) can allow you to find the factor after some calculations. After a certain amount of scientists added, you can see that the actual research time doesn't match with the research time that you should get if no research bonus is added (I guess that is what you did). It's probably too much work for most people to find the number of civilizations that know a technology through such cumbersome calculations.

If you aren't researching a technology than using multiple scientist (or artists who produce 1 beaker) can allow you to find the factor after some calculations. After a certain amount of scientists added, you can see that the actual research time doesn't match with the research time that you should get if no research bonus is added (I guess that is what you did). It's probably too much work for most people to find the number of civilizations that know a technology through such cumbersome calculations.

Yes, that's about what i did, and as you, i do not think it is worth doing it outside of a test. Too much calculations for such a small piece of information.

I just looked at such a save, where i am in 1270AD, after a long war while isolated on a small island with one other civ. That civ is destroyed, and i met Victoria recently. Setting is Monarch, standard size, normal speed, 7 civs.

Everything seems to go as Requies said: for exemple, i skipped researching Meditation...which at such a late date, i expect more than one AI to have. However, the "number of civ" modifier is clearly 1.04, as should be expected from "1 known civ out of 7 starting civs knows the tech".

As a side note: i wonder if dead civs count or not? My destroyed neighbour was even more backwards than me, so i can't check on this save...but what would happen if he had researched Meditation before his death? Would the modifier be 1.04 or 1.08?


Actually, if you have the savefile, I could take a look and see (I have my ways, :mischief:). Unfortunately, it looks like there's a limit to civfanatics if you wanted to upload it, but if you could make it available through another website (or if the zip fits - it would need to be < 500K), I could look into it and confirm if the dead civ really does alter it or not.

Req

Ok, here is the save file. I don't know if the dead civ had any tech i have not researched yet though.
The save is from the turn after i finished researching Alphabet, so there is an overflow in beakers from last turn.

By the way, i found amusing that the tip i received when loading that file, after reading this article, was along the way "do not research too much into one tech branch, as not researching older techs can slow you down". As if Firaxis was saying: "Ok, now that you know about the prerequisite thing, we can give you that one."

Ok, here is the save file. I don't know if the dead civ had any tech i have not researched yet though.
The save is from the turn after i finished researching Alphabet, so there is an overflow in beakers from last turn.

By the way, i found amusing that the tip i received when loading that file, after reading this article, was along the way "do not research too much into one tech branch, as not researching older techs can slow you down". As if Firaxis was saying: "Ok, now that you know about the prerequisite thing, we can give you that one."

Ok, got it. If you want to delete the savefile, you can.

Also, the article is updated.

Short version. Dead Civilizations do NOT contribute to the modifier.

Thanks for your idea and save game!

Req

Short version. Dead Civilizations do NOT contribute to the modifier.

Thanks for your idea and save game!



Thanks for the quick update, and that awesome article.

Finally read it. You've done great work !

What's bigger: your satisfaction solving this problem or your anger that Firaxis
couldn't make technology clear and simple and yet deep ?
So now we must calculate the different bonussus for the techs and MM-ing
the overflow... ( in dutch we call mm-ing 'mierenneuken', = 'ant***-ing').

Thanks for clearing the origin of the extra beakers :goodjob:

Asperge

Finally read it. You've done great work !

Thank you.

What's bigger: your satisfaction solving this problem or your anger that Firaxis
couldn't make technology clear and simple and yet deep ?

Well, neither one is that big, so I'd have to say they're the same. What I'm more angry at w/ Firaxis is their lack of documentation for modders and their haphazard way of allowing access to certain parts of the code.

So now we must calculate the different bonussus for the techs and MM-ing
the overflow... ( in dutch we call mm-ing 'mierenneuken', = 'ant***-ing').

Thanks for clearing the origin of the extra beakers :goodjob:

Asperge

Yeah, the MM-ing is a pain. Hopefully, they can "fix" it so that it and production don't require MM-ing.

As is, for the milkers and perfectionists, MM-ing is still a must....

Req

As is, for the milkers and perfectionists, MM-ing is still a must....

The available benefit from manipulating the overflow looks pretty modest, to me. My impression is that, in most cases, you would probably be better off just finishing the current research one turn sooner, than trying to arrange for a large overflow.

My hat off for you, Requies.
What a nice work!

I think there is a typo in the example, it says...
FLOOR (FLOOR ((37 + 1) * (1 + RDDW (0.30 * 3 / 7))) * (1 + 0.2 * (0.2 * 0))
...and it was meant to say...
FLOOR (FLOOR ((37 + 1) * (1 + RDDW (0.30 * 3 / 7))) * (1 + 0.2 + (0.2 * 0))
...I guess.

The available benefit from manipulating the overflow looks pretty modest, to me. My impression is that, in most cases, you would probably be better off just finishing the current research one turn sooner, than trying to arrange for a large overflow.

Actually, in v 1.52 the overflow problem has apparently been fixed for production, so it might have been fixed for research.

Actually, in v 1.52 the overflow problem has apparently been fixed for production, so it might have been fixed for research.

Ok, just upgraded to v1.52 after finishing the GoTM, and this has NOT been changed.....

So, everything is still valid.

Req

There is annother factor that you missed - team penalties.

For each additional player in your team, there is a 0.5 (or 50%) penalty added to the Difficulty Modifier.
This makes the final formula as follows:

Technology Cost = FLOOR (FLOOR (FLOOR (Base Cost * (Difficulty Modifier + Team Penalty)) * Map Modifier) * Speed Modifier)

With this formula, you can find the following:

(Noble has a difficulty modifer of 1, so...)
On Noble, a team of 2 yeilds 33.3% more research than a Solo Noble game.
On Noble, a team of 3 yeilds 50.0% more research than a Solo Noble game.
On Noble, a team of 4 yeilds 60.0% more research than a Solo Noble game.
On Noble, a team of 17 yeilds 88.8% more research than a Solo Noble game.
On Noble, a team of infinity yields nearly 100% more research than a Solo Noble game.

(Diety has a difficulty modifier of 1.3, so...)
On Deity, a team of 2 yields 44.4% more research than a Solo Deity game.
On Deity, a team of infinity yields nearly 160% more research than a Solo Diety game.


Compare this to noble -- the deity research penalty is lessened by being in a team, because of the way the formula works!)


What can be learned from this:
1) If you have a LAN party, it's more profitable to NOT be a team, and instead get a permanate alliance very late in the game. One person should to Alphabet, and the other person should get other technologies. When you meet eachother, continue to get seperate technologies and gift them to eachother when they are completed. Because it requires so much communication, I wouldn't reccomend it except on a LAN.

2) Two players who are at peace but not a team (the LAN party idea from #1) can beat the technology research of a team of 16 players. This means that you can win a 2v16 in a space race. Because research is so important, you could win a 3v15 using the same tactic with any type of victory condition. Using that tactic, you would have a 200% research boost, but the 15 player team would have only a 88.2% research boost.

3) If you choose a partner that can't match half as much research as you, then, because of the Team Penalty, he is actually hindering your science. In a team of two, both players need to be researching like they do in single player games.

4) The Difficulty Modifer is added only once per TEAM, and not per PLAYER. This lessens the effect of the difficulty modifer. Deity mode is still hard, though. :)




If you could quote me, and put this on the first page, that would be nice. :)

Like almost all other aspects of the game, it's a tradeoff. If you beeline for a tech, it means that your research will have the least bonuses possible. However, you DO get the benefit of that tech quicker as well as the advantage of having that tech when others do not.

Yep. The benefits of beelining are generally worth the missed techs AND the small loss of beaker bonuses. Most likely, the bonuses are to BALANCE beelining (it was pobably overpowered), not to NERF beelining.

One thing that is still overpowered is beelining to Alphabet, because missed techs are not nearly as much of a problem because you can trade for them afterwards.

And I really don't understand why they put in the +1 beaker when THEY DON'T USE IT IF YOU HAVEN'T FOUNDED A CITY.
Haha, yea, it doesn't really make sense, but there are a few times it is used:
-When you are in anarchy.
-When you have 0% science and have no beakers from specialists.

It is one way to get rid of "integer divided by zero" errors.

What I would have done is to make my OWN dividing function, and to make an exception for zeros. When dividing by zero, I would print "???" instead, to show that you have no research beakers. It's really annoying when it gives unrealistic estimates when you are in anarchy.

There is annother factor that you missed - team penalties. The formula is as follows...

T = 0.5 + 0.5N

...where N is the number of players and T is the Team Modifier

As N (the number of players) approaches infinity, T/N (the ammount of reseach required per player to get a tech) will become closer and closer to .5. Basically, this means a team of an infinate number of players will reseach technologies only TWICE as fast as a single player.

A team of 2 yeilds 33.3% more research.
A team of 3 yeilds 50.0% more research.
A team of 4 yeilds 60.0% more research.
...
A team of 17 yeilds 88.8% more research.
...
A team of infinity yields nearly 100% more research.


What can be learned from this:
1) If you have a LAN party, it's more profitable to NOT be a team, and instead get a permanate alliance very late in the game. One person rushes to Aphabet, and the other person gets other technologies. When you meet eachother, continue to get seperate technologies. Because it requires so much communication, I wouldn't reccomend it except on a LAN.

2) Two players who are at peace but not a team can beat the technology research of a team of 16 players. This means that you can win a 2v16 in a space race. Because research is so important, you could win a 3v15 using the same tactic with any type of victory condition. Using that tactic, you would have a 200% research boost, but the 15 player team would have only a 88.2% research boost.

3) If you choose a partner that can't match half as much research as you, then, because of the Team Penalty, he is actually hindering your science. In a team of two, both players need to be researching like they do in single player games.



If you could quote me, and put this on the first page, that would be nice. :)

Ah. I didn't do any research related to teams since I don't play teams :lol:.

I will quote you on this if you can clear up some things for me:

1) What exactly is the factor? Is it T = 0.5 + 0.5N (because that would mean that a 0.5 multiplier would be added for every new team member).

2) Where does this factor fit into the formula?

3) Does the modifier and/or the product of the modifier and whichever part it multiplies get floored?

Haha, yea, it doesn't really make sense, but there are a few times it is used:
-When you are in anarchy.
-When you have 0% science and have no beakers from specialists.

It is one way to get rid of "integer divided by zero" errors.

What I would have done is to make my OWN dividing function, and to make an exception for zeros. When dividing by zero, I would print "???" instead, to show that you have no research beakers. It's really annoying when it gives unrealistic estimates when you are in anarchy.

Ah, I guess that would make sense.....

Thanks,
Req

I found some other things that can be changed:
-All of your XML file paths are wrong (they are in the Assets\XML\GameInfo folder). The patch probably moved them.
-You are missing Marathon speed. It was added in the patch.
-The Word Size factors have changed in the patch.

I will quote you on this if you can clear up some things for me:

1) What exactly is the factor? Is it T = 0.5 + 0.5N (because that would mean that a 0.5 multiplier would be added for every new team member).

2) Where does this factor fit into the formula?

3) Does the modifier and/or the product of the modifier and whichever part it multiplies get floored?

1) T = 0.5 + 0.5N is the factor. Because the factor is added (see #2), you can just add Base*0.5*(N+1)*Speed Factor

2) It modifies the ammount of beakers required, so it changes the Technology Cost (insead of the beakers per turn formula). I did a bit of testing. On a Normal Duel map, Fishing went from 40 to 46 when I changed from Normal to Monarch. When I did the same thing but added a teammate, it went from 60 to 66. After a bit of thinking, I realized it couldn't be multiplied and produce numbers like that. It appears that it is an added factor, not multiplied, which is strange because all of the rest are multiplied.


The final formula is the following:
Technology Cost = FLOOR (FLOOR (FLOOR (Base Cost * Difficulty Modifier) * Map Modifier) * Speed Modifier) + Base Cost * 0.5 * (Number of Player +1) * Speed Modifier

3) Because the factor is added (see #2) and the Base Cost is always even, it does not need to be floored.

Edit: I edited my orginal post with the new info, and an additional use for it. Oh and BTW, thanks for this awesome guide! :)

I found some other things that can be changed:
-All of your XML file paths are wrong (they are in the Assets\XML\GameInfo folder). The patch probably moved them.
-You are missing Marathon speed. It was added in the patch.
-The Word Size factors have changed in the patch.

Ok, I might just remove the speed and World Size factor information as they will probably keep changing with each patch. Thanks for the headsup.



1) T = 0.5 + 0.5N is the factor. Because the factor is added (see #2), you can just add Base*0.5*(N+1)*Speed Factor

2) It modifies the ammount of beakers required, so it changes the Technology Cost (insead of the beakers per turn formula). I did a bit of testing. On a Normal Duel map, Fishing went from 40 to 46 when I changed from Normal to Monarch. When I did the same thing but added a teammate, it went from 60 to 66. After a bit of thinking, I realized it couldn't be multiplied and produce numbers like that. It appears that it is an added factor, not multiplied, which is strange because all of the rest are multiplied.


The final formula is the following:
Technology Cost = FLOOR (FLOOR (FLOOR (Base Cost * Difficulty Modifier) * Map Modifier) * Speed Modifier) + Base Cost * 0.5 * (Number of Player +1) * Speed Modifier

3) Because the factor is added (see #2) and the Base Cost is always even, it does not need to be floored.

Edit: I edited my orginal post with the new info, and an additional use for it. Oh and BTW, thanks for this awesome guide! :)

Ok, so this is a change in TECHNOLOGY COSTS, right? Ok. that makes more sense :D. Wouldn't the modifier be 0.5 * N (where N is the number of teammates a player has) or am I completely misunderstanding you? So, Fishing with no teammates on Noble/Duel/Normal would be:

FLOOR (FLOOR (FLOOR (40 * 1.0) * 1.0) * 1.0) + 40 * (0.5 * 0) * 1.0 = 40

While Fishing with a teammate on Monarch/Duel/Normal would be:

FLOOR (FLOOR (FLOOR (40 * 1.15) * 1.0) * 1.0) + 40 * (0.5 * 1) * 1.0 = 46 + 20 = 66

Also, is it the map modifier which affect the teammate technology cost? Or is it the speed modifier? (Or is it both?)

You say map modifier in your text, but in your formula you have speed modifier.

Thanks for the clarification!
Req

From a programming standpoint, it doesn't make sense to use FLOOR three times in one expression.
Could you test to make sure all three FLOORs are used? Most often (in my experience) only the outtermost expression is floored (and that's only because some programs store numbers as integers instead of a floats or doubles).

Ok, I might just remove the speed and World Size factor information as they will probably keep changing with each patch. Thanks for the headsup.
Nah, just update them. They are a nice refrence. :)



Wouldn't the modifier be 0.5 * N (where N is the number of teammates a player has) or am I completely misunderstanding you?
Number of teammates = number of palyers in the team - 1

We are both right. ;)

So, Fishing with no teammates on Noble/Duel/Normal would be:

FLOOR (FLOOR (FLOOR (40 * 1.0) * 1.0) * 1.0) + 40 * (0.5 * 0) * 1.0 = 40

While Fishing with a teammate on Monarch/Duel/Normal would be:

FLOOR (FLOOR (FLOOR (40 * 1.15) * 1.0) * 1.0) + 40 * (0.5 * 1) * 1.0 = 46 + 20 = 66
Correct.



Also, is it the map modifier which affect the teammate technology cost? Or is it the speed modifier? (Or is it both?)
D'OH! :blush:

Thanks for asking, I forgot to test the map modifier.

The difficulty modifier does NOT effect it, though. There is an easier way to write it now:

Technology Cost = FLOOR (FLOOR (FLOOR (Base Cost * (Difficulty Modifier + Team Penalty)) * Map Modifier) * Speed Modifier)

I edited the post again.

From a programming standpoint, it doesn't make sense to use FLOOR three times in one expression.
Could you test to make sure all three FLOORs are used? Most often (in my experience) only the outtermost expression is floored (and that's only because some programs store numbers as integers instead of a floats or doubles).

I agree with you. Unfortunately, that's what Firaxis has done :p. Yes, I tested it, and yes, I didn't believe they would do that, but the beast is what it is.

Nah, just update them. They are a nice refrence. :)

Unfortunately, I'm lazy :lol:


Number of teammates = number of palyers in the team - 1

We are both right. ;)


Correct.

Ok, gotcha.


D'OH! :blush:

Thanks for asking, I forgot to test the map modifier.

The difficulty modifier does NOT effect it, though. There is an easier way to write it now:

Technology Cost = FLOOR (FLOOR (FLOOR (Base Cost * (Difficulty Modifier + Team Penalty)) * Map Modifier) * Speed Modifier)

I edited the post again.

So, the map modifier DOES affect it then?

Req

So, the map modifier DOES affect it then?

Req
Yep. I modified my orginal post again. This time I am sure it's right.

*bump* so that everyone has a chance to read it.

Repercussions

1) It can be VERY important to establish contact with all the other civilizations in order to speed your beakers applied count. You could potentially be making 28% (17 known civs w/ tech/ 18 civs total) more beakers than you normally could on a tech. This is especially true on harder difficulties. If you just meet half of the other civs, your research on techs known by the others would improve by 14%. This is probably the biggest repercussion of the calculation.

Req

In the first example you give, you'll only be making 0.3*(17/18)/(1+0.2) -> 24% more beakers, because of the prerequisite 0.2 modifier that applies to everything but the starting techs. The percentage will be slightly smaller if more than one prerequisite modifier applies. The same effect means the 14% is wrong, too.

Just thought I'd point this out to help you improve an already excellent guide.

Actually the valuse stated are correct because the Tech knowm modifier and the Prerequisites known modifier are multiplied, not added as so many other ones are.

Actually the valuse stated are correct because the Tech knowm modifier and the Prerequisites known modifier are multiplied, not added as so many other ones are.

Oh yeah, you're right. My bad.

If tech overflow does work like hammer overflow then there might be a factor that I didn't see mentioned.

Hammmer overflow is limited to your base hammers I believe. (I checked once but it was a quick check - there is definitely a limit however - you can't build a wonder in 1 turn by building explorers and building up the surpluss).

If tech was also limited to your base number of beakers, then hitting one beaker below what is required would be bad because you would get a multiplier of 1.0 with the rest being lost.

It might be worth investigating if there is a maximum overflow for tech. It would change where you want to aim to maximize your beakers.

The maximum hammer overflow is equal to the production cost of the previous just finished project. If a similar limit existed in research, then it would only possibly hurt you if you were researching at a rate close to one technology per turn.

Also Research does not have something like Projects/ Wonders that you are not supposed to 'store up' for. There would be no reason to put a cap on overflow.

This whacked out formula kind of messes up a mod im trying to make. Basically I need to figure out how many research points are actually getting put into a tech each turn. Obviously simply calling the function getCommerceRate(CommerceTypes.COMMERCE_RESEARCH) wont give me an accurate number because it doesnt include all the factors in this formula. Is there another .get command that will provide me with the actual number? Or is there a way to subtract the current turns research progress from what it was the previous turn in order to get the real number?

There is annother factor that you missed - team penalties.
*snip*
1) If you have a LAN party, it's more profitable to NOT be a team, and instead get a permanate alliance very late in the game. One person should to Alphabet, and the other person should get other technologies. When you meet eachother, continue to get seperate technologies and gift them to eachother when they are completed. Because it requires so much communication, I wouldn't reccomend it except on a LAN.


Hm ok now I know why the AI somewhat manages to keep up when I play team with a friend vs. AI.

But I'm not sure if the advantages of gleaning the 33,3% on research is greater than the teaming-up advantages of somewhat linked starting positions, the early health/happyness resources trade and shared wonder effects to name a few?

Thanks for doing so much gruntwork and analysis! Once I'm awake enough to understand half of this, I'm sure it will help a lot.

I don't know why the program works as it does, that is giving you extra research which you can, in play, only detect because the increments of research per turn are larger than the amount of flasks reported. It would have been simpler for the player if the shown cost of the research was modified. This would in a way show how many other civs had a tech, as its research cost to you would fall progressively as the game progressed, rather than there being the concealed boost which is the subject of this thread.

The problem is any change in the cost of something can have much wierder effects than increases in the production rate.

In any case they should just have had the Flasks reported on the empire level show all the effects (ie X flasks from Cities + x% from modifiers for this tech)

Hi Requies,

Thanks for such a wonderful article! It was made even better by the work of all of the additional contributors.

Further to that point, the fact that you kept the first two posts up-to-date is what really made your article very useful. If everyone followed this intuitive and collaborative approach, it would make their contributions that much better and more appreciated.

I would like to note that there were a couple of points in your first post which I found to be ambiguous. Maybe you can help by cleaning up the wording just a slight bit.

Specifically, where you wrote:
"2) Divide by the number of civilizations which STARTED on the map and ROUND DOWN to the hundredth place (0.01) of the quotient."

it might be a bit clearer if you changed it to something like:
"2) Divide by the number of civilizations which STARTED on the map, including your own civilization, and ROUND DOWN to the hundredth place (0.01) of the quotient."

It wasn't until I read through your repercussions that this point was clear for me.

A similar clarfication could be made in your example, to re-inforce this point, or for the benifit of those people that only read the example:
"You produce 37 net beakers per turn and you have met 3 other civilizations who know it out of 7 who started the map."
->
"You produce 37 net beakers per turn and you have met 3 other civilizations who know it out of a total 7 civilizations, including your own civilization, who started on the map."


Further, where you wrote:
"Tech Known by Civilizations modifier = 1 + RDDW (0.30 * # known Civs who have the tech / # of Civs who started the game"

does RDDW mean RounD DoWn? I was first misled into thinking that "RDDW" referred to some strange constant that I'd missed, until I read through your example. :)

I guess maybe just an additional line defining RDDW, something like the following, would add a bit more clarity:
"RDDW = ROUND DOWN to the hundredth place (0.01) of the quotient"

Overall, masterfully explained.

Oh, and one further thing. I believe I read in another thread that the bug represented by Repercussions 3) and 4) was corrected in patch version 1.61. Do you know if this point is true? Maybe someone else can confirm it. If it is true, maybe you can make note of it somewhere at the top of this thread, such as in your second or third post?

Also, though I like some features that are driven from your theory (discount for optional prerequisites is one of those), I dislike some other features (the +1 beaker that you get in any case, totally NOT needed and wrong IMHO).

Yeah, I like the optional prerequisites, but I DON'T like the way overflow is calculated for the reason Roland points out. And I really don't understand why they put in the +1 beaker when THEY DON'T USE IT IF YOU HAVEN'T FOUNDED A CITY.

I think that I have a decent answer for why the +1 beaker is not provided when you do not have a city.

Consider what would happen if you did receive such a beaker. For most players, if they settle right away, they will not even notice the difference made by the extra beaker. Admit it, before the reasearch for this article was done, I'll bet very few of you knew about this extra beaker.

However, assume that you choose that instead of settling, you would like to find a different starting spot that takes you at least one turn to get there. Civ 4 GOTM 10 is one such example, where in the pre-game discussion forum, several players have discussed spending their first turn to move to a grassland hill.

If those players received +1 beaker for that first turn, what would happen? Well, a tech-selection dialogue would pop-up. Yet the costs of each technology would be the full amount. So for a tech which costs 120 beakers to research, the time to research would appear to be 120 turns!

On the following turn, after they found their city, the time to research might jump to, say, 10 turns! What a crazy usability nightmare!

Nearly everyone playing the game would think that it's buggy. People would laugh at the game, try and return it, or just discard it. Few of us would be sitting here right now, talking and reading about the mechanics of a totally awesome game, just because of a seemingly simple change that would give the appearance of very buggy software.

Another implication of getting a tech selection screen without founding a city would be that the concepts of "having cities" and "researching techonologies" would be de-coupled. Consider a first-time a player who chose to move instead of settle on their first turn. They'd run into this situation. Sure, eventually people would figure it out--you need cities to actually make a decent amount of research. However, a first impression is a strong one. The impression would be that cities are not necessarily relevant to technological research. The association that you want to build in the minds of new players is that they must build cities in order to properly research technologies, and such an association would be lost.

Any of you reading this post could easily extrapolate that "yes, the +1 beaker is minimal compared to even just the contribution of your capital with its +8 commerce palace and its initial center square of +1 commerce, in addition to any commerce from your first citizen working a tile. Therefore, it should be obvious that I need to build cities". However, how about the initial impressions of someone just learning the game, like your girlfriend? She'd think that it was very stupid for the tech rate to jump around from 120 to 10 over the course of one turn. She probably wouldn't play the game past the first few turns and she would likely convince you not to play it, either.

Personally, I think that this game has a very strong appeal to both sexes, unlike a lot of games that you have probably played. So I'm quite happy that they did not introduce this potentially disasterous usability issue and that both my girlfriend and my brother's girlfriend enjoy playing this game.

It is one way to get rid of "integer divided by zero" errors.

What I would have done is to make my OWN dividing function, and to make an exception for zeros. When dividing by zero, I would print "???" instead, to show that you have no research beakers. It's really annoying when it gives unrealistic estimates when you are in anarchy.

Building on what kryszcztov said, LordTerror makes an interesting point about how the whole concept of the +1 beaker breaks down and might have been better designed.

However, my point is that since they chose to use the +1 beaker concept, they could not afford to give it to a player, at least at the start of the game, until a player has at least one city.

If those players received +1 beaker for that first turn, what would happen? Well, a tech-selection dialogue would pop-up. Yet the costs of each technology would be the full amount. So for a tech which costs 120 beakers to research, the time to research would appear to be 120 turns!

This always happens, if your research is at 0% so you're only generating 1 beaker per turn. It's not a "usability nightmare", at all.

Agreeing with DaviddesJ, the real usability nightmare would be when you're in the middle of anarchy or simply running at 0% science and all of your techs say they'll take an infinite number of turns. You wouldn't be able to, at a glance, determine which techs are more expensive than others. The 1 beaker per turn minimum avoids this scenario nicely.

Anyone notice that in 1.61, tech overflow is lossy? Instead of getting either the current multiplier (which would be the correct behavior) or the previous multiplier, overflow beakers don't get any multiplier at all -- in effect you lose at least 1/6, often more, of your investment. So, overflow is no longer exploitable, that's a good thing... but on the other hand, this brings us back to the situation we had in previous versions of Civ, where you were usually compelled to micromanage the last turn before discovering a tech.

Anyone notice that in 1.61, tech overflow is lossy? Instead of getting either the current multiplier (which would be the correct behavior) or the previous multiplier, overflow beakers don't get any multiplier at all -- in effect you lose at least 1/6, often more, of your investment. So, overflow is no longer exploitable, that's a good thing... but on the other hand, this brings us back to the situation we had in previous versions of Civ, where you were usually compelled to micromanage the last turn before discovering a tech.

Is this true? Nobody seems to have commented/confirmed this... but if it is true, it makes this entire thread dated (at least all the discussion specifically about overflows) and would have a huge implication in terms of micro-managing...

Is there any direct way within the game to check what the overflow is? I have been trying to see, and am having some difficulty. When one finishes researching a technology and is asked to choose the next one, it always shows the current research status as '0 beakers out of X beakers' (where X is the cost of the new tech, of course), instead of showing the 'overflowed' beakers as already inputted into the new research. Then in the next turn, it shows 'Y beakers out of X beakers' as the amount of research you have accomplished into the new tech. Y always seems to be more than the number of beakers you are actually generating (as shown by the Finance advisor) but it is not clear whether the excess is due to 'overflow' from the previous tech or because of the 'modifiers' for the new tech which have given a bonus on the beakers generated in the first turn of research into the new tech. Is there any way to see what the overflow actually was?

Is this true? Nobody seems to have commented/confirmed this... but if it is true, it makes this entire thread dated (at least all the discussion specifically about overflows) and would have a huge implication in terms of micro-managing...

It's certainly not "huge". You can just turn your research rate down to the minimum to complete the research, on the turn you finish it. This is what most people tend to do anyway, for flexibility, I think.[/QUOTE]

It's much less of an issue than the cases, in previous versions, where you sometimes wanted to maximize overflow, rather than minimizing it.

Anyway, it's a known issue, and I believe it's going to be fixed in the upcoming Warlords patch.

You can just turn your research rate down to the minimum to complete the research, on the turn you finish it. This is what most people tend to do anyway, for flexibility, I think.

In Civ3, I used to do that too - because there was no 'overflow' and the excess beakers on the last turn simply used to be lost. One of the nice thing about civ4 was this notion of 'carry over' (for hammers, beakers etc) so that one didn't feel the need to micromanage the last turn.

In any case, to repeat my question, is there any way to actually CHECK what the overflow of beakers is? In the case of hammers, the overflowed number is explicitly shown by the game (within the city screen). Why isn't this the case for beakers? Are we even sure that there IS an overflow? (or could version 1.61 have gone back to the civ3 model of 'no overflow'?)

In Civ3, I used to do that too - because there was no 'overflow' and the excess beakers on the last turn simply used to be lost. One of the nice thing about civ4 was this notion of 'carry over' (for hammers, beakers etc) so that one didn't feel the need to micromanage the last turn.

True, in principle, but it's much, much less of an issue with beakers than with hammers. With beakers, you often want to turn down the research rate anyway, as it preserves flexibility as to what to research next (and how quickly). With hammers, it's a huge problem, both because you have to do it in every single city, not just one global screen, and because there's not always something to do instead of generating hammers, while you are almost always happy to take gold instead of beakers (and then beakers instead of gold, later on).

And the effect is also much smaller than in Civ3.

Especially if it's going to be fixed anyway, it just doesn't seem worth getting worried about.

In any case, to repeat my question, is there any way to actually CHECK what the overflow of beakers is?

I don't see why this is hard. Just play another turn, with research at 0%, and see how many beakers end up in the research project.

I don't see why this is hard. Just play another turn, with research at 0%, and see how many beakers end up in the research project.

Hmm... why couldn't i think of that myself!! :blush:

Upon reflection, i agree with you that the research overflow (without modifiers) isn't such a big issue. However, i do wonder how they plan to 'fix' it... the way research is structured in the game, it seems that ANY solution they favour (no overflow/overflow but with no bonus modifiers/overflow with previous modifiers/overflow with new modifiers) would all lead to some 'micromanagement' compulsions...

Upon reflection, i agree with you that the research overflow (without modifiers) isn't such a big issue. However, i do wonder how they plan to 'fix' it... the way research is structured in the game, it seems that ANY solution they favour (no overflow/overflow but with no bonus modifiers/overflow with previous modifiers/overflow with new modifiers) would all lead to some 'micromanagement' compulsions...

When you're researching technology 1, you get research multiplier X1 (i.e., generating B beakers puts B*X1 into researching technology 1). When you switch to researching technology 2, you get research multiplier X2. So the beakers that go into tech 2 should be (overflow from tech 1)*X2/X1.

This is already how production overflow works; it's no harder to do the same for research.

Since research in Warlords is computed to 1/100 of a beaker, even rounding issues are not material.

But whether it will actually be right after the patch, I don't know.

So the beakers that go into tech 2 should be (overflow from tech 1)*X2/X1.

Yeah, you're right... that WOULD fix it. :goodjob:

If they have managed to see the above logic for production overflows (i didn't know it worked that way for hammers) then i am sure they should be able to do the same for beakers in the next patch.

In any case, i don't have warlords (it hasn't reached shelves in my part of the world yet), so i hope they release a patch applying the same fix for vanilla civ4 too...

In any case, i don't have warlords (it hasn't reached shelves in my part of the world yet), so i hope they release a patch applying the same fix for vanilla civ4 too...

My impression is that there will never be any more patches for vanilla Civ4, after 1.61. :(

My impression is that there will never be any more patches for vanilla Civ4, after 1.61. :(

There is a user-created fix at http://apolyton.net/forums/showthread.php?s=&threadid=157232.

I ve following problem.
I play MP with 7 teams.
For research of a tech (with Prerequisites modifier = 1,2) with cost 149, I get following answers, if I change to the tech, also no overflow:
1) with 13 k in 9 turns, also >= 17 beakers
2) with 14 k in 9 turns.

with the formel in post 1 I get:
from 1) 13 + 1 = 14 *(1 + k*0,3/7) >= 17/1,2=14,17 also ist k=2
from 2) 14 + 1 = 15 *(1 + 2*0,3/7) = 16,2 also 16*1,2 = 19,2 also 19 beaker, also research in 8 turns, against the ingame message of 9.

Question: what's wrong with the situation, how many teams have the tech?

btw sry, if my english is not so good; it's not my native.

The overflow is calculated by the modifiers from the PREVIOUS Technology.


Does the overflow stack up? Say, you make 500 beakers a turn and want to grab a few ancient techs which you avoided (no tech trading), like Aesthetic, Literature, Drama and Music. If after that your research a more costly technology which would normaly need more than one turn, will you get an overflow to which all the modifiers where applied multiple times? Or is it cut like the production overflow and it would be more efficient to lower your research level?

I realize this is an older thread and unlikely to be edited, but I was just pointed here in order to answer one of my questions (it was answered) and found an error. True I use BtS and the HOF mod so maybe things have changed. The error is in step 2 of the basics where it says So, yes, you WILL get AT LEAST one gold from each city that has a commerce that is not a multiple of 10, if your science or culture is not 100%

I have 3 cities and my commerce is not a multiple of 10 in any of them. If my gold is at 10% I should get at least 3 gold per turn according to this statement, but I get only 2. Here are the numbers. City #1 pulls in 16 commerce. Both other cities pull in 4 each, for a total of 24 commerce each turn. At 10% gold, I generate 1.6 + 0.4 + 0.4 gold which is 2.4 gold floored to 2. Or it could be that the rounding (to nearest) is happening before the addition, so let's disprove that. (By this I mean 2(1.6) + 0(0.4) + 0(0.4)). If city #1's commerce is reduced to 14 then 1.4 gold would be rounded to 1 and I'd get only 1 gold per turn. Since I get 2 we know the rounding happens after the addition. And further to prove that the type of rounding is flooring and not rounding to the nearest, we increase the commerce to 26. 2.6 still turns out 2, not 3, so 2.6 must be floored.

So, given that I have 24 commerce (and ignoring the +1 science for having a city and all other modifiers), if I set it to 100% science I get 24 science and 0 gold. If I set it to 100% gold I get 0 science and 24 gold. Unfortunately, if I set it to 90% science and 10% gold I get 21 science and 2 gold. Similarly, if I have 10% science and 90% gold I get 2 science and 21 gold.

So the correct formula for science and gold generated is, quite simply;
FLOOR (rate * commerce)
(+1 science if there is a city).

Therefore, you will often lose 1 commerce if your slider is not set to 100% of something. What I often do to achieve a 80% science rating, say, is do 1 turn of 100% gold then 4 turns of 100% science. This might not always be a good idea though.

I realize this is an older thread and unlikely to be edited, but I was just pointed here in order to answer one of my questions (it was answered) and found an error. True I use BtS and the HOF mod so maybe things have changed. The error is in step 2 of the basics where it says

I have 3 cities and my commerce is not a multiple of 10 in any of them. If my gold is at 10% I should get at least 3 gold per turn according to this statement, but I get only 2. Here are the numbers. City #1 pulls in 16 commerce. Both other cities pull in 4 each, for a total of 24 commerce each turn. At 10% gold, I generate 1.6 + 0.4 + 0.4 gold which is 2.4 gold floored to 2. Or it could be that the rounding (to nearest) is happening before the addition, so let's disprove that. (By this I mean 2(1.6) + 0(0.4) + 0(0.4)). If city #1's commerce is reduced to 14 then 1.4 gold would be rounded to 1 and I'd get only 1 gold per turn. Since I get 2 we know the rounding happens after the addition. And further to prove that the type of rounding is flooring and not rounding to the nearest, we increase the commerce to 26. 2.6 still turns out 2, not 3, so 2.6 must be floored.

So, given that I have 24 commerce (and ignoring the +1 science for having a city and all other modifiers), if I set it to 100% science I get 24 science and 0 gold. If I set it to 100% gold I get 0 science and 24 gold. Unfortunately, if I set it to 90% science and 10% gold I get 21 science and 2 gold. Similarly, if I have 10% science and 90% gold I get 2 science and 21 gold.

So the correct formula for science and gold generated is, quite simply;
FLOOR (rate * commerce)
(+1 science if there is a city).

Therefore, you will often lose 1 commerce if your slider is not set to 100% of something. What I often do to achieve a 80% science rating, say, is do 1 turn of 100% gold then 4 turns of 100% science. This might not always be a good idea though.

This was changed some time ago. In the earlier versions of civ4, gold and science production in cities was rounded to integer numbers which resulted in all kinds or rounding issues and making a on-off research policy even more important. There was some discussion about it in those days and in some patch or expansion pack it was changed so that gold and science and culture is calculated with more accuracy.

While the rounding system now does take into account the .xx component of the commerce, when the commerce or science is displayed on the main screen next to the slider rate, the decimal number is not shown.

The 20% bonus for prerequisite is still floor'd afterwards, right? (Hammers too, if they get modifiers.)

I have either 11 or 9 commerce at start. To research mining (cost displayed 585 beakers) I take 42 turns if I work the lake (11 commerce) or 49 turns if I work the forest (9 commerce). I have a mandatory prerequisite of it, mining.

Floor((11+1)*1.2) = 14, 14*42 = 588
Floor((9+1)*1.2) = 12, 12*49 = 588

Is it calculated like this?

Now for something interesting. Though not surprising, but it seems to contradict what VirusMonster says (BTS).

I have 1 town, producing 11 commerce.
At 90% slider, that becomes 9.9
If I research a technology that I have a 20% bonus for, I get 12 beakers/turn.

Floor(9.9+1)*1.2 = 12

It can't be Floor((9.9+1)*1.2), for that is 13.
It can't be Floor(9.9*1.2+1) either. That one is 12 as well, but at 9 commerce, 100% slider I get 12 commerce per turn.

So rounding errors still make your life harder. Of course, I believe, the more cities you get, the better it will be, cause I suppose the numbers only get floored after all cities are added up.