The science of science

[freshman]

Well, OK, just one facet of science anyway; topics in this post include effects of Science Wonders, and also science rate rounding. This issue came up in another thread (Perfect Timing in OCC) because in order to be able to anticipate what your beakers will be the turn your wonder is built, you need to understand its effects.

Ignoring specialists, improvements, and wonders, your tax/luxury/science output is calculated from your tax-rates and your net trade (minus corruption) with rounding. If a fraction is above .5 it is rounded up, if it is .5 or less, it is rounded down. All of your trade should be accounted for, except possibly 1 more excess, which gets added to your GOLD.

As an example if you have 5 trade:
a 0-5-5 (tax-lux-sci) rate yields 1/2/2 (50% of 5 is 2 rounded down, only 4 trade are accounted for so there was 1 excess which goes to tax).
a 0-4-6 rate yields 0/2/3 - no rounding in this example
a 0-3-7 rate yields 1/1/3 - (30% of 5 is 1 rounded down, 70% of 5 is 3 rounded down, 1 excess goes to tax)
a 5-0-5 rate yields 3/0/2 (50% of 5 is 2 for tax and sci., 1 excess goes to tax)

Thats the story of the base quantities calculation.

Specialists = add 3 to your base tax/lux/sci

Improvements = get that extra 50%,100%,150% and always round down if your base is an odd number (fractions of .5 are always rounded down)

Wonders: special

Here's a table of all combinations of Science Wonders and Improvements:

Improvements__None__Library__Univ__Lab
None_________x1____x1.5r____x2___x2.5r
Cops_________x2____x1.5r,x2__x4___x2.5r,x2
Isacs_________x1____x2______x3___x4
C+I__________x2____x4______x6___x8

Here's the true story of wonders effects:
Isacs does NOT double science output as is mentioned in the Civilopedia; it does however double the bonus from a science improvement.
Compare the None line with Isacs line.
A library is +50% (1.5x) and with Isacs is +100% (2x)
A University is +100% (2x) and with Isacs is +200% (3x)
A Research Lab is +150% (2.5x) and with Isacs is +300% (4x)

Copernicus simply doubles the previous calculation, which includes any rounding.
A science base of 9 with a Library and Copernicus is [9*1.5]*2 = 13*2 = 26

So a one line summary is Isacs doubles science improvements, Copernicus doubles your science after improvements are taken into account.

[Marquis de Sodaq]

ahem...

This looks like a good start for compiling info for the Great Library! Are you interested in culling the archives and current discussions for relevant info to make a summary thread?

Did you test using any particular size cities, or does this apply across the board?

[fittstim]

With the 0-5-5 rate, the extra trade goes into tax (for some unexplainable reason).

But when you change the rate to 5-0-5 or 5-5-0, does the extra trade go into the empty slot (the one with 0%) or does it always end up in tax?

[freshman]

Marquis,
I don't really understand what you are asking me to do. This one post seems sufficient on its own. If you want it to be linked in the library, go ahead. I don't exactly know how to do it myself.
I'm happy, though, that you think it's worthy enough. As a newbie, I've sure learned a lot from the GL.


fittstim,
as I mentioned, and I'll quote myself:

a 5-0-5 rate yields 3/0/2 (50% of 5 is 2 for tax and sci., 1 excess goes to tax)

So yes, excess ALWAYS goes to tax. I guess this is to prevent fire sales in a tight game; and gold really is the most liquid commodity vs. science or luxuries.

[freshman]

Did you test using any particular size cities, or does this apply across the board?

Sorry Marquis, I forgot to answer you. I tested a city which had 17 trade, which when adjusting the science rate from 40% to 100% gave be base science of all moduli of 4, which was necessary to figure out how the rounding worked with the multipliers (ie. at 40% science beakers are 7 = 3 (mod 4), at 50%, 8 = 0 (mod 4), at 60% 10=2(mod 4), and at 100% 17=1(mod 4) )
I did play around with other amounts of trade, but it always works the same way. It is a really easy test to do, and I'm surprised nobody has published results on it yet.

[Blaupanzer]

Someone is publishing results. Thank you, Freshman.

[freshman]

Cool - I'll have to update it because : I've just discovered an anomally with rounding. It happens when there is 6 or 7 mod 10 trade (ie 6,7,16,17,26,27,... trade) and rates set to 80-10-10
Then it appears that there is a trade deficit (vs. excess going to gold) and I'm not sure how Civ handles it because I don't have Civ with me here at work:
10% of 7 is 1 rounded up
10% of 7 is 1 rounded up
80% of 7 is 6 rounded up
which means 8 tax/sci/lux out of only 7 trade. (does the deficit get subtracted from gold?? Can't test this out yet). Or do you actually get more out of your trade this way??

[freshman]

Near as I can tell these are the only cases when you have an excess gold:
rate____trade(mod10)
9-1-0____5
8-1-1____3,4,5
7-3-0____5
7-2-1____2,5
6-3-1____4,5
6-2-2____2,7
5-5-0____1,3,5,7,9 (of course!)
5-4-1____1,3,5
5-3-2____1,5,7
4-4-2____1,6

And these are the only cases when you have a deficit (I don't know how this gets applied - is it bonus, or is it subtracted?)

rate____trade(mod10)
8-1-1____6,7
7-2-1____8
6-3-1____6
6-2-2____3,8
4-4-2____4,9

[Paul]

City with 7 trade and 80-10-10 tax-sci-lux gives 5 tax, 1 sci, 1 lux.
10-80-10 gives 0-6-1
10-10-80 gives 0-1-6

So everything gets rounded to the nearest integer (.5 rounded up) and if that adds up to more or less than the total amount of trade arrows, the difference is added to or taken from tax.

[freshman]

So everything gets rounded to the nearest integer (.5 rounded up) and if that adds up to more or less than the total amount of trade arrows, the difference is added to or taken from tax.

Thanks Paul for verifying that it gets subtracted in those other cases; I feel lost without a copy of civ to verify these things. BTW .5 is always rounded DOWN.

[Paul]

You're right of course. .5 is rounded down.

[Marquis de Sodaq]

Originally posted by freshman
Marquis,
I don't really understand what you are asking me to do. This one post seems sufficient on its own...

As a reader eager to see more details like this, the idea would be to make a summary thread for this and closely related information. My suggestion to cull the archives is only to gather any other relevant info that has been discussed. This would include falsehoods, more examples, and such. However, if you feel this is enough to summarize the topic, thank you for what you have posted! I find the truth about Isaac Newton's College to be enlightening. Maybe Mr. Newton will need to drop tuition now...

[freshman]

I dont really have time to "cull the archives", though I'd really like to help out.
I do have another experiment I'd like to perform, but once again I don't have a Civ-game handy right now. Once you've built a University, can you sell your library? Or sell your University after you've built your lab?? My guess is that the bonus you'd get would be +50% for each improvement, no matter which ones you still have after selling.

[cpemma]

Selling library or uni gave me a drop in beakers in that city. (I had SETI)

Same with market/bank/SE - effects are strictly cumulative

[Blaupanzer]

Same is true with factory/manufacturing plant. This is a "feature" of Civ II, correcting this exact behavior in Civ I, where many players sold the lesser improvement once the next one in the chain was completed. In Civ II, each improvement contributes its share.