I just thought I'd jot down this quick tactical tip before I forgot it.


It's usually impossible to have the science slider adjusted to keep your net income at exactly 0, but even if you could, you really shouldn't want to.


If you have libraries or universities building, run your research lower to put yourself in the black, so that you can run deficit research later when it'll count for more.

Likewise, if you have markets/grocers/banks building, run deficit research until you can get your money's worth out of them (25% of 10% of your nation's commerce is pretty pathetic compared to 25% of 20%).


Just a rule of thumb I like to keep in mind. It's perfectly logical and easy to work out, but it's not something you want to have to extrapolate in the middle of a game.

so that you can run deficit research later when it'll count for more.

i'm quite a newbie, but how to run deficit research???

A tip is only good if your audience understands it.

What does deficet research mean, and how does one do it?

Very respectfully,

Cowabunga

I can help! Click the <+> button close to the little green bottle on the top left of the screen until it reads 100%. Then continue some turns and you will experience 'deficit research'. That's all!
/Blue

To be clearer, when I said "deficit research", I meant keeping the science bar high so that your net income is negative each turn, and eating into your treasury.

What does deficet research mean, and how does one do it?


Deficit research is shorthand for "converting commerce to beakers at a rate such that gold per turn is negative"

The game normally starts running at 100% research, but as expenses (city/unit maintenance) rise, the beaker rate is automatically lowered each time you run out of gold. You can micro manage this by adjusting the science rate yourself - either on the main screen (using the +/- buttons next to the beaker per turn report), or on Financial Advisor screen.

When you have researched Drama, you can do the same thing with the culture slider.

The strategy note also suggests that the Free Market civic (available with economics) allows deficit spending, but I haven't experimented with that (although, in looking this up - I haven't found anything that confirms the strategy note. For example, the description of Free Market on the civics screen makes no mention of this.)

You have tried to define your way out of this, but the English language does not work this way.

http://www.wordreference.com/definition/deficit

Therefore Deficit Research = Negative number of beakers.
Or at least, less beakers than you consume in a turn. (Assuming that is even possible)

Further Proof:
http://www.investorwords.com/601/budget_deficit.html
http://www.investorwords.com/5020/trade_deficit.html

rupertlittlebea, you are giving the definition for "research deficit".

The definition of "deficit research" is similar to "deficit spending".
http://www.investorwords.com/1373/deficit_spending.html

rupertlittlebea, you are giving the definition for "research deficit".

The definition of "deficit research" is similar to "deficit spending".
http://www.investorwords.com/1373/deficit_spending.html

Similar? It's the exact same thing. You are spending more money than you're bringing in to fund the research.

Put your science slider above 100%?
I don't understand what are you talking about?

This would be help if I built all of my libraries, universities etc. at the same time in each city. But things never work out that way.

Well, just keep it in mind if you're building like 2 libraries at the same time, or perhaps a university/acadamy in your biggest commerce city is upcoming. The savings really add up, and altogether, simple management of the science bar can shave 2-3 turns off of your overall research throughout the course of the game.

One strat that works out nicely if you banks in place is to put research to 0 for a few turns and build up a huge gold supply. Then running a deficit for more research later on. In a pinch, that gold can be used for an emergency upgrade of your units too, should someone declare war on you out of the blue.

I go much further than this.

When i've just discovered the tech for libraries or universities, i'll set research to 0% until i've got the most important ones built up. Then i'll set research to 100% for as long as i can. The same thing applies to banks, markets and grocers, but in reverse. I'll let my gold slide down to zero, or as close to it as i can while building them.

In fact, i never set both research and taxes at non-zero values at the same time. This is the real optimal way to do this. I played this way in Civ, in Civ 3, and i still do it now in Civ 4. Here's why.

Let's say that your best commerce city produces 20 commerce. It has +35% science and +25% gold. Anyway you slice it, if one of your percentages isn't set to zero, you'll be losing fractions each turn. For example, if you set science to 80%, you'll get 16 + 35% = 21.6 science, rounded down to 21. You'll also get 4 + 25% = 5 gold. There is no percentage at which you won't be losing fractions, especially when you consider the other cities in your empire.

In 5 turns, you'll get 105 beakers and 25 gold. By instead setting science to 0% on turn 1 and then to 100% on the next 4 turns, you'll get 27 * 4 = 108 beakers, and 25 gold. Congratulations, you've just saved 3 beakers of wasted fractions.

As soon as at least one of your cities gets any kind of bonus to either science or commerce, or both, the most optimal way to go, no matter what the percentages are, no matter what the bonuses are, no matter what kinds of cities you have, is always to have either science or commerce at 0%, and fluctuate between the two.

Sure, it's a little more micromanagement, but it pays off in the long run. For a perfectionist such as myself, it's a must, and i wouldn't do it any other way.

This is what i have underdstood about the beaker/gold slider thru various threads.
Some income producing methods such as cottages (call this method A)make you gold that you can use every turn to invest in research. You need to make money to pay for this research, just like in the real world. Then you have other income methods that make you money such as selling stuff to other civs or sending a merch to another civ (just some examples, call this method B), These provide you with cold hard gold, like a paycheck. This gold goes straight to the treasury.

Now you have the BEAKER slider that is an adjustment between how much gold you SAVE and put in your treasuries (from method A stuff) and at what capacity your civ runs research. The higher research capacity you run at the more gold is needed per turn. When the per turn gold generated by cottages (for example, method A) is not enought to cover what is needed for research, then your financial guy gets what is needed from your treasuries. So you may be trading every turn and making money (using method B)for the treasury, but be runnung in the red when it comes to the BEAKER slider.

Can some one comment on this please. Also does any one have a better list of what method generates gold for research and what methods make gold for the treasury?

thanks

What you call "gold from A" and "gold from B" actually have two different names. The first is called commerce, the second is called gold. More specifically, commerce is the total number of "thingies" which gets divided into gold and beakers, depending on your slider, and then gets bonuses from banks, libraries, etc.

Anything generated by a tile is commerce. Trade Routes are commerce (someone correct me if I'm wrong). What you trade in trade deals is gold which goes straight to the treasury. Merchants also generate gold, and (unlike in trade deals) it is affected by banks and so forth.

All right, maybe someone said it before, but I was too dumb to get it. At which point are the "gold" boni from buildings like marketplace etc. added? Is it added to your town income (commerce), which is afterwards divided into gold and science? Or is it added to the money that you decide (via the slider) to put into your treasury? So, if I would always put 100% into science, I would not get any boni from the marketplace?

This was a good question. So how come nobody bothered to answer it?

Since this is the articles forum, people may well not have noticed there was a question there. The other possibility is that the question indicates some confusion between gold and commerce, and people were sick of explaining the distinction.

As a rather belated answer; whatever percentage of commerce is converted to gold, depending on your slider settings. This is then added to gold from other sources, and the market, etc bonuses are applied to that before it is added to your treasury.

Let's say that your best commerce city produces 20 commerce. It has +35% science and +25% gold. Anyway you slice it, if one of your percentages isn't set to zero, you'll be losing fractions each turn. For example, if you set science to 80%, you'll get 16 + 35% = 21.6 science, rounded down to 21. You'll also get 4 + 25% = 5 gold. There is no percentage at which you won't be losing fractions, especially when you consider the other cities in your empire.

In 5 turns, you'll get 105 beakers and 25 gold. By instead setting science to 0% on turn 1 and then to 100% on the next 4 turns, you'll get 27 * 4 = 108 beakers, and 25 gold. Congratulations, you've just saved 3 beakers of wasted fractions.

This statement is accurate in Vanilla.

However, it is only partially true in Warlords and BtS, because financial values at the city level are rounded to the 100ths decimal place. Only bottom line financial values (in the <F2> Financial Advisor window) are rounded to whole numbers.

Therefore, you cannot lose more than 2.97 :science: :gold: :espionage: total per turn due to fractions.

This remainder of this post contains copious amounts of fuzzy math, which is revealed and proven false in later posts. I've left it here only for reference ...

This was a good question. So how come nobody bothered to answer it?

Strategy articles should need very little (if any) explanation. Most people visit this forum to have questions answered -- not to answer them.

A tip is only good if your audience understands it.

Since this is the articles forum, people may well not have noticed there was a question there. The other possibility is that the question indicates some confusion between gold and commerce, and people were sick of explaining the distinction.

And now to complete the puzzle ...

The strategy of running the sliders at 100% all the time is undoubtedly effective, but the difference is usually unappreciable.

I think it was Vale who explained this to me a few months ago, but I can't find the thread now ... I'll try to do him justice.

If you want to know exactly how much difference using the "Always 100%" strategy makes, you need to determine a few values first -- all of which can be observed in the <F2> Financial Advisor window:


"Normal" research amount. The amount of :science: you pull in when running your sliders using standard practice (just barely in the blue/positive).

"Normal" gold amount. The amount of :gold: you pull in when running your sliders using standard practice (just barely in the blue/positive).

0% research amount. The amount of :science: you pull in when running your research slider at 0%. This represents beakers contributed by specialists and buildings.

"100%" gold amount. The amount of :gold: you pull in when running your gold slider at 100%.

0% gold amount. The amount of :science: you pull in when running your research slider at 0%. This represents gold contributed by specialists and buildings.

"100%" gold amount. The amount of :gold: you pull in when running your gold slider at 100%.

Total Expenses. The cost of running your empire, as represented by the value next to "Total Expenses" in the Expenses column. (Does not change based on the slider %.)


From those values, we can determine the following variables:


R = "Normal" Research Amount.
R0 = 0% Research Amount.
R1 = 100% Research Amount.
R2 = R1 - R0 (the research amount affected by the slider)
G = "Normal" Gold Amount.
G0 = 0% Gold Amount.
G1 = 100% Gold Amount.
G2 = G1 - G0 (the gold amount affected by the slider)
E = Total Expenses.


The formula:


Difference% = ( G2 / E * R2 + G2 ) / ( G2 / E + 1 ) / ( R - R0 + G - G0 ) * 100 - 100

-or- as executed 'verbose':


Subtract the 0% Gold amount from the 100% Gold amount. (G3)

This value represents the total amount of research affected by the sliders.


Divide the value from step #1 by your total Expenses (E).

This value represents how many turns of 100% science one turn of 100% gold can pay for.


Subtract the 0% Research amount from the 100% Research amount. (R3)

This value represents the total amount of gold affected by the sliders.


Multiply the amounts from steps #2 & #3 then add the amount from step#1.

This value represents the total amount of gold and research one turn of 100% gold pays for once realized over the amount of turns determined in step #2.


Add Step #2 + 1.

This value represents the total number of turns used making and spending the one turn of 100% gold.


Divide the amount from step #4 by the amount from step #5.

This value represents the average total amount of gold and research pulled in per turn from the sliders over the amount of turns determined in step #5.


Subtract the 0% Research amount from the "normal" research amount.

This value represents the amount of research gained from the slider using standard practice.


Subtract the 0% Gold amount from the "normal" gold amount.

This value represents the amount of gold gained from the slider using standard practice.


Add the values from steps #7 & #8.

This value represents the total amount of gold and research gained per turn from the sliders using standard practice.


Divide the amount from step #6 by the amount from step #9.

Multiply the amount from step #10 by 100 then subtract 100.

This value represents the percentage of increase (or decrease) you will realize from running your sliders at 100% and 0% all the time.



Here's a screenshot with the non-important values blurred out ... I also cut-copy-pasted all three slider values onto one screen for simplicity. Let's use these values to see how much difference the "Always 100%" strategy will make in that empire (it's Sisiutil's Round 6 save from ALC 19, btw).

http://i167.photobucket.com/albums/u128/OTAKUjbski/Always100Strategy.jpg

Our Variables:


R = 141
R0 = 48
R1 = 235
R2 = 187
G = 103
G0 = 15
G1 = 192
G2 = 177
E = 98



D% = ( 177 / 98 * 187 + 177 ) / ( 177 / 98 + 1 ) / ( 141 - 48 + 103 - 15 ) * 100 - 100
D% = ( 1.806 * 187 + 177 ) / ( 1.806 + 1 ) / ( 181 ) * 100 - 100
D% = ( 337.745 + 177 ) / ( 2.806 ) / ( 181 ) * 100 - 100
D% = ( 514.745 ) / ( 2.806 ) / ( 181 ) * 100 - 100
D% = ( 183.436 ) / ( 181 ) * 100 - 100
D% = ( 1.01346 ) * 100 - 100
D% = 101.346 - 100

Difference% = 1.35


So in this situation, you would increase your efficiency by 1.35% (+2.44 :science: or :gold: per turn) by running your sliders at 100% and 0% all the time.

The efficiency of this method typically increases as ...

... more :commerce: pours in.
... fewer specialists are used throughout the empire.
... your empire's overall +:science:% and +:gold:% buildings begin to favour one side (more of one than the other).


Personally, I'm not sure it's worth all the micromanaging.


-- my 2 :commerce:

^ As far as I can tell, the vale/OTAKUjbski effect is an artifact of the way the numbers are computed by the game; like rounding, but more complicated. Not something I myself would enjoy thinking about, especially if the effect is likely in the 1-2% range.

But what is interesting to me, assuming the effect is often enough larger than 1-2%, is:
* buildings, like Zombie69 talked about
* known-trade effects - better to run research when tech is known by others
* tech trading effects
* effects of having money in the bank (money available for events, upgrades, etc; possibility of AI demands)
A discussion of that stuff as a whole - that is the faith I am searching for.

Otaku, this financial advisor math and beaker per gold ratio sounds eerily similar to a strategy article I wrote a couple months ago here (http://forums.civfanatics.com/showthread.php?t=242530).

I didn't check all the details of your math because it seemed to me you go wrong already in the second step. If it was my article you are thinking of, you misunderstood what the beaker-gold ratio is. It's the amount of extra beakers you get over your standard research rate by running deficit research over a given amount of gold. It's not a way to get extra beakers by running binary research.

Can you confirm where you came up with this? Even if it was from Vale and not me, I pretty sure it is mistaken, and I don't want to get into the details until I know.

This is still bugging me for some reason, so I'll go into details now. I think what you are trying to get at is a big-picture concept about how gold and beakers relate, and has nothing to do with micromanagement. I'll use your variables, although they are slightly different in my article.


R = "Normal" Research Amount.
R0 = 0% Research Amount.
R1 = 100% Research Amount.
R2 = R1 - R0 (the research amount affected by the slider)
G = "Normal" Gold Amount.
G0 = 0% Gold Amount.
G1 = 100% Gold Amount.
G2 = G1 - G0 (the gold amount affected by the slider)
E = Total Expenses.


Subtract the 0% Gold amount from the 100% Gold amount.

This value represents the total amount of research affected by the sliders.

Divide the value from step #1 by your total Expenses, E.

This value represents how many turns of 100% science one turn of 100% gold can pay for.

The amount of gold you make with one turn with the slider off is (G1 - E). The amount of gold you lose at 100% research is (G0 - E). So the number of turns in step 2 is actually (G1 - E)/(G0 - E), which is not equal to (G1 - G0)/E, as you claimed.

That's where I stopped looking at your formula in detail, but the way you described it sounds very similar to a formula I presented in my article. R and G implicitly contain information about E, so if you do the correct math, the formula simplifies nicely. It is just (R1 - R0)/(G1 - G0).

Now if this turns out to be a number like 2.44 beakers/gold, this doesn't mean you get an extra 2 or 3 beakers per turn by doing binary research. That would indeed sound like a bunch of irrelevant micromanagement to me.

What it means is that if you get 1000 gold from a tech trade, you will make 2440 extra beakers by doing deficit research than if you didn't have that gold to spend. That's far from micromanagement. It also means you lose 2440 potential beakers by setting your slider to 0% until you make 1000 gold.

Even if your formula has nothing to do with mine, you should not be able to get any extra beakers by doing 0-100 research (except by vanilla rounding errors, which has nothing to do with your analysis). Just look at the units on your final answer. It doesn't make any sense to interpret it as extra beakers per turn.

I'm pretty sure he is not trying to replicate the formula in your article (or he's doing a pretty bad job if he is ;)). It appears to be on the right track to estimating the efficiency of binary science, but as you do I believe there are mistakes there. In particular, I don't see why E comes into at all.

In fact, the real formula is pretty simple. Under binary slider management, how often do you have to run 100% science to emulate* a 50% science slider? Well, unsurprisingly, 50% of the time. Weighting the binary output by that ration, we get average gold and science of:


0.5 * G0 + (1-0.5) * G1 = 103.5
(1-0.5) * R0 + 0.5 * R1 = 141.5


So you make an average of an extra half beaker and half a gold a turn. That's a whopping 0.412% extra output.

* In fact, to be extra anal, the rate you choose to run depends on what you mean by emulate - since you get extra output with binary science you could choose to take that all as gold, or all as science or some point in between. Whatever you choose could move your turn % slightly off the value you are trying to emulate. In this case, by making the value the same, we basically choose "probably a little of both, depending on the details of the rounding gains during the two turn types" - the result here is an equal split between extra gold and extra science.

The efficiency of this method typically increases as ...
... more :commerce: pours in.
... fewer specialists are used throughout the empire.
... your empire's overall +:science:% and +:gold:% buildings begin to favour one side (more of one than the other).

Which method? Binary science? If so, why are the above true? The specialists one may be true if it is rephrased "a smaller number of cities run at least one specialist that produces beakers or gold". It's not really the number of specialists that hurts binary science, but the number of cities with nonzero specialists.

Ah, I see now. I wasn't aware that the game still has rounding errors at civ wide level, and this is what you are trying to deal with. I still think the math is mistaken, and I don't like mixing gold and beaker units, but sorry for shamelessly plugging my article ;)

Well it's not clear to me if that game was played with two decimal place accounting or not, because in any case examining the F2 screen as suggested comes up with a reasonable estimates of the benefit of running binary science in either case.

In the BtS case (rounding only at the end) it's just that the maximum loss is basically capped at 0.99 per turn per resource type, as OTAKUjbski points out, whereas in the per-city rounding case it is a rather complex function of the number of cities, their production levels, multipliers, etc. Since the loss in this case was under the cap, it's hard to say without digging up the ALC if this was BtS or before.

This post contains copious amounts of fuzzy math, which is revealed and proven false in later posts. I've left it here only for reference ...

Damnit.

I had a whole post written up and I lost it when I tried to submit it ... now it's late, and I'm tired.

I'll try to sum it up adequately. (sorry no quotes)

Your calculation of GPT was also wrong, because it omitted Net Foreign Income. GPT = Total Income - Total Expenses.


I intentionally left out Net Foreign Income and gold from specialists and buildings, because I wanted to isolate the slider.

Whether the sliders are at 100% or 0%, that income remains constant, and thus any deficit research granted by it is also constant and can be omitted to isolate the slider.


The efficiency difference has nothing to do with rounding errors at all! It has everything to do with the distribution of commerce and +science% & +gold% buildings throughout your empire.

Let's take these two cities for example:

City A = 20 commerce & a Library
City B = 8 commerce & a Market
Total = 28 commerce

With sliders at 100% Science:

City A = 20 * 1.00 * 1.25 = 25 science
City B = 8 * 1.00 * 1.00 = 8 science
Total = 33 science

With sliders at 100% Gold:

City A = 20 * 1.00 * 1.00 = 20 gold
City B = 8 * 1.00 * 1.25 = 10 gold
Total = 30 gold

So even with no rounding involved, we can already see there's a 3 unit difference between 100% Gold and 100% Science. Running at 100% Science results in a 10% better conversion rate for our commerce. So we should want to run 100% Science here.

Unfortunately, fees and other costs prevent us from running 100% Science all the time. Let's say our 2 cities cost us 5 gold per turn in Expenses.

1 turn of 100% Gold nets us 30 - 5 = 25 gold, which allows us to run 100% Science for the next 25 / 5 = 5 turns.

1 turn @ 100% Gold = 30 gold
5 turns @ 100% Science = 165 science
Total = 195 economic units over 6 turns
195 / 6 = 32.5 average total economic units per turn

So even though we can't get to 100% Science, by alternating between 100% Science and 100% Gold, we're able to get within 0.5 units.

Had we used conventional management, we would have run at a constant 80% Science:

City A = 20 * 0.8 * 1.25 = 20 Science
City A = 20 * 0.2 * 1.00 = 4 Gold
City B = 8 * 0.8 * 1.00 = 6.4 Science
City B = 8 * 0.2 * 1.25 = 2 Gold
Total = 20 + 4 + 6.4 + 2 = 32.4 total economic units per turn

Without any rounding again, we see the 'balanced' approach results in a slightly worse conversion rate than the "Always 100%" method -- about a -1.846% difference.

However, if this was a real scenario, we would lose 0.4 science from rounding for a final realized effeciency difference of -2.857%.


That's the efficiency difference my formula calculates. The efficiency difference is there regardless of specialists, buildings, foreign trade and expenses ... they simply affect how much it impacts the empire's economy.


-- my 2 :commerce:

Ah, I see now. I wasn't aware that the game still has rounding errors at civ wide level, and this is what you are trying to deal with. I still think the math is mistaken, and I don't like mixing gold and beaker units, but sorry for shamelessly plugging my article ;)

I typically don't like to either, but I think NET beakers and gold are equal. In many of my examples, I add the net values to determine the conversion rate of :commerce: to :science: and :gold: like I did in my last post.

So basically allways run 100% / 100% as it saves some beakers even if it doesn't seem like alot when your generating ton of beakers it is certanly alot when it is the same as running free religion(+10% research) basically it is ok to slack the slider in the late game but in the early game running anything but 100/100(or amounts that doesn't lose you 1 commerce like say 80% for 15 commerce etc) is totally unforgivable if you want to play your best. Of course there is also the factor that you might allways need gold for emergency upgrades so it is allways nice to have money in the bank.

Basically i am talking about the first 200 turns or so of the game. It isn't going to be equal to be first to liberalism but is going to be quite some beakers and you shouldn't pass up on it...

Well, this originally had nothing to do with my article, but you're discussion of science and gold multipliers is a bit confused. You get the 3 unit difference because a smaller fraction of your commerce distribution has a market as opposed to a library. That has nothing to do with rounding. And net beakers and gold are not equal, even though they are converted from commerce at the same rate. Getting 3 more beakers than you do gold isn't necessarily 'better.' I would suggest you take a look at what I wrote, it's not entirely obvious.

Edit: and I'm going to sleep now...

This post contains copious amounts of fuzzy math, which is revealed and proven false in later posts. I've left it here only for reference ...

1 turn @ 100% Gold = 30 gold
5 turns @ 100% Science = 165 science
Total = 195 economic units over 6 turns
195 / 6 = 32.5 average total economic units per turn

...

Had we used conventional management, we would have run at a constant 80% Science:

City A = 20 * 0.8 * 1.25 = 20 Science
City A = 20 * 0.2 * 1.00 = 4 Gold
City B = 8 * 0.8 * 1.00 = 6.4 Science
City B = 8 * 0.2 * 1.25 = 2 Gold
Total = 20 + 4 + 6.4 + 2 = 32.4 total economic units per turn

26.4 Science * 6 turns = 158.4 Science
6 Gold * 6 turns = 36 Gold

Over the 6 turns observed, the actual difference you get is:

165 - 158.4 = +6.6 Science
30 - 36 = -6 Gold

So by running 100% back and forth, you gain +0.6 Science (the 6 gold and 6 science negate because 80% Science results in +1 GPT, which can also be used later for deficit spending). When you start dealing with 500+ commerce, it gets larger. However, it's hardly worth it and is truly micromanagement.

Using the Always 100% method doesn't result in an X more beakers than gold (like a tradeoff of beakers instead of gold) ... it literally results in more science and more gold than if the slider is left alone.

Well, this originally had nothing to do with my article, but you're discussion of science and gold multipliers is a bit confused. You get the 3 unit difference because a smaller fraction of your commerce distribution has a market as opposed to a library. That has nothing to do with rounding.

:agree:

The efficiency difference has nothing to do with rounding errors at all! It has everything to do with the distribution of commerce and +science% & +gold% buildings throughout your empire.

And net beakers and gold are not equal, even though they are converted from commerce at the same rate. Getting 3 more beakers than you do gold isn't necessarily 'better.' I would suggest you take a look at what I wrote, it's not entirely obvious.

We're using different methods to observe the same phenomenon -- commerce conversion efficiency. You're comparing the efficiency of commerce-to-science and commerce-to-gold conversion and using that to determine the value of a :science: and a :gold:.

But by it's very nature, that's comparing the effeciency difference of 100% Science and 100% Gold.

In the same way you point out having no +whatever% buildings results in a ratio of 1:1, the same thing happens in my equation if no +whatever% buildings exist, because both sliders become equally effective at converting commerce into science or gold. So, there's no difference between 100% Science and 100% Gold no matter how you slice it in those situations. (This same thing also happens in both of our examples if every city has equal amounts of +:science:% and +:gold:% per city.)

Edit: and I'm going to sleep now...

Me too.

In closing, I'm not a proponent of the Always 100% method. I think it's unnecessary micromanaging for too 'micro' of a gain.

Well, I lied, I have wierd sleeping patterns, and I'm not surprised I found another response. I'm sorry Otaku but we are not saying the same thing. What you are calculating with your method is not a rounding error or anything real, it is an artifact of using 'economic units' instead of gold and beakers.

I'll show you:


1 turn of 100% Gold nets us 30 - 5 = 25 gold, which allows us to run 100% Science for the next 25 / 5 = 5 turns.

1 turn @ 100% Gold = 30 gold
5 turns @ 100% Science = 165 science
Total = 195 economic units over 6 turns
195 / 6 = 32.5 average total economic units per turn

So even though we can't get to 100% Science, by alternating between 100% Science and 100% Gold, we're able to get within 0.5 units.

Had we used conventional management, we would have run at a constant 80% Science:

City A = 20 * 0.8 * 1.25 = 20 Science
City A = 20 * 0.2 * 1.00 = 4 Gold
City B = 8 * 0.8 * 1.00 = 6.4 Science
City B = 8 * 0.2 * 1.25 = 2 Gold
Total = 20 + 4 + 6.4 + 2 = 32.4 total economic units per turn

Notice something in the second example, you get 6 gold but your maintenance is 5. So you are netting 1 gold per turn. (In the terms of my article I would say your 'ideal slider rate' is slightly more than 80%)

Notice also you get 26.4 beakers. Over 6 turns you get 6 gold and 26.4*6 = 158.4 beakers.

So the first way you get 165-158.4 = 6.6 beakers, while the second way you get 6 gold.

What happens if you use this 6 gold for deficit research? Surprise! You get 6.6 beakers back. 6.6 beakers = 6 gold, there is no 'economic unit.' There is nothing to be gained by going either 80% research or binary, except rounding errors which we both ignored in this analysis.

How did I know that you get 6.6 beakers from deficit research? I used my magic formula. Science due to commerce at 100% is 33, gold due to commerce at 0% is 30. (33/30)*6 = 6.6

The math really is that simple.

I (also of the weird sleeping patterns) agree completely with Quecha.

OTAKU, explain qualitatively how changing the slider, without rounding error, can net you more gold and science? As Quecha points out, gold and science have a particular exchange rate based on the multiplier buildings currently in your empire - you cannot compare them 1:1. Your examples must end up with greater on both (or equal on one) to prove anything.

Here's a simple thought experiment to show that binary science doesn't get you anything. Consider a single city. This city can any type of gold or science multipliers.

Let the commerce this city produces be C.

Let the science multiplier percentage be S.

Let the gold multiplier percentage by G.

Let the science rate you normally run your empire at be R.

Consider a series of 10 turns.

You will recieve

Science of: 10 * R * C * S
Gold of: 10 * (1-R) * C * G

Now consider binary science. To emulate a rate of R, you need to run n turns of science, where n is R * 10, and m turns of gold where m is (1-R) * 10. You receive:

Science: n * 100% * C * S
Gold: m * 100% * C * G

Really, this example is getting stupid, but substituting back in for n and m, you get identical formulas to the original:

Science of: 10 * R * C * S
Gold of: 10 * (1-R) * C * G

So each city in your empire produces identical gold and science. If you chose to run at some OTHER m and n values, you would produce more science but less commerce, or vice versa, over 10 turns the non-binary city could do EXACTLY THE SAME THING by changing R such that m and n have the relation above, again.

I think if you read Zombie's excellent article (http://forums.civfanatics.com/showthread.php?t=159109) where binary science was discussed ad-nauseum, you'll find no mention of this magical violation of mathematics enabling extra output.

I think even my example was too complicated and a bit ridiculous, so here is an even simpler way of thinking about it without explicit formulas, based on pie.

Every turn you can slice your commerce up into 10 slices - some into science and some into gold. Choosing 60% means six slices of science, four of gold.

The amount of gold you get from any gold slice is the same as any other gold slice, on any turn. The amount of science from any science slice is also the same. The number of science in a science slice is NOT, in general, the same as the gold slice, because you may have more multipliers for certain science slices - 200% for example, while having only 100% for gold.

Now, whether you run binary science, which corresponds to making every slice in a particular turn of the same kind, or non-binary science, which corresponds to a mix of slice types each turn, you have the same TOTAL number of slices, and EITHER mechanism can allocate those slices in the same way (well binary has some granularity problems, but ignore that).

Explain to me how anything about binary science changes the size or efficiency of a slice? So what if you take your first 50 slices (5 turns) as gold and then 50 of science, and I take 5 slices of each for the first 10 turns? We end up with 50 equal slices at the end.

Apparently, I had some "fuzzy math" in there. I guess that's what I get for growing up with Reaganomics, eh?

After another bout with Math 101, I see where I went wrong. (I probably could've avoided it if I hadn't been doing math at 3am.)

... you get 6 gold but your maintenance is 5. So you are netting 1 gold per turn.

That's pretty much the head of the nail right there. If every 5 turns of "standard practice" I spend that +1 gold on one turn of deficit research, it evens out. Likewise, if a non-100% slider results in 0 GPT, it evens out over any number of turns.

So, no matter how you slice it, 2 is not equal to 1, and jimmying the slider doesn't net any gain.

The most anyone stands to gain from "Always 100%" is 0.99 :science:, 0.99 :gold: and 0.99 :espionage: due to rounding by the Financial Adisor.

That's it!

I hate being wrong but even more so being wrong and not realizing it. So for that I owe you two a quick "thanks".

Thankfully, I never practiced this theory, so I feel I've lost nothing and instead gained insight.

me = :crazyeye: I guess.

EDIT: I think I'm going to self-impose a new rule: no more late-night/early-morning math. :D

Don't worry about it, I know the concepts are a bit subtle and it's easy to get lost in the details of an example. I know what it's like trying to think when you're tired, I certainly would be lost if I hadn't worked this out for myself earlier.

I added the algebra leading to my formula in a spoiler in my article, if you're interested.

It is quite often that you gain 1 beaker though. When you are generating only 12 commerce a turn that is quite allot though. Hence why you should always go 100/100 in the beginning. Unless of course you know the exact multiplier for prerecqs + number off opponents then fix the slider to mainimize the lost fractions after multiplying. I don't think it even come close to catch up to the 1 beaker gained(in most cases) from 100/100. Say your generating 13 commerce. IF you go anything but 100/100 you are going to get a total of 12 gold + beakers and hence lose one per turn, or about ~8% of your research because of sloppy slider management.

Another somewhat unrelated thing is that under bureaucracy odd amount of commerce are always round down so trying to have even number of commerce(and hammers of course) Get maximum effect from the multipliers.