Gold, Beakers, and Deficit Research

Quechua

Unique Unit
Joined
Jan 30, 2007
Messages
356
In this article, I hope to clarify the research value of gold. The discussion won't involve any hidden game mechanics, and it may already be well understood by experienced players. Still, we will give an unambiguous answer to certain key questions. Can you cut research times by clever manipulation of the slider? Can running merchant specialists be more benificial to your tech rate than running scientists? How much do buildings like courthouses or markets affect your research? What is a fair trading price for techs?

But before we begin, what is gold even good for in the first place? We can certainly use gold in trades, but why does gold have value for our trading partners? One important answer is that through Universal Suffrage or unit upgrades, gold can be an empire-wide substitute for production. These abilities can be critical, but they are not used on most turns, and we will not consider them much here. But every turn from the time the second city is founded, gold is necessary to pay the costs of our empire.

The Ideal Slider Rate

If you don't already have enough gold in your treasury, you must use a fraction of your incoming commerce as gold to pay maintenance each turn. We will consider an 'ideal' percentage of commerce at which there is no net change in the treasury. Since the slider is limited to increments of 10% this is rarely exactly possible, but in practice it is no different from adjusting the slider above and below the ideal point.

Now, if you do already have enough gold, you can just leave the slider at 100% and let the maintenance eat away at your treasury. If we consider our 'standard' science rate to be that at the ideal slider point, after a number of turns we find we have lost a certain amount of gold from the treasury and we have produced more beakers than we would have at the standard rate. It is as if the gold has been converted into beakers - this is what we mean by deficit research.

So this situation defines a beaker value for any given amount of gold - the amount of extra beakers we produce if we set research to 100% until the given amount is fully spent on maintenance. But gold also has a beaker value in terms of the beakers we would lose if we set research to 0% until we have produced the given amount of gold. If you do the math (it's easy to check any statement I make here), you will find that the two beaker-per-gold ratios are exactly the same.

Instead of researching at the ideal slider rate, we might turn off research for several turns to build a treasury, and then use that treasury for deficit research. But the fact that there is one beaker-per-gold ratio means that we produce exactly the same amount of beakers using either method (ignoring rounding errors). This is true for any two paths of research that begin and end at the same treasury value. And if they end at different treasury values we can easily find the difference in beakers produced by converting the treasury difference using the ratio. This is why it makes sense to talk about an ideal slider rate. Constantly adjusting the slider above and below the ideal point so that there is not much change in the treasury will produce almost exactly the same tech rate as the ideal.

These concepts allow us to blur the distinction between gold and beakers. In an abstract sense, we always research at the ideal slider rate, regardless of the position of the slider. If the slider is set below the ideal slider rate, some of our beakers are 'stored' as gold. If the slider is above the ideal rate we unlock some extra beakers through deficit research. If we are in the happy situation of running a surplus at 100% science, it is as if the ideal slider rate is higher than 100%. Since we can't ever set the slider higher than this ideal point, some of our ideal beakers must always be stored as surplus gold. We can never unlock extra beakers through deficit research in this situation, but the equivalence implied by the beaker-per-gold ratio still has abstract meaning.

Finding the Ratio

This magic ratio is much easier to find than you might think. It is simply the total amount of beakers that can be produced due to commerce, divided by the total amount of gold due to commerce. To find this, turn the slider to 100%, and record the net change in gold (typically negative), which we'll call M, and also find the total amount of beakers produced, B, using the Financial Advisor. Now switch the slider to 0%, and find the total amount of gold produced, G, and also record any beakers, b, which are produced at 0% research. The ratio we are looking for is just (B - b)/(G - M)



So in this case our beaker-gold ratio is (736-38)/(359+93) = 1.54

My choice of parameters is conventional. Instead of using the numbers G and M, we may use the gold values listed in the Financial Advisor. And as will soon become clear, we may compare the four parameters at any two distinct slider values.

Gold and Beaker Multipliers

If you have no beaker or gold multiplying buildings (libraries, markets, etc), this ratio will be exactly 1, since commerce is converted into beakers and gold at the same rate. This suggests the beaker value of gold depends in some sense on the presence of multiplier buildings in your empire. In fact the ratio is just equal to the average beaker multiplier divided by the average gold multiplier, where the average is weighted by the fraction of commerce a city produces. So the beaker value of gold is fairly stable over time, it only changes if you build new multiplier buildings or significantly change the commerce distribution of your cities. It does not depend on many economically significant actions like hiring or firing specialists, building courthouses, producing wealth or research from production, and so forth.

But what happens when the beaker-per-gold ratio does change? If you already have gold in your treasury, its value for deficit research also changes. You can take advantage of this by manipulating the amount of gold in your treasury. If your ratio increases, you will get more extra beakers from deficit research than before, but you will also lose more potential beakers in accumulating a given amount of gold. So if you accumulate the gold before the ratio change, you will gain some extra beakers.

This is a little abstract, so let's consider an example. Suppose you're building Oxford in a commerce city (beakers from specialists complicate this example, but not the idea in general). You can set the slider to 0% a few turns before Oxford is complete, and then spend the gold on deficit research afterwards. Since you are producing no beakers to multiply, the situation is no different than if you had built Oxford a few turns earlier, when you had started 0% research. Spending the gold produced during these turns will give you the same amount of beakers as researching at the ideal rate, but here it is as if you already get the better science multiplier a few turns before Oxford is built!

It is important to realize that it doesn't matter how or when you accumulate the gold before the ratio increase. The advantage comes from the change in the value of deficit research. Setting the slider to 0% just before a new beaker multiplier comes into effect simply allows you to plan fewer turns in advance (and makes the example above easier to understand).

A similar situation holds for decreases in the ratio. When you build gold-multiplying buildings, you lose less potential beakers in producing a given amount of gold, but you also get less extra beakers from deficit research. This may be a little confusing - you do not actually get less total beakers when you spend gold on deficit research, but since your ideal slider rate increases, less of those beakers are 'extra.' So it may be wise to spend your treasury on deficit research before the beaker value of gold decreases. This lets you take advantage of extra beakers you couldn't get during those turns by researching at the lower ideal rate.

Gold vs. Beakers

So now we return to the questions we set out to answer. Running a merchant specialist reduces your net expenses, thus increasing your ideal slider rate - indirectly increasing your beakers per turn. Can a merchant produce more beakers than a scientist? The answer depends on what multiplier buildings you have in the city in question, as well as the average multipliers in you empire as a whole. If your cities have many beaker multipliers (libraries, monastaries...) but you've been neglecting your gold multipliers (grocers, banks...), then gold has a higher value in terms of beakers.

As an extreme example, say you have a library, university, observatory, and laboratory in each one of your cities - but you have almost no gold multipliers...just a bank in one city. In that city with a bank, a merchant will produce 4 gold (rounded down) while a scientist will produce 6 beakers. But since the beaker-per-gold ratio in your empire will be very close to 2, the merchant will help your research rate more than a scientist. This will be true in any city that has better gold multipliers than your empire-wide average (unless the beaker multiplier there is also much higher than average).

How much do buildings that reduce your maintenance affect your research rate? This question is easy to answer. If a developing city costs 8 gold in maintenance, a courthouse is effectively giving you 4 gold. With the magic ratio we can find the equivalent amount of beakers. And unless the city is bringing in significant commerce, or gold has low value in your empire, the courthouse will probably help your research more than a library.

What about buildings like markets and grocers? The extra gold from the building depends on the ideal slider rate, and this building will also change the current beaker-per-gold ratio. Unfortunately there is no simple formula that exactly determines the extra beakers produced.

But we can still make some assertions. For example, say you have libraries throughout your empire but not many markets. If your maintenance is bad enough that your ideal slider rate is near 50%, then building a grocer in a city has more immediate benefit to research than a university. If your ideal slider rate is higher, less commerce is devoted to gold and so gold-multipliers have less research value. This may just be considered common sense, but what is not obvious is the role of the beaker-to-gold ratio. If this ratio is high a grocer could still be better for research even for ideal rates approaching 70%. But for even higher ideal slider rates, it is doubtful that the value of gold could ever be high enough to compensate.

Tech Buying

So far we have been speaking about the research value of small amounts of gold per turn. What about decisions like whether to use a Great Merchant for a lightbulb or a trade mission? Large amounts of gold and beakers involve more strategic elements. Gold is not 'converted' to beakers instantly through deficit research. Your net expenses per turn (the number M in the above formula) determines the time for the 'conversion' to take place. Unless you plan to use the production aspects of gold it is usually better to get the same amount of beakers now in the form of a tech, rather than over several turns by using gold for deficit research. A Great Merchant still may present a tough decision since the beaker value of a trade mission is typically much higher than the beakers gotten through lightbulbing - and the beakers eventually produced through settling will typically be much higher than both.

So the 'value' of large sums of gold has no simple mathematical definition. Even so, the beaker-gold ratio gives a decent rule-of-thumb for pricing techs in trades. If you are buying a tech from an AI for more gold than the value of the beaker cost, you are probably getting a bad deal. You could research the tech faster than you could produce the gold you are trading. On the other hand - if it prevents a fair tech trade - it may be disadvantageous to sell a tech for its 'fair' gold value. The seller potentially gives up a tech now for the same amount of beakers over a delayed time.

It is still possible to have a mutually beneficial tech buying trade, though. The player buying the tech may have a lower beaker value of gold than the seller, and the production aspects of gold may have higher strategic value for the seller. A less common situation would be where the buyer is running a surplus at 100%. In this case the buyer can't actually research at the ideal slider rate, so it would take longer to research the tech than it would to produce the equivalent gold.

More importantly, in a tech buying deal the seller does not lose the traded tech, while the buyer loses the value of the gold. This means it often makes sense to price a tech for less than the beaker value in gold. Even so, the AI tends to give you close to the beaker value in gold when you sell to them. So tech selling can sometimes get you more delayed beakers than a tech trade, while the AI also loses a similar amount.

.......................

I hope this post wasn't entirely obvious to everyone. I know that I certainly didn't have a clear appreciation for how much things like merchants and courthouses improve your research rate until I did the math. I've included the derivation of the beaker-gold ratio in the spoiler below, but it's not necessary to understand the concepts in this article. And yes I spend too much time on this game - but if you got this far in the post, so do you :goodjob:

Feel free to argue or point out errors, thanks for reading!

Spoiler :

The numbers G, M, B, and b are the same as in the text.

We define the 'ideal' research rate, x, as that at which there is no change in the treasury.

So (1 - x)(G - M) + M = 0, which means x = G/(G - M)

At the ideal rate, we make x(B - b) + b beakers. This is x(B - b) more beakers than at 0%

And at 100%, we make B - (x(B - b) + b) = (1 - x)(B - b) more beakers than the ideal rate.

What happens if we use a given amount of gold G0 for deficit research?

We can sustain 100% science for G0/(-M) turns, so we make (1 - x)(B - b)*G0/(-M) extra beakers.
Using our expression for x, this simplifies to (B - b)/(G - M) * G0.

So (B - b)/(G - M) is our beaker to gold ratio.

What happens if we turn off research until we build up a given amount G0?

It takes us G0/G turns to build the given wealth, so we lose x(B - b)*G0/G,
simplifying to (B - b)/(G - M) * G0.

And again we see the ratio (B - b)/(G - M), and we note we can't get extra beakers by changing the slider.
 
Nicely explained. I have thought about this myself and I have come to the same conclusion: the key is your civwide beaker-multiplier versus gold-multiplier ratio.

I know that, before thinking about it, I would have taken the wrong decision in the 4g versus 6b example. So I find your post useful.

You might want to add that it is wise to accumulate gold a few turns before building a library, then use deficit research afterwards. It is implied in the text, but not explicitely stated.

Your discussion about "fair trading" may lead to mistakes. You are defining as "unfair" paying more for a tech then it would cost using deficit research. But with the trade you get the tech (and its benefits) inmediately. Or even better, you can trade the new tech to others the following turn. So the fact that a trade is "unfair" shouldn't deter you from going ahead anyway, if the trade makes sense strategically.

All in all, nice work.:goodjob:
 
Thanks for the kind words, I had thought this article had died a quick death. :D

You might want to add that it is wise to accumulate gold a few turns before building a library, then use deficit research afterwards. It is implied in the text, but not explicitely stated.

Yes thats a good point. And on the flip side, if you have a market due soon try to stay in deficit research until its done. The library increases the beaker value of gold for deficit research, while the market decreases the value of beakers lost in accumulating a given amount of gold.

Your discussion about "fair trading" may lead to mistakes. You are defining as "unfair" paying more for a tech then it would cost using deficit research. But with the trade you get the tech (and its benefits) inmediately. Or even better, you can trade the new tech to others the following turn. So the fact that a trade is "unfair" shouldn't deter you from going ahead anyway, if the trade makes sense strategically.

That's true, but I considered it unfair because you could research the tech yourself faster than you could produce the wealth you are trading. If you yourself have accumulated that wealth from tech trades then by all means a tech now is often better than more beakers over a delayed time. But producing the wealth yourself with the intention of tech buying loses you turns. (with the exception of having a surplus at 100%)

The use of the word 'fair' may have indeed been misleading, but in another sense. The buyer loses the gold and all its value, while the seller keeps the tech traded. A 'fair' tech buy, in the sense I used the word, still tends to favor the seller. Just like in regular tech trades, an unequal trade can be very advantageous for the player. But the AI is getting an even better deal, hence 'unfair.'

The discussion of tech buying was brief and maybe more questionable than the rest of article, but I just wanted to show how concepts like the beaker-gold ratio illuminate the discussion.
 
Good article. Just one comment. Due to rounding errors, your output will be maxed if you shift between 0% and 100% on the research slider. As an example, your "ideal" techrate is 80%. Run the slider at 100% 4 times as many turns as you run it on 0%, and you will still have balance. But due to the rounding calcs, you will be researching very slightly faster. I learned something, as I would definately have picked the scientist in the 4g/6b example :(
 
Excellent article! One other thing: Running deficit research is more useful for a Spiritual civ (or with Cristo Redentor). If the civwide science bonus is higher than the civwide gold bonus, it's better to run Free Religion while running full deficit research, and other civics while generating gold at 0% research (assuming a largely cottage-based economy).

So you can use the science slider at 100% in Free Religion, and then set it to 0% and run e.g. Org Rel while building a treasury. That way, you get the full 10% science bonus on (almost) all science commerce, while still having a number of turns of the benefit of other civics (eg faster building of commerce buildings).
Or switching to CS/Pacifism and running masses of merchants in the bank cities, while also generating more points towards Great Merchants for funding more research, then back to FR to spend it.

Another aspect (just to muddy the waters) is that in a science-building-heavy environment, building wealth is likely to be more useful than building research since the hammers only gain production bonuses and don't go through the relevant commerce buildings. And it's most useful in the cities with forges/factories/power.
 
Another aspect (just to muddy the waters) is that in a science-building-heavy environment, building wealth is likely to be more useful than building research since the hammers only gain production bonuses and don't go through the relevant commerce buildings. And it's most useful in the cities with forges/factories/power.

I don't think this is quite correct. Unless they changed it in the expansions, building wealth or research only depends on your base hammers (no forges, bureaucracy, overflow, etc), and beaker and gold multipliers do apply. So the decision between producing wealth or research is exactly the same as deciding to run either a merchant or scientist.

But the Spiritual-deficit research synergy is a very interesting idea - I had never considered that. Also Diamondeye makes a good point about minimizing rounding errors.

Edit - This is a very late edit...but just to clarify, since the mechanics in the expansions are indeed as Polycrates says, he's exactly right. In the expansions, wealth is best in any city when your ratio is greater than 1, and research when it's less than 1. In Vanilla, which I was playing, the decision is exactly the same as the merchant/scientist one, which is discussed in the article.
 
^ They did change it with the expansions so hammers get the same conversion to gold or beakers (or culture)

also Rounding errors no longer matter, Research gold, commerce, culture is all rounded off to the nearest 0.01 (not 1)
 
^ They did change it with the expansions so hammers get the same conversion to gold or beakers (or culture)

also Rounding errors no longer matter, Research gold, commerce, culture is all rounded off to the nearest 0.01 (not 1)

I knew it :( So my advice was useless after all... But as you say, Forges and other +:hammers:% does apply to wealth/research/culture building now.
 
Production multipliers do apply, but gold/beakers/culture multipliers do not, that's the catch.
 
I don't have the expansions so rounding errors matter to me. I use 0% or 100% only.

And to me building wealth/research/culture is independent of production multipliers but depends on the appropriate buildings.

This means that pre-expansion building wealth/research/culture is more favourable in cities specialising in wealth/research/culture whilst post-expansion it is more favourable in production cities.
 
Good topic - the same rules had occurred to me, but I am generally too lazy to calculate the ongoing ratio of my empire, so just use some rules of thumbs about which buildings provide better returns at various points.

This is exactly the kind of logic that should be built into the AI - easy for a computer to do it, to prioritize buildings correctly while it's very hard to come up with higher level strategy and especially war strategy. For humans it is often quite the opposite (I doubt more than 1 of 100 Civ players has the ideas above explicitly in their mind, but most are pretty capable of managing an army with some effectiveness).

I do disagree with the "fair value" comments for the seller of a technology - technology trading in a game with more than 2 civs is not zero sum so since the seller is not losing what he is giving. In a game with many opponents, a reasonable (increasing your chance of winning) price might be several times lower than the cost of the tech in gold/beakers.
 
You're right about the 'fair value' comment, and the difference between trading techs and gold. I realized the this was misleading and made the same point in my second post in this thread.

The interesting thing is that the AI will give you closer to the beaker value of a tech in gold when you sell to them, then you would get through tech trading. So you make more beakers (eventually) through selling, while the AI also loses a similar amount. This is a mistake in the AI programming in my opinion.
 
I agree. It's generally much more expensive to trade gold for a tech than to trade a comparable about of beakers away, the occasional strategic concern aside.
 
Thank you for this awesome article! I thought of one other consideration with deficit research. If you have powerful neighbors, then building up a treasury makes you vulnerable to gold tribute demands. Of course if you are ahead in techs then they will probably just demand a tech otherwise, but if gold is the only thing they can demand from you, then you might want to be careful not to let your treasury get too high.
 
I've sometimes run at a deficit and had cities build wealth to make up for it when I noticed I'd get more beakers by increasing the tech rate than by having cities build research. I've seen the A.I. do the opposite and have no comerce in tech and many cities in build research and wondered if the A.I. doesn't know that the way I do it is better, or if I just wasn't looking close enough at their cities. If they had a lot of production and gold modifiers and few science it could work out better for them.
 
These concepts allow us to blur the distinction between gold and beakers. In an abstract sense, we always research at the ideal slider rate, regardless of the position of the slider. If the slider is set below the ideal slider rate, some of our beakers are 'stored' as gold. If the slider is above the ideal rate we unlock some extra beakers through deficit research. If we are in the happy situation of running a surplus at 100% science, it is as if the ideal slider rate is higher than 100%. Since we can't ever set the slider higher than this ideal point, some of our ideal beakers must always be stored as surplus gold. We can never unlock extra beakers through deficit research in this situation, but the equivalence implied by the beaker-per-gold ratio still has abstract meaning.

You are correct that the "ideal rate" is constant in the long-term. But there is an opportunity cost if you research at exactly that rate. Usually it's better to research at exactly 0% or 100%.

You should run 0% science while building research improvements.
You should run 100% science while building gold improvements.
 
Yes, you can take advantage of changes in the gold-beaker ratio. Store up gold when it's low, run a deficit when it's high. This was mentioned above talking about waiting to run a deficit until you build a library or run free-religion. You're right it is probably important enough to mention explicitly in the article, given I keep saying you can't get an advantage by changing the slider. Maybe I'll add a paragraph.
 
I added a section discussing taking advantage of changes in the gold-beaker ratio. Hopefully there's still some continuity in the article.

Edit- I rephrased the new section to emphasize that your advantage comes from the change in the value of deficit research. Not from binary research.
 
Very nice article.
After the few changes you made, it now has some good strategical value.

It's a but "dry" though.
A few pictures could make it easier to read.
Which ones?
A graph for a typical game showing the gold/beaker ratio could be enlightening for instance.
A pair of screenies showing the outputs at 0% science and at 100% science could serve as a good example.

On the content side, I just wanted to add that (level dependant) there are loads of ways to get to money other than through commerce and that it's often unnecessary to fill your coffins too much. This is mostly true after you have currency, but often at the beginning you have scouts finding money in huts, so it's a game long fact.
OTOH, in BtS you always want to have some gold in store to face or use best some events.
 
Cabert,
You're probably right about making it easier to read. I originally intended it to be in an essay style, because that's what I'm used to, and I intentionally avoided using much math to make it less intimidating (I didn't include the math in spoilers until a couple months after I posted). I had considered a picture showing where the main four parameters are in the Financial Advisor, but simply never got around to it. Organizing it in sections would probably help too.

About your other points, I'd like to note that this is fully applicable to the money you get from huts, capturing cities, and trading with the AI. It's true I've pretty much ignored the strategic implications of the size of your treasury, like keeping some gold around for events. Jray also pointed out earlier if you have too much gold, it's easier for the AI to make demands. Both are good points, but they're very different from the other considerations I'm making here.
 
Top Bottom