Multiplier Buildings: A Practical Primer

Aabraxan

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MULTIPLIER BUILDINGS: A PRACTICAL PRIMER

Some time ago, Tone was kind enough to explain the basics of multiplier buildings to me in this post. With his permission, I have reworked his original post in an attempt to create a strategy article.

One of the items that commonly confuses new players is the issue of multiplier buildings. Multiplier buildings commonly increase science or tax output by 50%, but are these gains simple or compound? If a market increases tax revenue by 50% and a library increases research by 50%, what happens if I build both? Do they enhance each other, or conflict with each other? How do I decide when to build one, the other, or both? This article is intended to help you unravel the mysteries of multiplier buildings and decide when and where they should be built.

To decide when it makes good fiscal sense to build these improvements, you’ve got to know what each multiplier building costs and what the return is. I’ve divided the multiplier buildings into “Science multipliers” and “Tax multipliers.”

Science multipliers:
A library costs 80 shields, plus 1 gold per turn upkeep. It increases research by 50% and produces 3 culture per turn.

A university costs 200 shields, 2 gpt upkeep, adds 50% to science and produces 4 culture per turn.

A research lab costs 200 shields and 2gpt upkeep. In return, you get + 50% science, 2 culture per turn and 1 pollution marker.

Tax multipliers:
A marketplace costs 100 shields, plus 1 gpt upkeep, while increasing tax revenue by 50% and increasing the effectiveness of luxuries that are hooked up.

A bank costs 160 shields, has an upkeep of 1 gpt and increases tax revenue by 50%.

A stock exchange costs 200 shields, costs 3 gpt upkeep and increases tax revenue by 50%.

Before diving off into the math, it is important to understand that: (1) commerce is divided up according to the slider percentages prior to being run through any multipliers; and (2) it only runs through one type of multiplier. Raw commerce has corruption taken off the top, with the remainder being allocated to science and luxury spending. Whatever is leftover after that is tax revenue. Science is then run through the science multipliers and tax through the tax multipliers. Also, remember that specialist output is never affected by city improvements. That means that a citizen working a 2-gold tile in your capitol can often produce more beakers than a scientist.

Armed with that information, let’s take a look at one of Tone’s games:



This shows a city that has a base commerce of 18 raw commerce. You can count them from the individual tiles worked if you want to. The three red money bags represent that 3 of the 18 coins are being lost to corruption. My sliders have been adjusted to 80% research, 0% happiness and thus this gives 20% tax. That allocates the raw commerce as follows: 3 to corruption, 12 to research (80% of 15), 0 to happiness, and 3 to tax revenue (20% of 15).

The three red money bags represent that 3 of the 18 coins are being lost to corruption. As far as factors internal to this city, this amount will only change if I build a court or police station or the population grows. However, some external factors can affect this corruption, such as the Forbidden Palace is moved, I change government, I build another town closer to my capital, etc. I shall ignore these factors in the following explanation and just concentrate on how adding buildings to this town at this time in the game would affect the contribution it makes to my empire.

The base tax/research/entertainment commerce for this town is 3/12/0. The reason why my research shows as 18 gold rather than 12 is that the library is adding an extra 50% to the base research gold. This is good value as the cost of the library is 1gpt which is much less than the benefit of +6 beakers per turn. It was even better value before I messed around for this post because I had my research slider @100%!

Every research boosting improvement/wonder built in this town adds 50% to the base research value of this town. In this case, and at these slider settings, add a uni and it will increase research by another 6 beakers per turn. Adding a research lab would add another 6 beakers, while bulding Copernicus’ Observatory, Newton’s University or SETI will each add an additional 12 beakers per turn. (Note that the increase is not compound but simple as it adds to the base rate.) Each of these improvements offers good value because my research slider is high, although I would need my head seeing to if I built the wonders here with such a low base commerce value.

Markets, Banks and Stocks work in the same way but increase the tax element rather than the research element. The market in this town is about to be completed and will add an extra 50%. The base commerce is 3 gold. Adding 50% to that for a market gives 4.5, which will be rounded down to 4gpt. The cost of the market will be 1 gpt so building a market here would have no net effect on my empire's income because the gold I gain in tax is lost by the gold I lose in maintenance. (Of course I still gain the marketplace’s other effect of improving the effectiveness of luxuries.) On the other hand, if I have a city where the base tax commerce after corruption is 4 per turn, the tax boost becomes 2 gold per turn and I then gain 1 gpt over the upkeep cost. Keep the shield cost in mind, however. In a 1-shield town, it will be 100 turns before I start seeing any return on the investment.

Building a bank in the town pictured above results in a net 1 gpt gain. Having both a bank and a market place results in an additional 3 gpt to my tax revenue. The calculation is: [base tax + (50% for the marketplace) + (50% for the bank) = tax revenue]. So what you get if you add a bank is: (3+1.5+1.5=6 gpt), but the maintenance for the market and bank is 2 gpt (1 for the marketplace & 1 for the bank), so I've just used 260 shields to get 1 gpt. (Because the market is a prerequisite for the bank, it’s 100 shields for the market and 160 for the bank.)

Building a stock exchange in this town would be even worse. The additional gain from a bank to a stock would only be another 1 gpt (3 + (3*1.5) = 7 when rounded down) but a stock has a whopping 3gpt maintenance and so I'd actually lose gpt (in addition to the 200-shield investment) if I built that 'improvement.' Because the market and bank are prerequisites for a stock exchange, let’s look at the big picture. Here’s the formula: [base + (market) + (bank) + (stock exchange) – (upkeep costs) = net tax revenue]. That give us: [3 + 1.5+1.5+1.5 = 7 (rounded down) – 5=2]. That’s one less than we started with! In short, these commerce boosting improvements do not offer good value because my tax rate is so low.

Of course this would all change if I moved my sliders. For example, if I were running 0% science and 0% luxury (resulting in 100% tax), and built both a market and a bank, the net gold would probably make building both worthwhile. After corruption, I’d still have 15 raw commerce, but all of it would go to tax revenue, which would then be run through the market and bank. Each of those improvements would add 7 to tax revenue (15*0.5=7 after rounding down). Then deduct maintenance of 2, 1 for the market and 1 for the bank. So, the calculation would be: [15 + 7.5 + 7.5-2=28]. Add in a stock exchange and you get [15+7.5+7.5+7.5-5=32]. You can see that, at 100% tax revenue, we more than double this city’s tax income by building multipliers.

These numbers fluctuate over the course of a game, as populations change, tiles get reassigned, sliders are moved to afford more units and a host of other factors. However, I hope that this has helped explain how the various multiplier buildings affect your income and your science. I also hope that it explains why many players tend to concentrate on either research boosting improvements or tax boosting improvements, but not both. It may also give a clue as to why building these improvements in low pop towns may not always be of immediate benefit.
 
Good article.

One minor point:

This sentance:
Adding a research lab, Copernicus’ Observatory, Newton’s University or SETI will add an additional 6 beakers per turn per building.

is incorrect. Adding a research lab would add 6 - adding copernicus, newtons or seti will add 12 beakers - those double research.

And, of course Smith's makes the maintenance cost of all those income doublers go away, but not the shield cost.
 
Good article :yup:.
But in the penultimate paragraph, you seem to have rounded down in the wrong place. 15g tax multiplied by market + bank gives 30g not 29g.
 
Good article :yup:.
But in the penultimate paragraph, you seem to have rounded down in the wrong place. 15g tax multiplied by market + bank gives 30g not 29g.

Thanks, PaperBeetle. Is this where you're talking about?

Each of those improvements would add 7 to tax revenue (15*0.5=7 after rounding down). Then deduct maintenance of 2, 1 for the market and 1 for the bank. So, the calculation would be: [15 + 7 + 7-2=27].

If so, it looks like the addition of the multipliers takes place before the rounding. Is that correct?
 
Each of these improvements offers good value because my research slider is high, although I would need my head seeing to if I built the wonders here with such a low base commerce value.
examined?
slapped?
bashed in?

Good work. This has always been a rather mysterious area of the game. It gets explained a lot in Training games and such, which is fine if you get involved in one or read one. Otherwise, you tend to fumble around trying to figure out how this works.
 
Tone's British, isn't he? That's a fairly common sort of thing for people to say over here (at least in my experience). It would mean "examined".

Nice article, Aabraxan. Very clear. Thanks!
 
Thanks, PaperBeetle. Is this where you're talking about?
...
If so, it looks like the addition of the multipliers takes place before the rounding. Is that correct?

Yup. You had it correct in the para starting:
"Building a bank in the town pictured above results in a net 1 gpt gain. Having both a bank and a market place results in an additional 3 gpt to my tax revenue. The calculation is: [base tax + (50% for the marketplace) + (50% for the bank) = tax revenue]. So what you get if you add a bank is: (3+1.5+1.5=6 gpt), "

The order (1) implementation of corruption, (2) summation of mulitipliers, (3) application of multiplier to base, (4) rounding down is common to all the multiplier buildings including the factory family.
 
Great article, Aabraxan. When I was a newbie, I "got it" early on to not build every building in every town/city, but it took me a very long time to understand the whys/whens of multiplier improvements. A clear explanation like this has been badly needed here for a long time. :goodjob:
 
Is Smith´s Trading Co. powerfull then? - Free maintenance for Marketplaces, Banks, Harbors, and Airports. meaning in your formula at 100% tax revenue we will have: [15+7.5+7.5+7.5-0=37] for that city.

In a empire of 5 cities would be a 5*5=25 gpt earn in savings for Smith´s.
 
Is Smith´s Trading Co. powerfull then? - Free maintenance for Marketplaces, Banks, Harbors, and Airports. meaning in your formula at 100% tax revenue we will have: [15+7.5+7.5+7.5-0=37] for that city.

In a empire of 5 cities would be a 5*5=25 gpt earn in savings for Smith´s.

Don't forget they cost shields to build as well.

Only my core and semi-core cities get marked places, and they don't usually build banks, stock exchanges are out of the question. I only build airports in cities that specialize in building airplanes (just like barracks)

So that leaves harbors and marked places, mostly. On a huge map, this could add up to 50gpt. But a far cry from 5 gold per city.
 
Hum, what about govenment bouns to commerce? Republic gives +1 and Democracy +2 how will the math be?

Since it doubles the amount of coins from a working square, the +50% city improvment bonus will aply later like beeing explained, so the formula is correct, but this really points out the power of Democracy since it will generate much more income with markets and banks built then any other government.

The save tested is republic or monarchy?
 
Hum, what about govenment bouns to commerce? Republic gives +1 and Democracy +2 how will the math be?

Since it doubles the amount of coins from a working square, the +50% city improvment bonus will aply later like beeing explained, so the formula is correct, but this really points out the power of Democracy since it will generate much more income with markets and banks built then any other government.

The save tested is republic or monarchy?

The commerce bonus in both republic and democracy is the same +1!

What it does is, it increases the raw output of the land citizens work, it comes even before corruption. And yes, its powerful.
(Though, assuming an empire of well spaced metropolises, communism will give more uncorrupted commerce in the end)

An other important thing to note is the tourist money from old wonders (C3C only) The tourist output is commerce added to the commerce from the land, also before corruption. Your 20K city can potentially generate as much commerce as your next 5 biggest cities combined. Especially if the wonders include the Newton's and Copernicus'.

Also the output from the collossus works the same as the commerce bonus from republic/democracy.

And the golden age commerce bonus also works like republic/democracy!
 
Hum, what about govenment bouns to commerce? Republic gives +1 and Democracy +2 how will the math be?

Since it doubles the amount of coins from a working square, the +50% city improvment bonus will aply later like beeing explained, so the formula is correct, but this really points out the power of Democracy since it will generate much more income with markets and banks built then any other government.

Perhaps I'm splitting hairs here (and feel free to ignore me if I am), but neither Republic nor Democracy (technically) doubles the amount of coins from a square. On a 1-gold tile, they have the effect of doubling the gold, but that's just because it's a 1-gold tile. On a 2-gold tile, they don't double the gold, they add +1, as MAS pointed out.

The save tested is republic or monarchy?

Republic, I believe. I don't have the actual save, but take a look at the screenshot.
 
Getting back to the subject of multiplyer buildings, no matter what government you are in, the multipling effect of the building is the same. The government only affects raw commerce. Or is this wrong?
 
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