Mathematical Analysis of the Three 'Improvement wonders"

[Lawrence of Arabia]

I had some time to kill, so I decided to do a mathematical analysis of the three wonders which give free improvements in a city: the Pyramids, Sun Tzu's Art of War, and the Hoover Dam.
Disclaimer: This does not include all of the factors which may go into your decision to build the wonder. As you may see later, just because a wonder is inefficient at a certain level doesnt mean that you don't want to build it. eg. Building Sun Tzu's may be a way for you to get one improvement out of the way, so you can build another more improtant improvement or unit. This is in no way reflected in this analysis. Different map sizes will also come into play. Wheres 6 cities on a tiny map is a large number, six cities on a huge map is nothing to write home about. This analysis also ignores the long term effects of the wonder.

Breaking even is the point were the number of shields put into the construction of a wonder equals the amount of shields the rest of your civlisation would have had to spend on building the improvement everywhere. If you don't want the improvement everywhere, then the breaking even point will be even lower. If the amount of cities that you have is less than the breaking even point, then the cost-benefit of the wonder is too costly. If the amount of cities that you have is more than the breaing even point, then the cost-benefit of the wonder is cheaper, and a bonus at that.

The Pyramids: Cost 400: Free granery in each city on continent
Granary: Cost 60
Breaking even: 7 cities
Tiny Map: DONT BUILD
Standard Map: BUILD
Huge Map: BUILD

Sun Tzu's Art of War: Cost 600: Barracks on every city on continent
Baracks: 40
Breaking even: 15 cities
Tiny Map: DONT BUILD
Standard Map: DONT BUILD
Huge Map: BUILD

The Hoover Dam: Cost 800 Hydro plant on every city on continent
Hydro Plant: 240
Breaking even: 4 cities
Tiny Map: BUILD
Standard Map: BUILD
Huge Map: BUILD

NB: On most archipelago maps, these wonders will be useless as there will be very few cities on each island. These islands are counted as continents by the computer generator.

[Lord Merciless]

There are more factors on whether to build these wonders or not:
- Maintainance cost: a Granary costs 1 gpt, 20 Granaries on the same continent means 20 gpt.
- Denial of usage: especially the Sun-Tzu, allowing the AI to have it could mean much higher attrition for your troops. Preventing the AI from building Hoover Dam will greatly hurt their production effort that become very important in late game wars and space races.

[Lawrence of Arabia]

DOH! you are right about the first point. I dont know what I was thinking For point two, on higher difficulty settings, I have a problem getting the wonders I need (Colossus. Smith, Hoover, never mind denying their use to the AI

[Arrian]

A couple of other points for and against Sun Tzu:

For: it's really useful if you start conquering people on your continent. Captured cities will have an insta-barracks.

Against: Barracks are only 20 shields for militaristic civs. If you are militaristic... it doesn't make much sense. Denying it to the AI, however, is a worthy cause.

-Arrian

[vulture]

Originally posted by Arrian
A couple of other points for and against Sun Tzu:

For: it's really useful if you start conquering people on your continent. Captured cities will have an insta-barracks.

Against: Barracks are only 20 shields for militaristic civs. If you are militaristic... it doesn't make much sense. Denying it to the AI, however, is a worthy cause.

-Arrian

Even for militaristic it can be worth it just for the extra gpt you get from not having to pay upkeep on your barracks (plus you can sell off old barracks the turn before you complete Sun Tzu for a small cash boost as well, but that's fairly unimportant). It could be worth an extra 10-20 gpt at the time it is built, at a stage in the game where that can be enough to let you bump the science spending up one notch. Or, obviously, maintain a larger army.

A convenient fringe benefit is the ability to upgrade all your defensive troops without having to move them to a city with a barracks in it. Aside form anything else, you can spend several turns ferrying everyone around for upgrades, and I'm sure its not unknown for people to accidentally leave border towns undefended for a while due to not paying enough attention. More of a user convenience issue though.

Re the pyramids, I've only ever built it twice, both times with a GL from an early war. Possibly by coincidence, those ended up being two of my most dominating games. It's hard to gauge what the benefit of the pyramids really is. I normally figure that it's not worth building, since most of the time in the early game my cities are on the limits of happiness, which means that there is not much benefit to them growing any larger. But since I've had success in games where I got the pyramids, I'm not sure about my reasoning here.

Of course, a Lawrence-style cost analysis doesn't really apply if you build a GW by using a leader, only if you have to build it the hard way.

[DeepO]

Re: the pyramids again: I love the wonder, but haven't built it in months. I always use the very early GL (if I get one) on an army (for the HE), and was never that lucky to get 2 of them before I could build a FP. But it is very useful, not for the accelerated growth, but because you can set your workers to more prodcution and keep the normal growth. A city that only has 2 excess food will grow just as fast with 1 food and the pyramids, which normally gives you one extra shield. As such, I consider the pyramids as important as Hoover, but much earlier in the game.

And never mind the happiness issues: a city can afford to have an extra entertainer when you have a granary there, as it will grow more quickly. Or, you can set the slider to more lux from commerce, as bigger cities will mean that you have more commerce and thus the same beaker production.

DeepO

[IthacaMike]

Originally posted by vulture
Even for militaristic it can be worth it just for the extra gpt you get from not having to pay upkeep on your barracks (plus you can sell off old barracks the turn before you complete Sun Tzu for a small cash boost as well, but that's fairly unimportant).

Actually you can sell the barracks after you complete Sun Tzu. You can also sell the barracks in cities you have just captured.

Selling the barracks help you and slow down the AI if it manages to recapture the city (or the city flips back). A little bit of micro micro management but then every little bit helps.

[Ijuin]

Sun Tzu and the Great Wall make a deadly combination--plop down a city just outside the borders of a Civ you are about to invade, build/rush Walls, and stick a couple of Pikemen and Catapults in it for defense, and you have an instant impenetrable advance base from which to stage your invasion. The doubled City Walls protection means you get a 100% defense bonus, not counting any bonus from terrain, and the Barracks heal your units quickly. Combined, this will make your advance base city defensively stronger than anything the AI could have, and able to weather any attack short of a huge mass of Knights or Catapults. Plus, you can quickly retreat to this base to heal your units, and you can use it as a rallying point for your reinforcements.

[King of Rasslin]

Man, I remember loving Adam Smiths Trading Company because it was so great in Civ 2, where every city had a marketplace, bank, and stock exchange. In one of my games, I rushed ASTC and saved only about 20 gold per turn. I restarted and rushed Tzu, and saved almost 3x as much.

Hoover Dam sounds solid, but it isn't that good on smaller maps, where you will have the game won before it is available. On larger maps, in a close game, it is very good. However, you will only need about 10 hydro plants, because your cities past your core won't benefit very much from it.

The pyramids are close to being useless. By the time you finish them, the big land rush is over. It is a nice culture wonder, however. Overall, Sun Tzu easily wins, even for builders.

[Mad Cleric]

Hm, I am still an "aspiring begginer" but...

I always considered the barracks and SUn Tzu extremly important because of the gold you did not have to pay. Aslo, I found that an AI with Sun Tzu is generaly a lot more harder to beat if yu get in a military ingagement, this could be crucial, because the AI ussauly builds more then it upgrades. So, denying it the cahnce to have veteran units like you couild make a quick military assualt very easy, if not oppresive.

-Ronald

[Mad Cleric]

Also, ussauly, my great leaders are for armies so I can build the Heroic Epic like Deepo said but, after that, armies are void of all usefulness except for stack defense, so I ussualy just tell all the excess ones to make a Forbidden Palace or Sun Tzu, oh yea, one thing, I have learned that AI on regent will try and make a wonder race for the some really sucky wonders, this gives you time to make Sun Tzu, or if you like, the pyramids, although, I amn not sure this is the same on Monarch-Diety

[Panag]

hi ,

those three are wonders the AI can keep , if it where only to see the AI build more and get more money , ...

have a nice day