Analysis of when King Richard's is worthwhile

grigor said:

I still don't understand your love affair with King Richard. It seems to me that the power of Trade makes up for the low shield output until Railroad, and then it expires almost immediately. .. What do you see as the benefits of KRC?

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I would not say I love King Richard's and I do not always pursue it but it can be worthwhile and often I opt to build it. It is on my list of wonders that are nice to have but not essential (along with Adam Smith, Darwin, and a few others). If I decide to build it, it almost certainly will go in my science city which is typically far larger than any other city in mid game. Furthermore, I only build it if I can do so early enough that I am far from Industrialization and when I have the vans but no higher priority wonder to build.

That was the case in this game. I got Engineering from a hut in -300 and built King Richard's in +1 before I had the Monotheism or Astronomy. There were no useful wonders to be built at that point. I had vans waiting for mono and built Michelangelo the turn after I got Mono (+260). I lost both Copernicus and Magellan to Spanish not because of lack of shields but because of lack of tech. King Richard's lasted till +1540 and built Shakespeare and Newton from scratch among other things (structures).

Ever since Peaster mentioned his ROI (return on investment) theory of Civ2, I have been a fan and use that for a quite a few of my build decisions. It does not work for everything, but when it does it is very helpful to evaluate one option vs. another.

For example, a marketplace costs 80 shields or 160g. It costs 1g per turn and it increases your tax and luxury output by 50%. If n of your arrows are going towards tax+lux, then your ROI is (0.5*n -1)/160. If n=10, your ROI is 2.5%. Experience has shown that 2% and below are poor returns, 3-4% average, 5% and above are very good. We instinctively know this and that is why we do not build infrastructure till later in the game when cities are larger. To get 5% from a Marketplace, you need 18 arrows going to lux+tax. Assuming a typical T3L3S4, your city would be producing 30 arrows. That is about the out put of a size 8 city with good arrow specials and a couple of routes or a size 12 coastal city.

Applying the ROI to King Richard's, the investment is 300 shields. If I build it in a city of size n, I will get n+1 extra shields. If my city is size 14, the ROI is 5% which is very good. The ROI will go up with city growth and maxes out at size 20 for a whopping 21 shields or 7% return. Of course, King Richard's does expire by Industrialization and when compared against things that do not, its ROI should be reduced to take that into account.

By contrast Adam Smith costs 400 shields. Assuming 2.5g/shield (which is what you need to pay for vans not wonders), that is 1000g. It pays for Libraries, marketplaces, temples, and harbor (and a few others like granaries, ancient barracks, and coastal fortress? which are rare). For Adam Smith to return 5%, you need 50g per turn. Assuming you have, on average, 2-3 of those structures in your larger cities, you need 17-25 large cities to get 5%. At the end of my game, Adam Smith was paying for about 70 such structures or a 7% return. (In mercurious style games with tons of well developed cities the return on Adam Smith goes through the roof near the end. It can theoretically approach 100%.)

Warning. Warning. LONG WALL OF TEXT INCOMING.
You've been warned.

Furthermore, I only build it if I can do so early enough that I am far from Industrialization and when I have the vans but no higher priority wonder to build.

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But if you are playing a map where hut-popping and trading is being done on a larger scale (Disclaimer: this one was not super prominent hut/trade-wise due to the 20+ cities limit, and you got Engineering from a hut regardless so it doesn't really apply here to begin with) isn't it a disadvantage to research Engineering early on in the Republic period?

The reason for saying that is that it unlocks Invention for research , and then you're one unlucky hut pop away from losing half your van revenues (the risk is especially high if you don't have Warrior Code due to wanting to keep the 10s slot by avoiding a Feudalism pop, and even worse if you don't have the prerequisites for Economy. 27/93 chance of getting Invention scroll, owowow. 8/93 if Feudalism is available, but still.)

And of course, if you build it right before Invention, you have more important wonders to build in Leo's, Mag's, JSB if not done already and arguably Adam's as well, which means KRC's gotta wait. Too long often. It puzzles me: normally I'd play it safe and do the exact opposite (delay Engineering as long as possible) unless I'm specifically trying to grow out an SSC past size 12.


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To reiterate my reasoning. I'll be making the following hypotheses: An empire of 50ish cities (or any number) maintains a single one-way shipchain to an offshore Republic, with plans for another one soon-ish. Triremes, of course, so 2 vans every 2 turns. Let's assume that my vans take on average 6 turns, with a proper road network, to reach the station port: and another 4 turns waiting in port for their turn to embark. Let's also assume that vans are being IPRB'd every 2 turns at the cost of 113g apiece.

Let's assume, for the argument's sake, that the Republic of Hides is in session and that each van equals 50% of the tech bar, and 450g apiece of revenue. This means that an early Invention pop risks losing 225gpt and 225 bpt, for every van delivery, on top of decreasing profit margins needed to reinvest and grow. At max rank KRC gives 21spt, which equals out to 52.5gpt. Also have to take into account the lost taxes to compensate for lack of trade beakers.

Calculating ROI for one-time payment is a bit different, and the main thing that I'm interested in. The formula involved is, of course:
P=I(1+i)^n
P being the final result
I being the initial investment
i being the ROI (interest rate)
and n being the number of turns between van building and van delivery, as a squared function.

Punching in our example, we have the following. (Not including science beakers, double the value of P otherwise.)

PRE-INV:
P=I(1+i)^n
450=113(1+i)^10
3.9823=(1+i)^10
3.9823^(1/10)=(1+i)^10(1/10)
1.1481=1+i
i=14.81 ROI.
Which is insane.

POST-INV (everything else being equal, ceteris paribus: same city sizes and everything)
P=I(1+i)^n
225=113(1+i)^10
1.9911=(1+i)^10
1.9911^(1/10)=(1+i)^10(1/10)
1.0712=1+i
i=7.12 ROI. Which is honestly not that great, especially how important money is at this precise junction of the game, with all the infrastructure that needs to come online before Democracy is researched for a celebration push.

(NOTE: Does not take into account the opportunity cost of building something else, so feel free to add anywhere from 20 to 45g to costs if necessary, in the form of lost shield output. This dampens the mood especially hard post-Inv: you end up with around 3-5% ROI only... yeowtch.)

So, to recapitulate: Getting an unlucky Invention pop is a fairly low risk if Feudalism is available for a buffer, and you don't mind the carrying costs of Warrior Code: only 2% on each hut pop. But it can go as high as 6% at times. Don't really know when popping a hut becomes not-worth-it, and I sure as heck don't want to go through the math of calculating worth of all positive outcomes vs. expected amount of hut pops vs. number of turns left vs opportunity cost of Invention: but I generally wouldn't want to take the risk of researching Engineering early since it's honestly demoralizing when it happens.


Your ROI figure for KRC is also fine, but it doesn't take into account shield depreciation (a.k.a 300 shields on turn 100 are worth more than 300shields on turn 150) which can muddy up calculations. To calculate KRC's true worth, we'd need to use the math formula to calculate a financial annuity, and figure out what the present value of the annuity would be and compare it with its 300s building cost. Or estimate the total of shields gained, and extrapolate the interest rate from there.

PresentValueAnnuity(KRC)=KRCShieldsPerTurn*((1-(1+i)^-n)/(i))

If the first option is taken, the problem is figuring out what the interest rate would be like, when the ROIs on vans (and opportunity cost of building infrastructure instead if applicable) can be all over the place depending on what are the available demands and what the cities are supplying.
http://www.investopedia.com/articles/03/101503.asp

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Again, to reiterate: None of this applies to Ali's game. If you're already saddled with Engineering and have nothing else to build, might as well. I'm just pretty puzzled that it happens apparently often enough to mention it on the same rank as Adam Smith's when it can backfire so spectacularly, especially given how fast the wonder already goes obsolete with our playstyle.

UPDATE: @Grigor: Your tech order resembles mine. I typically build JS Bach a few turns before Invention, trying to delay Feudalism as much as possible for IPRB costs. (Might need to start getting WC as a stopgap for Inv huts if I get Engineering early.) However, if I end up getting the tech early due to large happiness concerns (need an extra boost) or if I get a Feudalism hut, I will detour immediately before researching all the other pre-Inv techs. Also need to mention the need for 30% luxuries instead of usually 0% (smallish empire) when JSB is built. (and getting a higher tax rate) However, it typically isn't worth it for that reason alone since you'd need 7-8gpt to compensate, which only comes at size 12 with trade routes.

EDIT NUMBER 2: With regards to Ali saying payouts are usually of only 200ish gold for demanded vans. GOTM 180 saw some Hides vans delivered to an offshore civilization reaching 300ish for demanded, and 400+ for payouts from my SSC pre-Inv. Not happening every time, but pretty good still. Normal map for what's worth. Maybe you were on large?

Cool analyses!

I don't think our understanding of Civ2 is yet at the stage where actual numbers tell us much. In Ali's scenario, the number of turns to Industrialization is a crucial variable for deciding whether KRC is worth it. As Jokester suggests, a normal tech path will certainly build Currency, Trade, and Republic before Engineering. Construction met come before Engineering. I nearly always build Banking quickly because it is cheaper to do it before Invention than after, and I want to get to Democracy as soon as possible after I am forced to research Invention. I commonly get Iron Working from the AI either before or after. Before allows Bridge Building before invention as well. Physics needs Navigation, which is also a candidate for delay, so I would build Seafaring and Astronomy first. Also, I would make sure to get Medicine. I usually get it as soon as possible. Also in the mix are University, Economics, and Chemistry. I like Econ early.

So if Engineering and Navigation are delayed as long as possible, the techs between Engineering and Industrialization are:
Navigation, Physics, Invention, Steam Engine, Railroad.
Along the way, I would also put Sanitation, Democracy, Magnetism, Guns, Explosives.

My order would be Inv, San, Demo (change govt), Nav, Phys, Magnets (start growing cities), guns, explosives, steam Engine, RR, Industrialization.

That's only 11 techs path, during much of which the advances will be made by Trade instead of Science, and often, when the civ is large enough, at the rate of a tech every 2 turns. So I don't see where KRC would ever be worth the shields unless you got it from a hut and had nothing else to build.

I thought Adam Smith was indicated in this game because I was having trouble making enough gold while running Luxuries at 40% with mediocre trade routes. I had harbors, temples, and markets in 15 cities so I saved 45g per turn at first, and eventually libraries too and a 5 more cities, so 80g per turn. It paid its initial investment in 20 turns, and then kept giving.

Great analysis Jokemaster!

Jokemaster said:

isn't it a disadvantage to research Engineering early on in the Republic period?

The reason for saying that is that it unlocks Invention for research , and then you're one unlucky hut pop away from losing half your van revenues (the risk is especially high if you don't have Warrior Code due to wanting to keep the 10s slot by avoiding a Feudalism pop, and even worse if you don't have the prerequisites for Economy. 27/93 chance of getting Invention scroll, owowow. 8/93 if Feudalism is available, but still.)

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How did you come up with 27/93 and 8/93?
I agree with your general theme. Engineering is rarely a research priority for me. However, I would like to point out:
- Engineering is needed for Sanitation. Growth of my science city is a top priority. Once I have Shakespeare (without it, it is hard to get past 13 and other odd sizes without a lot of support from trade routes and infrastructure) I want sanitation as soon as possible.
- While invention does cut trade, it is also a prereq for democracy and explosives, two very beneficial techs.

Jokemaster said:

Calculating ROI for one-time payment is a bit different, and the main thing that I'm interested in. The formula involved is, of course:
P=I(1+i)^n
P being the final result
I being the initial investment
i being the ROI (interest rate)
and n being the number of turns between van building and van delivery, as a squared function.

Punching in our example, we have the following. (Not including science beakers, double the value of P otherwise.)
PRE-INV:
P=I(1+i)^n
450=113(1+i)^10
3.9823=(1+i)^10
3.9823^(1/10)=(1+i)^10(1/10)
1.1481=1+i
i=14.81 ROI.
Which is insane.

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Interesting. Another useful tool to use for decision making; thanks. Particularly since you can roll that money into new vans and keep it going. Just two notes:
- Your assumption of 450 for the payout is overly optimistic for early mid game. Many deliveries in that era (of triremes) are around 100 and those that are above are typically below 200.
- Since your ships are not doing anything else, you should take their cost into consideration as well.

Jokemaster said:

I'm just pretty puzzled that it happens apparently often enough to mention it on the same rank as Adam Smith's when it can backfire so spectacularly, especially given how fast the wonder already goes obsolete with our playstyle.

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Putting King Richard in the same category as Adam Smith was not meant to imply they are of about the same value. It is just that based on my strategy, I divide the wonders into three groups: must have, nice to have, and do not care. In that sense they are both a nice to have. I will get them if I have the vans and no must have wonders to build.

How did you come up with 27/93 and 8/93?

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I looked up two separate pages on the Civilinic Books.

http://sethos.gmxhome.de/English/BookOfWisdom/hutoutcomes.html
http://sethos.gmxhome.de/English/BookOfStrategies/EarlyLandingGames.html#reschoices

The first one is quoted like this with regards to scroll outcomes:

"The result of a scroll outcome can be any unacquired Civilization Advance for which the Civ has all prerequisites. The chance of obtaining a specific Advance can be calculated by listing the position numbers of possible advances in an alphabetically-ordered list of all advances (as under @Civilize in Rules.txt). An advance's chance of selection is statistically equal to the distance between its position and the position of the advance above it (wrapping the list from bottom to top). "

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The second one, is of course Solo's list of techs in the game in alphabetical order, and their numerization (0, 1, 2)

Practically speaking, that means that when you research Alphabet, the odds of getting CB from a hut are very low, since Bronze Working is right above it (so only one number out of 93 will give a CB return) Same thing for Code of Laws: CB is 3 techs above, so only 3/93 odds of getting a CoL hut. (Factor in the 20% chance of a scroll pop afterwards.) It is from there that the 8/93 and 27/93 numbers are derived. There is a pretty yawning gap after Chivalry, which is activated if Economics (16/93) and Feudalism (8/93) are not available. If you get both of these techs early or lack the prereqs, danger danger.

Your assumption of 450 for the payout is overly optimistic for early mid game. Many deliveries in that era (of triremes) are around 100 and those that are above are typically below 200.
- Since your ships are not doing anything else, you should take their cost into consideration as well.

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Really? You must be doing deliveries that are closer to home than I tend to do: a 2x involving two size4cities gives me 264g with about 30squares distance on a large map, which carries a 20% debuff on trade. (Dual Republics Foreign Offshore obviously.) 150-200 seems to be on the low side once you celebrate your cities to size 7. Not sure how you can sustain your growth with low returns, especially how much it peters out post-Invention. Temporary shipchain I guess, as a stepping stone to greater things? Not sure how that works out tbh. (Although there is an argument that earlier deliveries speeds up techs like Democracy/Explosives that you did mention, which boosts speed of growth. Still lukewarm to the idea tho, unless it's a large flat map with few civs and foreign trading is unfeasible pre-Inv.)

Good catch on the ship maintaining costs tho. Not really sure how it affects pre-Invention vs post-Invention since you're going to be trading anyway, but I guess they can be factored in rushing costs and opportunity cost of not building a market/aqueduct instead. Technically you could also include the opportunity cost of not having a second trireme exploring, settling foreign lands and popping huts (instead you get unrest in Republic, uncontrollably so in Democracy) but it's going in territory that's really hard to quantify, so I'd steer clear of it. Microeconomic concepts can be useful in Civ2, but only when all the variables are known

Jokemaster said:

I looked up two separate pages on the Civilinic Books.

http://sethos.gmxhome.de/English/BookOfWisdom/hutoutcomes.html
http://sethos.gmxhome.de/English/BookOfStrategies/EarlyLandingGames.html#reschoices

The first one is quoted like this with regards to scroll outcomes:



The second one, is of course Solo's list of techs in the game in alphabetical order, and their numerization (0, 1, 2)

Practically speaking, that means that when you research Alphabet, the odds of getting CB from a hut are very low, since Bronze Working is right above it (so only one number out of 93 will give a CB return) Same thing for Code of Laws: CB is 3 techs above, so only 3/93 odds of getting a CoL hut. (Factor in the 20% chance of a scroll pop afterwards.) It is from there that the 8/93 and 27/93 numbers are derived. There is a pretty yawning gap after Chivalry, which is activated if Economics (16/93) and Feudalism (8/93) are not available. If you get both of these techs early or lack the prereqs, danger danger.

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Thanks for the details. I have read the early landing guide, but I had forgotten this part. I see where you get the 8/93 now. I think on the other one you have overlooked Currency and thus the chance is 17/93.

I also wonder where the 93 comes from? There are 89 techs in total not 93.

And finally, I have always wondered how come such detailed research on hut outcomes (your first link) could have such a glaring omission right at the start of not including the weeds (empty) outcome.

The discussion above started with a simple question in the GOTM 177 spoiler thread and took off. I decided it fits better here since it has already diverged from the particulars of that game significantly.

I also wonder where the 93 comes from? There are 89 techs in total not 93.

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The extra techs are plumbing and 3 User Def Techs. In MGE, there are an additional seven technologies for a round 100 total.

And finally, I have always wondered how come such detailed research on hut outcomes (your first link) could have such a glaring omission right at the start of not including the weeds (empty) outcome.

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I don't think you get weeds playing deity and raging hordes.

Regarding the value of KRC, I don't think there is much of an argument for it on the basis of direct shield output. It takes too long to even get the 300 shields back that you put into it, let alone the fact that the value of the shields declines over time. I think it is rather unusual to find yourself in a situation with an appropriately large city and 6 food or junk caravans and have no other wonder prospect for 20-30 turns. I guess that happened to Ali, but I don't think that is a sufficiently common occurrence to formulate a general strategy.

Is that the end for KRC? Maybe not. I build factories based on whether extra rows of shields will be produced each turn, which will lower rushbuy costs, usually by 25g per row, so a net payment of 21 gold per turn. Achieving an appropriate number of shields for efficient production of a military unit yields a similar calculus. If your SSC has a lot of things being rush-bought, then maybe KRC is valuable for the gold it saves. If KRC brings a city from 9s to 21s, for example, rushing caravans and buildings becomes 40-50 gold cheaper per turn. This starts to look like a more reasonable prospect. A pampered SSC could conceivably expect to have a long list of high priority projects in the mid game where funds for rushbuilding are available but not abundant, in which case KRC starts to look like it might be a decent money saver.

The other use for KRC that could be acceptable is building it near an enemy AI city, then constantly building settlers there to settle near an AI, disband and get inexpensive NONES. It can be done without KRC, but essentially doubles required funds by needing to rush 2 settlers instead of just one, which on top of Big Trade is too ambitious of a proposition. KRC can cut it to a single RB and save about 50g per turn.

That being said, it's still rareish to see it happen since it would also have to double as an SSC (or running dual size-20's earlygame) and it takes a lot of resources to get running (Especially when you consider that it would be a border city, and that vans would take more time to get there). Tried it once, but the results weren't satisfactory since Big Trade was lackluster and I didn't have the cashflow to support rushbuys and everything else.

It should also be noted that disbanding a city destroys any road/RR squares that were there beforehand, even is they were built before the city itself. So it becomes even more complicated and cumbersome if you don't pick a rivered spot to help settler movement pre-Explosives.

It gets easier after Railroad, but then the wonder expires.

I am playing GOTM 181 and once again I opted to build King Richard's. It was a hard decision and I am still not certain if it was the right decision.

In GOTM 181 (the pacific islander) we start in the middle of the pacific ocean and our land is an archipelago of small islands some of which can produce only 1 shield. Being in Republic even many cities with access to whales were down to 1 shield because of support costs. In a setting like this King Richard's is more valuable than usual due to the scarcity of shields. Furthermore, the long distances between your capital and many of your cities, means that even in Republic a lot of your arrows are lost to corruption and thus your income both from taxes and deliveries is not as great as it can be.

I got Engineering through tech trade with my key civ in -75. At the time I had all the ancient wonders I wanted and Marco. My top priority for vans was deliveries since I had no trade routes. I was in no hurry for the next wonder since none of the ones I could build were needed urgently:
- Michelangelo because at King level my cities were fine with Hanging Gardens and could not grow without seafaring and harbors. I did not have seafaring and no funds to make harbors with.
- Shakespeare because my science city was already size 8 and could only get to size 9 before running out of food.
- King Richard's because the vans would pay off more in deliveries and I rather save the food vans for Shakespeare or in case I have to snatch something quickly.

Then in +200 Sioux started work on King Richard's. 2 turns later Russians joined them. Neither had the techs to switch to any other wonder I wanted. Feeling that my other wonders are safe I decided to snatch King Richard's while I can and did so in +300. Both Sioux and Russians abandoned.

This did not quite work as expected. English developed Astronomy in +440 and Sioux got it from the Great Library. They immediately started on Copernicus at a time that I was ready to build Shakespeare. Not wanting to lose Copernicus I built that and delayed Shakespeare. This is at a time that I have reduced scientific research to 10% because I need money to build.

I am wondering if I would have been better off ignoring King Richard's and use those vans to build Shakespeare when I was ready for it.

There's a scenario called "Discovery" on Civ 2 Gold Edition, which illustrates how King Richard's Crusade could serve as a counter-balance to the shield-scarcity brought about by the Republic government-- you might want to play as the Dutch and check it out.

I think it would be worthy to ask though "How much production would seven new settlements bring?" when considering Richard's. I've noticed in many of Sid's games it can be dangerous to build more than, say, three wonders per Age-- just because of the amount of production that has to sit stationary as opposed to being diffused into other areas.

Edit: I'm feeling rusty here; with how I tend to play on Deity (not being so keen on the additional unhappy citizens due to the Civilization size penalty) I tend to gun for JSB, Magellan's, and Statue of Liberty. I nearly forgot how bad the corruption effects for distant islands could be; 1 sci each per colony at the cost of generating red-caps at home, ugh!