[Geek] Conversion to current values in Civ

[pomthom]

A very common discussion we can find in many parts of these forums is comparing immediate/short-term returns VS medium/long-term returns in Civ.

Ex:
- I have a GS, should I bulb and benefit from 800 (or whatever) now or should I build an Academy?
- Should I build an AP monastery in this city just for the +2 bonus knowing that I will tech Scientific Method in X turns?​

We usually compare raw investments and raw returns, but we all know that 1 / now is worth more than 1 / in 10 turns.

Estimating such things is very common in the business world, there are many methods but basically the idea is converting future returns to current value. You guys remember anyone who tried fooling around with accurate valuations of /// investments in Civ 4? If not I might take a crack at it just for fun

Of course choosing some axioms such as 1 = 2 = x ... would be in order (it's "simple" to compare investments VS returns but most of the time it's not so simple).

I tried searching with the forum tool but I don't know how to specify looking for several words in the same post...

 

[pomthom]

I am also very interested in the real value of fail gold compared to building wealth... I predict some surprise and debate on that matter

 

[soundjata]

Excellent research topic. I approve

 

[GKey]

Indeed fantastic topic to discuss. I doubt it can be covered in single thread though. This topic is HUGE and been discussed in many threads for years. Just take current SGOTM, players tinkering with this right now.

I can already tell you it will be way more complicated then x-food = y-hammers = z-commerce

If you succeed to give some kind of method for this - my sincere hats off to you.

 

[Fintourist]

FYI, this is the best thread/study about the topic that I've seen so far: http://realmsbeyond.net/forums/showthread.php?tid=4876

As a summary, the opening post claims that conversion rates between :: is ~8:5:3 and that a proper discount rate is ~3.5 %/turn. Later discussion and tests in the thread end up with similar results. If there are similar past studies here at CFC I would be interested if someone can link the relevant threads. This is a very complex topic, but I personally find it interesting as well and I use same principles and ideas when making my everyday micro decisions.

 

[Thrar]

That's a very interesting post.
The 3.5% seem to be for quick speed though. Since 2 turns on quick equal 3 turns on normal, would that mean the interest rate is 2.3% on normal, since cubic_root(3.5%^2) = 2.3% ?

 

[TheMeInTeam]

Long ago I brought up a similar thread including the AI's valuation of 10/6/4 //, hopefully we can shed more conclusive light on it this time. PV isn't a new concept, but the problem is valuation. In finance we have some nice formulas to follow, in Civ we'd still need to make and test them haha.

We have a few challenges to make any serious headway:

- Valuation of , and are not static. For example, if you're about to go into strike is more valuable than pre-currency, or more accurately you lose fewer by avoiding strike. early has more valuation regardless; there's no other way to attain at least writing without it. How much does this change? value alters based on city size, need for GPP, slavery, and more. In saying that comparing current to the returns in 30 turns from you, you're actually selling the difficulty short .

- There are break points. Specifically, things like writing, liberalism, nationalism, rifling, MT + gunpowder, assembly line, and astronomy can all have a potentially enormous impact on yields. We'd have to adjust for this effect in Civ IV.

- One of the most difficult things to value even with a basic opportunity cost comparison is the value of an additional unit. Buildings are somewhat simpler because you can predict their yield, but units are at once "risky" (IE might get very little for it) and "safe" (IE if you get declared on and die none of your investments otherwise matter). This is further convoluted in that units also have break points, and invested in a unit now can in some cases be worth less than those invested in the future.

A decision making heuristic that is consistently effective on the highest levels from a micro standpoint would be stupendous, and I've sought one a long time. I'm rooting for your success and will help if I can; it's basically the only way I can win on deity with any consistency since I'm not willing to take long turns!

 

[VoiceOfUnreason]

There's some prior art here.

 

[pomthom]

Very interesting read Fintourist

Long ago I brought up a similar thread including the AI's valuation of 10/6/4 //, hopefully we can shed more conclusive light on it this time. PV isn't a new concept, but the problem is valuation. In finance we have some nice formulas to follow, in Civ we'd still need to make and test them haha.

We have a few challenges to make any serious headway:

- Valuation of , and are not static. For example, if you're about to go into strike is more valuable than pre-currency, or more accurately you lose fewer by avoiding strike. early has more valuation regardless; there's no other way to attain at least writing without it. How much does this change? value alters based on city size, need for GPP, slavery, and more. In saying that comparing current to the returns in 30 turns from you, you're actually selling the difficulty short .

- There are break points. Specifically, things like writing, liberalism, nationalism, rifling, MT + gunpowder, assembly line, and astronomy can all have a potentially enormous impact on yields. We'd have to adjust for this effect in Civ IV.

- One of the most difficult things to value even with a basic opportunity cost comparison is the value of an additional unit. Buildings are somewhat simpler because you can predict their yield, but units are at once "risky" (IE might get very little for it) and "safe" (IE if you get declared on and die none of your investments otherwise matter). This is further convoluted in that units also have break points, and invested in a unit now can in some cases be worth less than those invested in the future.

You are absolutely right. The first hard part is making reasonable not-too-complicated assumptions that represent a particular break point and/or investment.

A decision making heuristic that is consistently effective on the highest levels from a micro standpoint would be stupendous, and I've sought one a long time. I'm rooting for your success and will help if I can; it's basically the only way I can win on deity with any consistency since I'm not willing to take long turns!

That would be incredible but I truely believe there are too many variables to end up with a simple generic tool.

However there are a lot of small truths out there that could be identified. A lot have already been found on these forums. Finding a good method to compare simple investments and returns in Civ would already be a tremendous headway.

 

[Fintourist]

That's a very interesting post.
The 3.5% seem to be for quick speed though. Since 2 turns on quick equal 3 turns on normal, would that mean the interest rate is 2.3% on normal, since cubic_root(3.5%^2) = 2.3% ?

Yeah, good point. 2.3 % for normal speed is equivalent to 3.5 % on quick speed.

Btw, if one reads that linked thread further the above-mentioned value is tested with some empiric data and it fits fairly well. As everything in civ, it is of course very much circumstance-related, but if I have to calculate something including the discount rate that would be a reasonable starting point.

 

[Fintourist]

And to add what TMIT wrote, even in fairly straightforward situations it is extremely extremely difficult to quantify future benefits and opportunity costs in a way that it actually helps you in decision making. E.g. "should I build a settler or Oracle" is quite a task to solve through calculations. That said, I'm looking forward to breakthroughs here!

 

[kossin]

There are other variables that makes this almost impossible to solve, e.g. how far along you've played.

So I'd say general models are about as good as you can expect to get.

 

[pomthom]

There are other variables that makes this almost impossible to solve, e.g. how far along you've played.

So I'd say general models are about as good as you can expect to get.

Encouraging!

 

[timmy827]

Whoops, didn't refresh page before posting. (was: link to the RB thread that fintourist put up).

 

[VoiceOfUnreason]

Looking at another thread, it occurred to me that one analysis I would love to see: does bulbing Education pay off in an OCC space game?

 

[barbertje]

Looking at another thread, it occurred to me that one analysis I would love to see: does bulbing Education pay off in an OCC space game?

You get about 1550 beakers for a great scientist bulb. In my last game I teched education in 10 turns at turn 126. Bulbing takes only 6 turns off.
The bulbing beakers don't have a prerequisite bonus, so they're only worth 1/1.2 = 0.833 normal beakers = 1291 beakers.

The city made about raw 140 beakers with an extra multiplier +95% before oxford (2 monasteries)

Bulbing gets you an extra 125% for 4 turns, since both the university and Oxford come 4 turns earlier. This produces another 140 * 6 * 1.25 = 1050 beakers extra.

So bulbing will get you about 2340 beakers extra. There are a few extra bonuses. currency (maybe 10 beakers/turn) and printing press (about 5 beakers for each village/town) will get researched sooner, producing some extra commerce if you get it earlier.
After education, the next tech target is biology.
Libbing biology was done 41 turns after getting education (not bulbing it). You would do this about 3 turns earlier when libbing biology. (in 40 turns, the settled scientist would produce about 1200 beakers, so the scientist has about half caught up.
This means a 3 turns earlier national park, and 3 turns earlier biology farms. It's rather hard to quantify this. You maybe get 10 gp after this, all of them 3 turns earlier. Ordinary scientists will also get hired earlier. Might be another ~1000 beakers.

However there were still about 200 turns from the turn, the scientist that bulbed education was produced, to a launch in the late 1800's. That's about 6000 beakers of tech, so the settled scientist should eventually overtake the education bulb.

If the edu-bulb will makes it possible to lib biology, instead of something cheaper, It could well be worth it.

 

[Dubioza]

• About // value and ratio:
  
  There really are too many variables to be considered and all of them are dependable on one another or on specific situation. And even those variables have variables. If you're looking for one basic equation to describe that in any given situation, you will fail; there's just too many things to consider. I'll be happy to be proven otherwise, but I feel like you're looking for Einstein's unified field theory. Unlike him, you do have all constants and no unsolved mysteries, but still...you might be headed that way. If you do get equations for every given situation, leave it there. Just be careful not to leave out one of the many many situations.
  
  Even if you do find all the equations, in practice you will turn this math upside down anyways with city specialization and maximizing , or in different cities without too much regard for idealized conversion rates. (source: VoiceOfUnreason, modified by yours truly)
  
  
• About Return of Investment (RoI):
  
  It's simple concept, but also hard to generalize and easiest to explain on example. Again, unified field theory warning.
  
  Example: The Great Library. There are lots of variables to be included, let's keep it simple.
  
  Cost: 350 . Say you build it in T75 while it obsoletes with Scientific Method; say you research SciMeth in T175. You have 100 turns in which you want your 350 back. With TGL you get 2 free Scientists, with base value of 6 and 6 . During 100 turns that's 600 and 600 (or 600 and 3 Great Scientists) which can be used in many ways, say 1 for Academy and 2 for bulbs. Quantify this however you want, it's worth it. All that is without modifiers (Marble, OR, Forge, Industrious) when building TGL and & modifiers for 2 free Scientists (Rep, Academy, Pacifism, NE, Philosophical) and others. You also have to consider if in that time you build it you maybe have more pressing stuff to produce in your city. You can calculate RoI for every situation if you catch all variables and even find the sweet spot to get the best RoI ratio.
  
  
• About the real value of fail gold compared to building wealth:
  
  Building Wealth or Research gives you ratio: 1 = 1 which is not efficient, even more so when you know that those are not affected by commerce buildings; but only hammers buildings.
  
  Example: City has 6 base commerce and 4 base production. Build or and you get 10 output. Get Library in the city and you get 25% boost on base commerce (6 becomes 7.5), but 4 from stays 4 - for total of 11.5 output; the same output is for as well, variations depended on slider. If you get Forge in the city you get 25% boost on base hammers (4 becomes 5) and get output of 11 without Library (6+5) or 12.5 with Library (7.5+5).
  
  Fail-gold building WW's is all about multipliers. You can have 1:1 ratio as well, but include Forge (25%), Organized Religion (25%), Resource access (100%), Industrious trait (50%) (and later other hammer multiplier buildings) you get 200% from you hammers. From previous example, your 4 are suddenly worth 12 with mentioned multipliers. Your one 30 chop is worth 90 . These hammers are converted to fail-gold when WW in question gets built. Bad side of this is if you don't want to finish that WW; then you're forced to wait for fail-gold until someone else completes it, so in some occasions when you urgently need or it's better to just do that. You can fail-build National wonders as well, just be careful - not all of them have resource multipliers, so return will be smaller.
  
  If you have decent-sized empire you can fail-build the same WW or NW in multiple cities; just queue WW in one city, put overflow or chop into it for a turn, next turn remove it from queue and put it in some other city and repeat.
  
  
• Call me Mr. Obvious for explaining this "rookie style" (I got into it and couldn't stop), I hope someone will find it useful. Maybe it gives you idea on how to approach your Theory of everything.
  
  
• I hope these info's are true, feel free to correct me if they're not. Or if you simply disagree.

 

[Thrar]

A difference seems to be that you are looking at the issue from the bottom up, tallying up numbers and trying to compare them.
The discussion over at RB took the opposite approach - they looked at how certain indicators develop over time to get an idea of how much average growth per turn to expect.

Going top-down, it's pretty easy to get reliable numbers. Get a reasonable number of games from players at comparable levels, measure the indicators of your choice and use a bit of math to calculate the growth rate.
This might not help too much to make micro decisions like whether to build building A, building B, or a unit, since there are a lot of variables involved. It can however tell you a lot about the big picture, e.g. comparing different tech paths, settling approaches, wonders etc.

 

[pomthom]

EDIT:
@Dubioza:
No, my intent is not to find the universal truth out there that will bind everything together because like you and many others I think there are too many variables and different situations in Civ.

What I would like to do is take very simple situations where 2 different choices can be made for the same investment and compare them. Try to breathe a bit more accurate mathematical life into well known concepts to see what the numbers really tell us.

Just like building Fail Gold vs building Wealth. FYI I'm preparing a first analysis on that...

Tomorrow hopefully?