Inflation in CivIII - Revealed!

[Capt Dizle]

I never took economics. Would the inverse of depreciation be appreciation?

Anyway, how can this number mean anything in a universe where the AI trades techs like crazy and/or you can sell a tech to each AI in turn for tons of stuff.

All I can see is that you have established some sort of baseline for completing the tree.

My lack of formal education assaults me.

[Azrael-42]

Wow. You guys are talking some pretty heady stuff here, and since im just in grade 11, hate business courses (they are a load of BS)(although im good at math) i won't make too many comments here about your financial math. I will just point however, that the quantity of analysis that you can make for a game actually goes down past a certain point of complexity. Consider that human knowledge is very largely based on generalizations. Newtonian physics, mathematical formulae, and musical theory are all examples of generalizations. All of them say, if such and such and such and such, then by doing x you can conclude y (or something to that effect). Of course, physics and math are precise whereas musical theory is not, but essentially both of them try and generalize. Rather than just taking one extremely specific situation, they take a whole bunch of similar ones and realize that you can do much of the same things with all of them. Human knowledge is essentially the sum of all these generalizations. In a computer game, there are so many factors and variables that it becomes more difficult to generalize... With so many factors there are much more exceptions to take into account, and your generalizations have to become more and more specific. Whereas in chess, chess is actually much simpler than CivIII. Yet, it is utterly impossible, and i mean impossible, to analyze civIII in the depth that chess has been analyzed. Nevermind that chess has been around much longer. Thus my point is, that in trying to generalize CivIII you may just be wasting your time. CivIII, and computer games in general do not lend themselves to such in depth analyses like chess. CivIII is trying to simulate something. Chess has no such pretensions. It doesn't need to be complicated. That's why you have computer programs that can actually numerically analyze chess situations. Good luck doing that in CivIII.

[David Weldon]

First, I absolutely agree that nothing can be said definitively based on my analysis. As I have said before, logging the actual production of your empire each turn and then averaging those results of a very large number of games and play styles is the most direct and accurate way to calculate "inflation". The world size and type will also certainly play an important role, and the base rate should probably be adjusted to make the result more accurate on non-standard worlds. However, I have found the results enlightening for the following reason:

We know that growth doesn't happen at 10% per turn. Myabe it's 2% in a game with lots of warfare, maybe it's more like 4% in a game with lots of trading and peaceful infrastructure improvements. Certainly there will be specific situations where the "average" growth rate shouldn't even be taken into consideration when making a decision. The point is that now we have a number (let's call it 3% so that it's a touch slower than my idealized scenario) that we can use to compare various civ traits, building strategies, etc...

One of the biggest problems with an "average" growth rate is that growth actually occurs in spurts. When one gets a particularly useful tech (like steam power or replaceable parts), then it's possible to very quickly increase the production of your empire or to quickly take over a weaker empire, thus causing instant growth.

It should be clear that this is a "rule of thumb" calculation to allow certain things to be debated with more accuracy. It's not a law that has to be considered while playing the game in order to be successful.

As for the term, I like "inflation" more and more as I think about it. Consider units not as goods, but rather as currency. Shields and Gold (pennies) can be combined to form units and city improvements (nickels, dimes, quarters, dollars, etc...). These units and improvements are used to buy the only good in the game, victory. Early on you certainly don't have enough money to buy victory outright so instead you purchase advantages. For example, you can spend cavalry to capture cities, or you can spend temples to build culture to include an important resource in your territory. Later units are definitely more valuable than earlier units, just as quarters are definitely more valuable than nickels. But the inflationary aspect is that the cost of an advantage increases over time because your competitors are growing.

In real life, there are reasons why the risk free rate of return is not equal to the rate of inflation, but they are mostly based on local economic imbalance (i.e. America's inflation might not be equal to the world-wide growth rate). For purposes of discussion in this forum, I think inflation (and discount rate) is a good and useful term.

Sorry for the length, but here's a quick example of how to use the inflation rate to properly discount future value:

Infation rate: 10%/day (i.e. X 1.1 per day)
Gift today:100 units
Net Present Value (NPV) of gift today: 100 units

Gift tomorrow: 105 units
NPV of Gift Tomorrow: 105/(1.1)=95.45 units. Take the Gift Today.

Gift in one week: 180 units
NPV of Gift in one week: 180/(1.1^7)=92.37 units. Take the Gift Today.

Gifts that are a fixed amount per turn over time also have an easily calculated NPV, but I'll leave that for your economics classes...

[Lucky_Shot]

Inflation in Civ III defined

What this string is struggling with is a method to quantify the phenomenon of a resource early in the game being vastly more valuable than an equal quantity of the same resource later in the game. We obviously understand this intuitively and make decisions that take the phenomenon into account. You are to be commended for attempting to understand it from a quantitative perspective, as it affects numerous decisions, including choice of traits.
I cannot resist commenting, in agreement with Blaupanzer, that the price of advances is irrelevant to determining the value of capital. A new paradigm is needed and it is not based on the consideration of the *price* of goods, which is typically invoked in the definition of inflation. The price of goods is fixed. What is in flux is the quantity of resources going after those goods. It is inflation to be sure, but it depends on how wealthy one is, which depends on what turn it is.

I would suggest that the value of any item be expressed as a fraction of one's total holdings. This already creates a problem because it requires a method to smoothly convert shields to coins to food to people to units, including the one spearman who is going to save your capital from a sneak attack by barbarians. For the sake of argument, let us assume that the multiple resources have some exchange rate, although unknown and possibly very difficult to quantify. The point I wish to make is that players subconsciously or perhaps consciously invest (risk) resources based on what fraction they constitue of their total capital. If I own a single settler at the beginning of the game, its value is very high: 100% of my total risk capital. The value of having a seond settler at that stage is thus equal to 50% of my total holdings. The Expansionist trait recognizes that the value-to-holdings ratio ("pre-inflation" value) of individual units is extremely high in the early game. As the game progress, the value of the kind of unit supplied by the Expansionist trait drops precipitously. Why is this so? It's not inflation, really. The number of dollars (or shields or delayed temple) to buy the unit is the same. The unit is devalued because its cost as a fraction of total investment capital is lower.
Civ is a game of resource management and the rate of growth is phenomenal; so phenomenal that the "opportunity cost" of improperly invested resources is nothing less than the quantification of failure. The risk of loss from opportunity costs is most acute at the early stages. I cannot afford to lose my first and only settler. I cannot even afford to screw around with my only settler. It is priceless. My second unit is almost priceless. Losing my third would still be a disaster possibly worthy of starting over. As gameplay progresses, the value-to-holdings ratio gradually drops. I can afford to risk losing units to enhance the investment value of the remainder of my "portfolio." In fact, I must risk a fraction of my portfolio to maintain the high growth rate I need to match that of the AI. Eventually, money, shields, units, even entire cities comprise sufficiently small fractions of my total holdings that I can afford to lose them and still survive. The reasons are two-fold: 1) they are a smaller fraction of my investment capital and 2) the time left for them to accrue "interest" is less. The value for game play, which is the only value that matters, is a function of the percentage of total loss.

Bottom line, Civ is a real estate investment game. I may pay for land and capital improvements with blood, or with knowledge, but what I am constantly focused on finding a place for my people to live, work, and acquire more real estate. The value of resources, inflation if we want to call it that, is measured by their relative importance in securing the goal of maximizing ownership and productivity of land and the wealth it creates. So what I do with the first shields and shekels my first city produces is calculated to derive the maximum benefit in increased holdings later. And their value is proportional to their instrumentality for gameplay: their potential to arrive at victory or their loss to lead to defeat.

I propose therefore that the value of any resource can be estimated quantitatively as a fraction of total holdings. The cost of advances or wonders or units is only moderately relevant because at any given turn, that amount always translates into a percentage of the player's net worth.

This obviously offers little help for precise calculations but it does offer some hope of incorporating game time into the value of things. Now any sensible player is shaking his head and saying, "It's not what you have, it's what you do with it." How very true. But size does matter. And I would maintain that, whatever our playing style, each of us calculates what we are willing to risk by what we have.

I do see a great problem in translating coins into shields into food and I have seen discussions that would equate the three. I don't know how to feel about that because I have not actually played Civ III. Yes, I am basing my comments on an abstract understanding only! (I'm holding off buying Civ III until I have enough time to play without getting fired.) But based on my experiences In Civ II, I have to guess that it comes down to cases. Depends on the level of play, depends on the piece of land, depends on the combat environment. It may be different in Civ III. In Civ I and II, shield production was of paramount importance in the long run. I killed for coal. To paraphrase the Fabulous Furry Freak Brothers, shields will get you through times of no gold better than gold will get you through times of no shields. But you do have to have money, and you do have to have food.

Irrespective of the particular rules, I suspect it may be difficult to come up with a "gold standard" to compare resources one-for-one simply because they do different things. But IF one could arrive at a currency exchange rate, or some reasonable facsimile, I believe the value of one extra gold per tile might be compared to the ability of a worker to get twice as much done. Especially if what the worker is doing leads to a gold-to-gold comparison. What you are plucky enough to wonder is how that relates to game time because small differences early in the game matter a great deal. I am simply suggesting that that "earliness" that can be captured by expressing values as a percentage of net worth. I do think it is a worthwhile exercise to try given that people are somehow intuitively making the decision already. I may have more ideas when I actually buy a copy!