KB Small City Analysis

# Objective

Our objective here is to quantify the differences between small and large cities by analyzing COW formulas, in particular to evaluate the new proposed danger value formula.

# Assumptions

The assumption is that the COW formulas are intended to provide a level playing field for all cities, including pioneering cities. This is probably incorrect since the bias is so strong against cities with less than 15 active citizens.

More than 1 month after the beginning of the game period Katimavik Bay is still only at 13 Active Citizens. The attitude seems to be that pioneering cities should write off the first game period and just focus on building population?

The formulas apparently break down for a population under 15 ?

While pioneering cities should not be able to take advantage of their size unfairly, they should also not have to pay a penalty.

# Active Citizen Factor

(1)
$$Active Citizens Factor = 15 + 0.8 (ActiveCitizens - 15) = 0.8 active citizens + 3$$

There are 2 problems here.

1) for the first 2 weeks of the game period the number of Active citizens is 15 for all cities. This obviously give a huge advantage to large cities. The cost of an expansion was the same, regardless of population.

Why not simply set the initial Active citizen number to the average number over the last game period. Thats suree ly a better staring value than 15 for everyone.

2) The minimum value for ACF is 15. So 1 month into the game, KB's 13 active citizens have to make

City AC ACF City expansion donations per citizen
Katimavik Bay 13 15 30 30 / 13 =2.3
World VIllage 74 62 124 124 / 74 =1.7

How about for AC < 15 : ACF = 0.4 AC + 6

# Danger Value

The danger value is a critical parameter in the game. All cities should have an equal ability to protect themselves from the barbarian

(2)
\begin{align} Danger value = \frac { (Culture value Buildings + Culture value Active Citizens)} { Protection value} Protection Value = CitizemDonations + ArsenalDonations = C + A. \end{align}

The problem here is that the numerator is normalized by ACF , but the denominator isn't. Big cities pay more for building expansions and the total culture value of all active citizens possessions is divided by ACF to give citizens contribution.

The citizens donations in the denominator are not divided by the ACF. If all citizens makes 1 city guard donation a week, larger cities will make many more donations. This is an obvious mistake.

The proposed new protection value corrects for this and adjusts the arsenal value to be of the same magnitude

(3)
\begin{align} New Protection Value = \frac{C}{ACF} + \frac A {50} \end{align}

Unfortunately, it is still biased against small cities because of the ACF but less than the old one.

The following comparison assumes Level 2 arsenal for 6 weeks and 1 contribution per AC per week.

City AC ACF Arsenal citizen Old Protection Value New Protection Value old % citizen cont. new % Citizen contribution
Katimavik Bay 13 15 210 78 288 9.4 27 55
World VIllage 74 62 210 468 678 11.74 69 64

and with no arsenal for large city

City AC ACF Arsenal citizen Old Protection Value New Protection Value old % citizen cont. new % Citizen contribution
Katimavik Bay 13 15 210 78 288 9.4 27 55
World VIllage 74 62 0 468 468 7.5 69 64

We see that with the old formula, ACs contributing once a week, even WITH a level 2 arsenal for 6 weeks we're still nearly a factor of 2 off! How can this possibly be considered a level playing field? At least with he new formula, the balance tips in our favor with an arsenal.

# Dice and riddle Game

The intent was that 1/4 of the ACs must participate WITH A MINIMUM OF 15. Now the level playing field starts at 60 ACs. This effectively cuts us
out from effectively competing in these games for the foreseeable future, I'm sorry, this just doesn't seem right.

If the concern is really that I think the concern is that the larger cities would create a "small elite team of players" and game the system that way., let's find better ways of addressing this concern without penalizing small cities..

page revision: 0, last edited: 31 Oct 2010 23:13