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City Cost Idea


Guest Frawley
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Guest Frawley

Noting the following ideas from @Alex's thread on Nuclear Meltdowns.

1. Alex would like to slow down the growth of upper tier nations, and or speed up the early growth of new nations
2. Players do not want cities to be able to be destroyed
3. Upper tier players should keep the majority of the marginal growth they achieve per city

Therefore for discussion I'd like to present an idea that slowly reduces the costs of upper tier cities, as more an more players acquire them, I would suggest that this is not unlike reality, humanity has not built cities in the desert of Dubai without looking at cities in the USA or elsewhere.  Economically its called early adoption curve.  My formula is below:

unknown.png

DF = Discount Factor
CP = City Price
Roundup(x,2) rounds the calculated DF up to 2 decimal points (this amplifies earlier purchases, but is immaterial in the mid-tiers)

If you don't know what a the function of a square root looks like here it is:

unknown.png

Essentially discounts will initially be larger for each additional nation that purchases a city, because of the large number of people who join P&W and then only ever build a couple of cities (51.6% of nations have 3 cities or less), I propose that this only kicks in after the purchase of city 10 by a nation.  Prior to that they will always receive the maximum Discount Factor.

I have made a graphic with examples:

unknown.png

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Good idea, nice implementation, nice posting, but too complicated mathematically. You're pitching this idea to a guy who has over 100% probabilities in a probability of meltdown chart despite being an Econ student.

Also, I'll point out that if this is tested on the test server post-reset, the formula will trigger a NaN error due to there being 0 cities above 10 cities. Easily-patched with an if function and setting 0% discount there if there are no cities at 10 cities.

Edited by Inst
  • Upvote 2

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Guest Frawley
7 hours ago, Inst said:

Good idea, nice implementation, nice posting, but too complicated mathematically. You're pitching this idea to a guy who has over 100% probabilities in a probability of meltdown chart despite being an Econ student.

I didn't bother to check Alex's math there, but seeing as his stipulation was that there was 4,380 chances for a meltdown to occur over the course of a year a probability over 100% just means you would expect the event to occur X number of times.  Aka a 'probability' of 230% would be an expected event occurrence of 2.3 times per year at a set number of cities.

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More that you'd state "average number of occurrences" instead of screwing with probability, or do a proper 99.99% etc odds.


Early adoption does have the advantage of not being time-based (as I'd suggest) instead, so you'd end up with 3 nations left in the game with more than 1000 cities each. It'd also create a left-skewed distribution of city count, although whether that's desirable (80% of actives have around 30 cities) is another question.

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  • 5 weeks later...

@Frawley

 

Just curious what you'd think, but what if we used sigmoid functions?  x / (1+|x|) is centered on 0, but we can easily adjust it to center on the averaged city count with x = current city count - average number of cities. We also need a more elegant way to filter out micro-cities and cities from players who don't play; the city count is left-skewed and just discarding cities with less than 10 cities is rather off, especially if the "people who go idle and inflate nation counts for 3 months" number keeps on moving as a consequence.

 

Arithmetic mean gives you a number below the true peak of city counts, median gives you 5 cities, and mode gives you 1 city. Would a geometric mean work?

 

The reason I prefer sigmoid functions is that a healthy game doesn't go into bimodal distribution based on city counts. Instead, it sees a numerically large center, perhaps around the Thin Roq Line (16 cities), with essentially gaussian distribution with Typhon-land and TKR-land being outliers, instead of tiers.

Edited by A Boy Named Crow

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