dCity is a town simulation game that borders on DeFi running a reward pools worth over 100k in current USD value (@dcityrewards).

This post is a part of a series that attempts to demonstrate the game mechanics for new players. Anyone specifically interested in the 3rd Edition upgrades can skip it and refer to the manual instead.

## No Need for Millions

#dCity has just recently launched a brand new graphic user interface. One of the things I like is showing a lot of global stats that allow you to see how large your piece of the pie is in various departments. Population might not be the best example (counterintuitively, it might vary a lot) but let us have a look anyway. The total population of dCity universe is 24.8M which happens to just barely beat the population of New York's metropolitan area. I am not asking your dCity to compete with that when - on the day of publication - the top dCity falls somewhere between Budapest and Cologne-Bonn metropolitan areas with 2.2M population.

Every dCity has the NY-Numbers, even before you learnt what they were.

Anyone should know the NY-Numbers for their dCity but there is no point in knowing them before understanding what they mean.

I have recently asked you to follow an imaginary deserted island growing from a single-Hotel start-up to a thousand-Hotel mess in the Beach tutorial. Every time we added a Hotel card to the existing city, we added 15 jobs to the economy. The population effects were wild and seemingly unpredictable - only learning we never added enough population when the city was small and we added way too much once it grew too large.

This post is intended to turn the chaos into a predictable urbanism excercise without unnecessary math.

## Population Formula

I am going to avoid the formula that has the ugly `x^0.7`

component in it. I can deal with it but I have a Masters degree in math. You should not need one. All you need to know is what an extra Hotel card with Population: +4 and Popularity: +5 does to your dCity *total* population.

I emphasised the word *total*. The *total* population is not the total of your cards' population scores. That is what we call *base* population.

Then comes the popularity effect. The higher the total of your cards' population scores, the higher your popularity *multiplier* is. We do not talk of *base* popularity anywhere as much because to be useful, it needs to be crunched (through that ugly `x^0.7`

thing) to arrive at a popularity *multiplier*. Than you can just multiply the *base* population with popularity *multiplier* to arrive at a *total* population.

## The Trick

Adding Population: +4 and Popularity: +5 all at once is tough math. Let's cheat a little. Pretend we are adding 4 Worker cards and 5 imaginary Popularity: +1 cards instead - one by one.

First of all, when we are adding the Worker cards, the effect is constant. I mean, you can observe that one card adds 2 *total* population while another card adds 3 *total* population but that is no big deal. While adding say 2.33 population per card, the rounding goes up or down in turns. You never add four, you never add one.

Secondly, we never need to know what cards are in the city already. All we care for is the current base population and the current popularity. If the numbers are identical for two cities (even if composed from different individual cards), the effect of adding any card to each of them is also identical.

Lastly, adding those imaginary Popularity: +1 cards (that do not exist in the game and can only be executed within our minds or in a spreadsheet) is more tricky than adding Worker cards. The effect of the second card is different from the effect of the first one. This did not happen in the population experiment. Blame the `x^0.7`

for that! In practice, the change is not too bad for a reasonably sized city. The bigger city, the more robust city (against this issue).

## NY-Numbers Definition

Two important characteristics of a dCity are starting to shape from this experiment. For a dCity of A that has a given *base* population and given *popularity* we can note down a number that tells the difference between "Popuation of A" and "Population of A + 1 Worker".

You better compute both numbers without rounding and treat the diference as a real number (not an integer). Shortly, we shall see why.

But first, we do the same computation for "Population of A" and "Population of A + 1 popularity".

If it was just one number, I could call it J-Number (for Jelly-Number) because that is what everyone in science tends to do for centuries. Unfortunately, I was too smart to ~~invent~~ discover two of them so they need distinct names. P-Number (for Population) and P-Number (for Popularity) do not work so let's call them N-Number (how much a single populatioN adds to a city) and Y-Number (how much a single popularitY adds to a city).

Now, when we know N-Number and Y-Number for our dCity (up to a reasonable amount of decimals), computing 4N+5Y gives a great approximation what a Hotel card adds to our *total* population. The closer the result to the number of jobs added by the card, the better fit the card is to our city!

## Playing on the Beach

You should feel tempted to apply the knowledge to the beach example. I can inform you that a dCity of 286 Hotels (*base* population of 1144, popularity of 1430, *total* population of 2994) has a N-Number of 2.6171 and Y-Number of 0.9055 which makes it a great town to add a Hotel in as 4N+5Y totals to 14.996 that rhymes with the 15 jobs created.

For now, I will leave it to you to decide whether or not you want to set up a dCity of 286 Hotels or not and whether the numbers actually behave in that area. If there is an action in the comment section, i will happily come back to compare my views with those of the readers.

The tough part is calculating your NY-Numbers. N-Number is easier to get as it is exactly what I called popularity multiplier. In the new interface, you can find "Popularity bonus" in the City-Map section in the population popup. The Popularity bonus is shown as a percentage so you first need to divide by 100. However, that is just the bonus, not the multiplier. You need to add one to use it the way it was treated in this post. The bonus can be as low as zero but +1 on population still adds at least one person. A bonus of 50% would be an N-Number of 1.5 (just as you would call it a 1.5 popularity multiplier). A large city with 520% bonus is at a greater risk of mistaking N-Number for 5.2 when the value is 6.2 (adding six or seven people a pop).

Y-Number is tougher. It can be as low as zero and depends on both population and popularity so it needs a 3D graph to be plotted. Fortunately, it is the more stable of the two and for most practical cities, it varies less than the N-Number on common changes. Spreadsheet fans can surely track it down after picking up the formula from the Info page. Others should probably bother the devs of their favorite interface (there are actually a couple centered around dCity markets) to have the NY-Numbers shown on screen.

Thank you for reading.

If you feel curious, you can check the previous posts on dCity population - Park Teaser - Population Tutorial - Beach Post

If you liked the challenge but feel dCity is not your thing, you might like my First Hour and First Day posts on Rabona game.