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By Celestial_Dawn
May 20, 1999

note: A discussion on the recent column by William Westwater begun on our forums. WW in response posted an example with numbers. We post it here, along with Celestial Dawn's reply.

Mr Westwater

Section I - Your initial Assumptions

I'm afraid that your concrete example isn't quite concrete.

City 1:
Pop 5. Pop are currently on:
Forest 20 P, 5 F
Forest 20 P, 5 F
Shallow with Net 10 P 20 F, 5 G
Shallow with Net 10 P 20 F, 5 G
Shallow with Net 10 P 20 F, 5 G
Total: 70 P, 70 F, 15 G
Total after crime: 63.5 P, 63.5, F, 13.5 G
Food Eaten: 22.5 F

Since you want 'concrete' examples, we'd best make sure that the base city model you are trying to sell us is realistic.

First of all, you obviously didn't open this up in the scenario editor, but rather simply plucked a few numbers out of a hat. Or shall I say, you carefully chose those numbers instead.

A few observations:

1. You forgot the effect of the initial city tile. That tile produces too, in addition to the other five tiles above. This is the most obvious proof that you plucked numbers out of thin air and didn't try it in the Map Editor.

2. You've ignored the effect of trade goods. You are aware that players who do not ICS almost always place a city within reach of at least one trade good.

3. It seems that you've chosen your tiles carefully to suit your arguments. A city has twenty tiles surrounding it, and you chose such an unlikely site for your city that the best you can do is pick is two forests that give no gold? Where did you build your city? In the Amazon? And even the Amazon has rivers ...

Is there not even one hill? More water? No rivers? No trade goods? None of these in 20 tiles? I can understand if the AI is forced to place one forest, but two?

Certainly you've artificially reduced the gold production somewhat. As a test, let me ask any of you reading this to open up your scenario editor and build a city, anywhere. Edit the city so that its base population is 5. Let the AI place workers by default for you. Tell me how often you end up with a tiny 15 base gold.

I believe that just a city of size one alone with Trade Goods would make 15 Gold. If a city of size 1, can produce 15 gold, how more so a city of size 5?

The numbers I used as my assumption in my spreadsheet = 10g for first population unit, and 5 gold thereafter is pretty accurate, Mr Westwater, once you consider Trade Goods, rivers et al. I ran over 50 iterations in the Scenario editor just to make sure that the assumption was more or less accurate.

I believe that in a city of size 5, gold production would more accurately be in the region of 25-30, unless you deliberately built your city at the South Pole.

Section II - A more 'concrete' Base Gold

So let's make your initial assumptions a little more 'concrete', shall we?

You forgot base tile production, and chose such an unlikely site for your city that in 20 tiles you couldn't find one hill, river or trade good to play with.

So, let's be conservative, and say this city has no rivers in 20 tiles, your city tile is on a plains or grassland square, and you have only one trade good, and it's in a forest, which explains why you'd pick a second forest to work on when there are 20 tiles to choose from.

So add +10 gold, base Gold = 25.

Section III - Your understanding of how Crime works is wrong

I hate to have to tell you this, since you're the lead designer for CTP at all, but your conception of how Crime works is flawed.

Total: 70 P, 70 F, 15 G
Total after crime: 63.5 P, 63.5, F, 13.5 G

Actually, Crime is only applied after Gold multipliers have been applied and not before.

In other words:
Surplus Gold = (Base Gold) * (Gold Multiplier) - Crime - Upkeep - Base Gold
and not
Surplus Gold = (Base Gold - Crime) * (Gold Multiplier) - Upkeep - (Base Gold - Crime)

Believe me, they are not the same.

The correct equation actually works out in your favour as the magnitude of the Crime effect is greater. But I will be my own devil's advocate on this particular issue just to show that I approach this from a strictly mathematical and conceptual point of view.

I form my conclusions from my results, and confirm them by observation, not decide what result I want to get and then fudge the numbers to get those results. *ahem*

Let's investigate the magnitude of your Crime effects under the different models:
Let Base Gold be x.
Let Upkeep be y.
Let Crime Rate be 0.1.

Eq 1 - Surplus Gold = Base Gold * Multiplier - Crime - Upkeep - Base Gold

= 1.5x - 0.1(1.5x) - 5 - x (the correct eqn)
= 1.5x - 0.15x - 5 - x
= 0.35x - 5

Eq 2 - Surplus Gold = (Base Gold - Crime) * Multiplier - Upkeep - (Base Gold - Crime)

= (x - 0.1x) * 1.5 - 5 - (x - 0.1x) (your eqn)
= 0.9x*1.5 - 5 -0.9x
= 0.45x - 5

To show that I got your equation correct, let's substitute 15 for x and we get 1.75 gold, which matches your results.
If we substitute 15 for x in the correct equation, we get only 0.25 gold, which as I've said, works in your favour because the magnitude of the crime effect is greater.

However, I've already pointed out to you that your 15 gold example is unrealistic. How many of you have actually built a Marketplace in a city of size 5 and then found that your gold level only increased by 0.25 gold per turn? Does this match anyone's real life experience, really? Yet another example to show how WW picked his numbers to illustrate his point.

Section IV - The Rounding Effect

Ok, now that we've dealt with the faulty assumptions and the correct equation of the Crime effect, let's move on.

First of all, let me say this - even the above mathematical formulae is not an accurate presentation of how things work in CTP, since it doesn't take into account rounding effects.

In CTP, fractions are rounded down. Meaning if you have 3.99 Science, you only get 3 Science. If you get 4.1 Gold, you only get 4 Gold.

It doesn't round to the nearest figure, it always rounds down.

Simplistically, you can ignore rounding effects to get rough values of how production works, but if you want the real effects, you need to factor in rounding. The reason I want to be precise about this was that in WW's Value of School, he wanted realism - he told us to factor in Crime etc etc. Since he wants a realistic model, he'll get one.

As you will see in the next section, rounding effects do make a difference.

(My spreadsheet takes into account all these rounding effects if any of you are wondering)

Section V - The Actual Calculations

Wow, we're finally here. At least no one will accuse me of not being thorough.

Marketplace alone:
Surplus Gold = Base Gold * Multiplier - Crime - Upkeep - Base Gold
= ROUNDDOWN(25 * 1.5) - ROUNDDOWN(0.1*25*1.5) - 5 - 25
= 37 - 3 - 5 - 25
= 4 Surplus Gold. Check the actual result in the Map editor for a Crime Rate of 10% and a Base Gold of 25 with Marketplace if you don't believe me. You'll see Crime = 3 and Net Gold = 34. (37 - 3)

4 Surplus Gold translates into 2 Science and 2 Gold.

So Marketplace:
+2 Sc
+2 Gold

TOTAL: for a cost of 2 gold savings per turn, earn 1.75 science per turn

Your calculation for Academy is correct, except that once you take into account rounding:

+1 Science
-2 Gold

So a Marketplace produces, for a city of size 5, twice the amount of Science an Academy produces, and gives you 2 extra gold. And all this assumes that you only have 25 base gold, which I have already pointed out in Section II as being conservative. Most well-placed cities have 30 gold for size 5, which would increase the output for a Marketplace to 3 Science and 3 Gold. Which makes the Academy look even worse, by comparison.

But we'll stick to 25.

Marketplace and Merchant:

Here again, you've misapplied the Crime equation.

Marketplace and merchant (taken from Forest)
+9 Gold for merchant (after crime)

For a Base Gold of 25,
Surplus Gold = ROUNDDOWN{(25+10)*1.5 } - ROUNDDOWN{(25+10)*1.5*0.1 } - 5 - 25
=52 - 5 - 5 - 25
=17, which gives 8 Science and 9 Gold. Yes, when CTP has to divide odd numbers on a 50% Science Rate between Science and Income, it rounds the proportion that goes to Science down.

So Marketplace and Merchant:
+8 Science
+9 Gold

Scientist and Academy:

Net Science = (10+2.5) * 1.5 - 2 = 16 Science.

Scientist and Academy looks really good, doesn't it? After all, it creates twice as much Science as a Merchant.

But *ahem* one slight problem. The issue here isn't that Scientists are good, but rather that Science buildings are useless. WW is desperately trying to shore up the credibility of the Science buildings by linking Scientists with them.

To elaborate:

Say I have a city of size 1. I dedicate 1 Scientist. I don't need an Academy to dedicate a Scientist - I can do this from the very start of the game.

Ok. City of Size 1 with 1 Scientist - what do I get? 10 Science.

Now let's look at City of Size 12, NO SCIENTIST but with an Academy. What Science do I get? (12*0.5) * 1.5 - 2 = 9 - 2 = 7 Science.

Ummm, so ... you tell me. An Academy by itself in a City of size TWELVE (12) is being outperformed by ONE (1) Scientist in a City of size ONE (1).

Ok, let's also take into account that the Scientist was working on a gold producing tile. Ok, say we took him off a tile that was producing 5 gold. So the Net Science effect of a Scientist is now 10 - 2 (remember, becuase of rounding effects only 2 Gold goes to Science, the other 3 going to the Treasury).

To summarise:
ONE Scientist in City Size 1 (one) working on a 5 gold tile -
+8 Science
-3 Gold
-10 Production, - 5 Food (assume he was working on a Hill, which also explains the 5 gold lost)

Academy with no Scientists City Size 12 (twelve)
+7 Science
- 2 Gold

Which begs the question - which is the real performer here - the Scientist or the Academy?

Quite simply put, without Scientists, Science buildings may as well not exist.

WW is trying to confuse the issue by putting together an excellent performer with a horrible one and hoping that the audience will be so distracted by the first performer's antics that they will overlook the abject hopelessness of the second one.

Unfortunately for WW, not all the audience is stupid. I am a great ancient city of 12 times as much population as my next door neighbour. But the barbarian nomads next door with their single wise man shaman produces more useful ideas and inventions than 12 of my guys going to school.

Why go to school? Is there any real value in it?

The Value of School can now take its place along with The Joy of Combat in the pulp fiction department.


P.S. I wouldn't be so mad about the flaws in this game if the developers would simply just admit it, and address these issues in a patch. The fact is, these things can be worked around, because of the great customisability that comes with the game. Saying ok - we goofed - we'll see what we can do - we could then move on and then make this game better.

But no, Activision's approach is - there is nothing wrong with this game - it was designed this way and it works the way it was intended.

Everytime they come up with such poorly thought up excuses for something which is so obviously wrong, and deny reality and hard numbers - it gets me really worked up.

It's really sad, because I love the customisability in this game, but I can't say the same of the developers' attitude.

WW's response
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