Wow. Great work Ben The Vizier. I just checked two more of my completed cities and it works!

Is there some significance to the value 10/5, or could it just be 2?

(((Funds*10 + Population*1,5)*2) + (Culture*2 + Prosperity*2 + Kingdom*2 + Monument*2))*4 / (Time in months*2)

Vaia

Hi Ben,
it seems your formula could even be further simplified. Anyway, it fits what huge cities have shown, money in Pharaoh quickly becomes everything, also the timing weight becomes less and less important when the game lasts.

(((Funds*10+Population*1,5)*10/5)+(Culture*10/5 + Prosperity*10/5 + Kingdom*10/5 + Monument*10/5))*4/(Time in months*10/5)

or

(((Funds*10 + Population*1,5)*2) + (Culture*2 + Prosperity*2 + Kingdom*2 + Monument*2))*4 / (Time in months*2)

or

(((Funds*10 + Population*1,5)*2) + (Culture + Prosperity+ Kingdom + Monument)*2)*4 / (Time in months*2)

or, to back up one step

(Funds*20 + Population*3 + (Culture + Prosperity+ Kingdom + Monument)*2)*4 / (Time in months*2)

and another

(Funds*20 + Population*3 + Culture*2 + Prosperity*2 + Kingdom*2 + Monument*2)*4 / (Time in months*2)

or

(Funds*10 + Population*1,5 + Culture + Prosperity + Kingdom + Monument)*2*4 / (Time in months*2)

or

(Funds*10 + Population*1,5 + Culture + Prosperity + Kingdom + Monument)*4 / Time in months

heehee This is fun. Haven’t done this since college.

I’m not making light of the good work that you did Ben. I’m just having fun with numbers.

So, 4 is the magic number for Normal Difficulty. What are the others. (Anxiously awaiting your next post.)

Vaia

This really sounds good chaps

But I sure hope someones going to write the formula down in English for the likes of me !!!!

Keep the good work up !!!

Ben The Vizier,

I didn’t want to mess up your Calculate your own score thread, so I’m posting is this one. In your new thread, you wrote down the formula as:

(Funds*10 + Population*1,5 + Culture + Prosperity + Kingdom + Monument) / Time in months * D

According to the information in this thread, it should be:

(Funds*10 + Population*1,5 + Culture + Prosperity + Kingdom + Monument)*D / Time in Months

BTW, I’m very impressed that you could do this when you are only 14. I have a 13-year-old son, and when I showed him your formula, he didn’t have a clue as to how to use it. Maybe he will learn a lot this year. lol

Maybe I can help you a little with the math for coming up with the other values for D.

If:

Score = (Funds*10 + Population*1,5 + Culture + Prosperity + Kingdom + Monument)*D / Time in Months

Then:

Score * Time in Months = (Funds*10 + Population*1,5 + Culture + Prosperity + Kingdom + Monument)*D

So:

D = (Score * Time in Months) / (Funds*10 + Population*1,5 + Culture + Prosperity + Kingdom + Monument)

You should be able to download some completed cities that were played at Very Hard, Hard and Easy. I think that you can do the math.

Vaia

[This message has been edited by VitruviusAIA (edited 08-21-2001 @ 11:26 AM).]

Hello!

Rocky

I think now that the formula is clear enough for everyone!
Thanks for your comment...

VitruviusAIA:
The final part of the formula can actually be either * D / Time in moths or /Time in months * D, because of the comutative property of the multiplication, I think...
Oh, of course, thanks for your comment... I'm sure your son will learn lots of things this year... I personally did... This year I had one of the best teachers of my school, for sure...
I'm currently downloading some cities at Hard an Very Hard, to try to discover the value of "D"!

Well, goodbye and keep writing...

Ben The Vizier

You are absolutely correct Ben The Vizier. The formula can be written either way. And, since D is the variable, I like your way better.

S = (F*10 + R*1,5 + C + P + K + M) / T * D

Where:

S = Final Score
F = Total Funds
R = Total Residents
C = Culture Rating
P = Prosperity Rating
K = Kingdom Rating
M = Monumennt Rating
T = Completion Time in Months
D = Difficulty Level Factor (1 for Very Easy, ? for Easy, 4 for Normal, ? for Hard, ? for Very Hard)

BTW Ben, you might want to check some cities other than mine. All of the cities that I have downloaded have 100% Ratings and “Perfect” scores. There could be some sort of bonus factor, or something like that. I don’t think that is true, but you might want to check and be sure.

Vaia

[This message has been edited by VitruviusAIA (edited 09-14-2001 @ 02:24 PM).]

Great job Ben!
At 14, you sure did a good job.

BTW Vitru and Ben, its ok to put D in denominmator as it can always be a fraction!

Well, for the past few missions I have tried to plug values into the formula and I don't get anything close to what the game calculates. Perhaps the score formula changed with Cleo?

I just finised Baki for the first time and came up with these results from the game:
Culture: 70
Prosparity: 100
Kingdom: 100
Cash: 382,092 db
Population: 12,363
Monument: 35
Time: 390 months
Score (from game screen): 36,438

Score from S = (F*10 + R*1.5 + C + P + K + M) / T * D
39,382

Er..not even close.

Using: S = (F * 9 + R * 9 + C * 9 + P * 8 + K * 8 + M * 8) / T * D
I get 36,437. Damn close to game score. However using stats from Sawu:
Culture-65
Prosparity-72
Kingdom-100
$-230,966db
Population-10,132
Score-28,490
Finished in 294 months
The formula doesn't work for Sawu stats. Fiddling with it I can get close with:
S = (F * 8 + R * 8 + C * 8 + P * 8 + K * 8 + M * 8) / (T * 0.92) * D
I don't know what the monument rating was in Sawu so its just a guess at 15.

Any of you math gurus make any sense of this? I sure would like to have a formula that actually works for all stats under Cleo.

Anyone make any advacement of the formula for Cleo?

Hi wolfie,

Why don't you try to discover it?
The formula I discovered was tested in Pharaoh only, so Cleo's system may have been improved.
The formula worked fine with all cities I download from Pharaoh Heaven and opened in Pharaoh.

Goodbye,
Ben The Vizier

Because, unfortunately, I am not nearly as good with algebra as you others obviouslly are. The last time I took a math class was sometime in the 80's.

This makes may head hurt, that and the fact that Ben is only 12!

You go, Ben!!

Hi Basteta!

Thanks for the kind comments, but... I'm 14 years old!!!

Bye,
Ben The Vizier

[This message has been edited by Ben The Vizier (edited 10-22-2001 @ 09:06 AM).]

Hi guys
I've tested Brugle's 'over quota' feature in South Dashur.
Since the city is very stable, I decided to run some tests in order to learn more about the score formula.
There is a request for 2000 deben, which you can meet or not.

Fixed variables:
Culture: 50 / 0
Prosperity: 60 / 25
Monument: 21 / 21
Kingdom: 100 / 50
Residents: 3600 / 3500
Time: 76 Months

Difficulty	Funds	Score	X = D * 10 * F / T	Y = S - X	Z = Y / D
hard = 4	27998	19706	14736	4970	1243
hard = 4	25998	18653	13638	4970	1242
normal = 3	27998	14779	11052	3727	1242
normal = 3	25998	13990	10262	3728	1243

So far it seems that the part of the formula, which determines the relation between Score, Funds, Time and Difficulty is S = D * 10 * F / T, because the rest is always the same.
But then I continued for another year (Time = 88 Months) and got these results:

Difficulty	Funds	Score	X = D * 10 * F / T	Y = S - X	Z = Y / D
hard = 4	27998	16946	12726	4220	1055
normal = 3	27998	12709	9545	3164	1055

Any ideas?

[This message has been edited by Max (edited 10-22-2001 @ 09:54 AM).]

Hi people - Is the same formula still used in the sold out software version of Pharoah? If not has anyone got the right one? Ben the Vizier's wonderful scoring formula doesn't seem to work for me, so I wondered if they had changed it - maybe it matches the cleopatra forumula now. Here's a few examples to prove that I haven't done something stupid (I hope). Looks like they reduced the weight given to city funds a bit. ........Cathy

Saqquara
city funds_____11,931__21,426___62,457
population_____4,006____4,351 ___3,503
culture__________15______35 ______40
prosperity_______51______52 ______ 89
monuments______19______19 ______19
kingdom_________51______52 ______85
time in months___216_____221 _____205
difficulty______v hard___v hard__ normal
total score_____4,194 __ 7,217 __ 10,886

ben's score ___ 3,485 __ 5,998 __ 12,294

Hi Cathy

Welcome to the forum. You have opened up a very old thread on a subject that hasn't drawn very much attention. The score of the game in Pharaoh (or Cleo) and the accompanying high score table the game keeps track off is largely ignored by most players, mainly because of the large relative weight of money. If you want to get a high score, it is quite easy to set up a stable city and run it for a long period making much profit, all other aspects don't count. So most players focus on either speed, prosperity, population size, or a combination of these, or just try to play all missions at a given difficulty level. There are also contests in Pharaoh and Cleo, with any combination of winning criteria, but the score AFAIK has never been one of them.

Now you have brought up the subject, I can give some comment, though I don't have the answer. Most players agree that the equation is of the form

Score = (A*Money + B*Population + C*Culture + D*Prosperity + E*Kingdom + F*Monument) / Time

with A-F numbers (weight factors) that depend on the difficulty level. To find the numbers data from six differents cities (or different runs from one city) are needed, assuming this equation is correct, and if we may assume the numbers C-F to be the same, three sets of data can suffice. As you have only data for two cities, there can be no unambiguous answer. Maybe a combination of the data from all the posts could provide enough data. For the math experts, in order to solve N equations with N unknowns uniquely, the equations have to be independent. If I find some time I'll have a look.

My guess is the equation is the same for sold out version of Pharaoh that is marketed currently, what is relevant is the version number (Pharoah 1.x). Even then, I doubt whether the equation will have changed with version numbers of Pharaoh, but there is evidence the weights in Cleo (=Pharaoh 2.x) are different.

Thanks for the reply - I'm glad someone read it on such an old thread. I agree score is too heavily weighted to money, but I like to know how to up the score as the mission ends (make more money). Anyway I like knowing how things work!!

I did wonder if the forumula might be based on how much over the requirement or mission standard you were. that might explain why the math isn't that simple. So not D*prosperity but D*(actual - target prosperity). Just idle speculation here folks...

Difficulty is in there too of course - I think you missed it off accidentally

Cathy

cathy,
While many players may agree that the score is represented by an equation of the form in joshofet latest reply (perhaps with a term for difficulty added), I have my doubts, since there are many modifications (such as the one you just proposed) that would appear to work equally well. In any case, as joshofet said, many of us ignore the score--in some cases, a high score may indicate poor play!

I collected the data available in this thread, but it appears there is not enough data to unambiguously determine the weight factors. There are data from Wolfie, Max and Cathy, which I assume are all for Cleo. The data for Pharaoh are checked to be correct by Ben the Vizier for various games, and in non of the games reported here that is the case.

There is no clear trend, some scores are higher than Ben's equation, others are lower, so its not a simple scaling factor. Even if I restrict myself to the games played at normal (with a difficulty factor of 4) a plot of the 6 available data sets does not indicate a simple correction factor. Unfortunately the data in this set are not independent, as Max did vary only time and money.

If I assume the weigth factors C-F (for normal) to be the same, the data are inconsistent with an equation of that form. If moreover I use only the data from Wolfie and Cathy, I obtain a negative weight B for population. This indicates strongly the equation is more difficult, and may involve aspects such as starting funds and target ratings.

More, and more varied data are needed to possibly settle the issue, just for the sake of argument. I'll look at my own saves, and it would be helpful if other players, interested in the equation for Cleo, would provide their data (city, score, money, population etc.)

BTW: My equation is somewhat more general than Ben's, it allows all weight factors to be dependent on difficulty independently, where Ben's equation just has an overall factor D (VE=1, E=2, N=3, H=4 and VH=5). Max' data at two levels indicate it will probably be just the factor.

Cathy: Do you have Cleo installed and are you playing a Pharaoh mission (as Max and Wolfie) or do you just have a single installation of Pharaoh (1.x) without the add-on?

Edit: I have changed the difficulty factors to comply with my recent findings reported in the next post. Max uses the same factors I now give here, but it seems Ben uses a factor of four for Normal difficulty. Maybe that is another difference between Cleo and Pharaoh, maybe it is just the result of some confusion between difficulty levels.

[This message has been edited by joshofet (edited 06-23-2004 @ 08:16 AM).]

I did some further research in the matter and tested a few of the earlier cities, Nubt, Thinis, Perwadjyt, and other cities of which I had saves just before the finish. By adding a few buildings or deleting a few houses it is rather simple to vary the population size and treasury upon finish and test the result. Also difficulty can be changed rather easily and Nubt and Thinis are such short missions that they can quickly be played at full length, and investigate the effect of time. Moreover because they are short, the effect of adding a few months is relatively large, so it can be established even if there is still some small uncertainty left in the score. Changing of the other factors, Culture etc, is more difficult, and more importantly, the effect of those is very small. I have collected my data so far in an Excel file, anyone interested can send me a mail and I will send the file. The results are not yet conclusive, this is what I found so far

The hypothesis was an equation of the form

Score = ( W_m* Money + W_s* Pop.Size + W_c* Culture + W_p* Prosp. + W_m* Monument + W_k* Kingdom ) * Diff / Time

with W_m..W_k fixed weight factors, a factor for difficulty and the time in months. That is definitely not the correct equation for Cleo.

The difficulty is indeed incorporated by a factor, for VE Diff=1, for E Diff=2 etcetera (Note that I have corrected the above post). It also seems that the score is inversely proportional with the time in months, I have tested Nubt for 4-8 months and Thinis for 9-14 months and the results appear to corroborate the assumption.

To investigate the weight factor for money, I have placed some extra statues just before the finish, and made plots in Excel of Money*Diff/Time against score. The result is a straight line with slope W_m, and intercept the effect of the other parameters, which are kept constant. For all cities within round-off error I found W_m=10. Of course the intercept may include the effect of starting funds, which obviously are constant too. However, taking the backup loan has no effect on the score, i.e. there is no penalty, the money is taken into account straightforwardly. If you want to increase your score, it is often better to go broke in a short mission.

The weight factor for population size is investigated similarly. A difficulty is that changes in the population size often lead to (small) changes in the treasury. Hence I have plotted Pop*Diff/Time against Score-10*Money*Diff/Time, the score corrected for changes in Money. Within the range of population sizes investigated I do indeed find linear fits with slope W_s, but it appears Ws is different for each city investigated. For Nubt W_s=0.145, for Thinis W_s=0.45 and for Behdet W_s=8.2. So if the equation is correct, the weight factors differ from mission to mission. Moreover the weigth numbers are non-integer and differences between missions are large.

Of course the equation may be wrong, and the weight factor may depend on the population size itself. After all the population size in Nubt (200), Thinis (400) and Behdet (2500) is quite different. To further investigate whether the hypothesis of a constant W_s can be upheld, I tested Nubt for substantially larger population sizes by artificially depriving a large number of houses from food. It indeed appears that for higher population sizes the equation as given above, with the slope W_s=0.145 and intercept as determined for small population sizes underestimates the reported score. Whether the slope reaches the value determined for Thinis also for Nubt at similar population size I have not been able to establish conclusively yet, it seems to be lower still. Now the linear fit has been proven incorrect, the most obvious modification is an equation with a term W_s1* Pop + W_s2* Pop², but if those weight factors would differ from mission to mission there is very little predictive value, if the equation has any value at all.

The Money and Population are by far the largest two terms in the score for any city, so it is difficult to investigate the effect of the other terms. As far as I could tell from the data for the larger cities the weight factors were (substantially) higher than for the Pharaoh case. Also it seemed the weights W_c..W_k were not the same for all cities, or they depend on population size too.

Within the range where the data fitted the linear dependence on money and population for Nubt, I checked what the effect of the only remaining parameter, Kindom, is. Throughout the tests all other parameters were zero, and Kingdom took values 40 and 50 only, so this not a very thourough investigation, but the data fitted with an equation

Score_Nubt = ( 10 * Money + 0.145 * Pop + Kingdom-40 ) * Diff / Time

The weight factor W_k=1, like in Pharaoh. It seems there is an offset on the score, but with the uncertainty about Ws and the fact that there are only two independent data points (I wouldn't know how to generate more in Nubt) also this may not be the last word on this subject.

On the other hand maybe it will. If the Cleo equation is indeed more complicated than the simple form found to adequately describe scores for Pharaoh, than given the low importance of the issue I doubt whether anyone will be willing to give the subject much time. I do not. The answer can simply be obtained by asking the designers, if they would remember, or by reverse engineering of the program files, if that weren't forbidden by the EULA.

The main conclusion is that the Cleo equation gives the same weight to money as the Pharaoh equation, but for the larger cities the weight of population size is increased. I have not tested Pharaoh, but if I can trust Ben the Vizier's conclusion the weight in Pharaoh is 1.5. For Cleo smaller weights are found for small cities, but substantially higher weigths are found for larger cities. Maybe the same is the case with weights for the other parameters.

[This message has been edited by joshofet (edited 06-23-2004 @ 08:37 AM).]

Hi joshofet,
reading your last posts, I had some quick thoughts:
"A difficulty is that changes in the population size often lead to (small) changes in the treasury."
Maybe treasury can be equalized more comfortely by building/deleting some parts of an otherwise useless array of roadelements/wells (4/5@N).
In an improved score formula I would expect the weigth factor for population size to depend on the scenarios population target. Also missionspecific weight factors would propably make scores more valuable, but were still too much effort to implement, I think.

"[...] Kingdom took values 40 and 50 only, so this not a very thourough investigation [...]"
Cheats of Ra? 'Sun Disk'_KRup & 'Mesektet'_KRdown.
(Tryhard has shown with his monument experiments, that data of starting conditions is easy accessable, ie. not compressed. Of course this point is more comfortable in missions with Ra already there, especially as it can be performed with the game running no single tick.).

PR can be investigated (ceteris paribus) by changing the prosperity caps in pharaoh_model_XXX.txt.

CR may be easier to investigate, if the costs for the appropriate buildings are set to zero in the file mentioned above.

"[...] and the fact that there are only two independent data points (I wouldn't know how to generate more in Nubt) [...]"
Here I got lost. What do you mean with 'independent data points'?

Hi Civilis

Thanks for the ideas, with two (independent) data points I mean two different KR values. I wouldn't know how I would go about in Nubt to change the KR, you really can't do very much in that mission. Cheats are a good idea, but if I remember correctly the game won't calculate a score if you cheat. I'll check. Anyhow the ratings are not very interesting, 99.9% of the score is determined by money and population, and I now know how.

I did some further investigation in Nubt, Thinis, Perwadjyt and Nekhen. In Nubt I set up a market with access to a single hut without water, so I just had to connect the market to a few huts with water to finish. Similar tricks I used in the other missions. I have restricted myself to the effect of money and population, the effect of the other factors is so small it is difficult to find out the exact relation, especially in these early missions.

The equation for all four missions is

Score = Difficulty * [ ( 10 * Money / Time ) + W_s * Population + Rating Terms ]

As said I don't know about the rating terms, but it turned out the weight factor for the population in the earlier equation was not increasing with population, but with time (!), and linearly indeed. That means for this term time drops out of the equation, it does not matter for the population how old you city is, the effect on the score is just proportional to the population size and the difficulty level. Note that I haven't provided the numerical value for W_s, the reason is that it varies from mission to misson.

What I did is similar to what I proposed in the earlier posts, I finish the city at different population sizes and difficulty levels, and make a plot of Diff*Pop against Score-(10*Diff*Money/Time), the score corrected for the effect of money. The data for each separate city, using runs at different difficulty and with different length in months, fit a linear approximation, with slope W_s and intercept the rating effect (and possible other constant factors in the score). The results I found were W_s= 0.0325 for Nubt, W_s= 0.04 for Thinis, W_s= 0.0333 for Perwadtjyt, and W_s= 0.07 for Nekhen. In all cases the value of the intercept was small. The score appears to be well predicted by the equations

Score_Nubt= Difficulty * [ ( 10 * Money / Time ) + 0.0325 * Population ]

Score_Thinis= Difficulty * [ ( 10 * Money / Time ) + 0.04 * Population ]

Score_Perwadjyt= Difficulty * [ ( 10 * Money / Time ) + 0.0333 * Population ]

Score_Nekhen= Difficulty * [ ( 10 * Money / Time ) + 0.07 * Population ]

I don't know why the numbers for the different missions have these specific values. Note that the values are the result of a fit to the data, with more data and a better description of the remaining effect their value might change slightly. I am not 100% sure the values for Nubt and Perwadjyt are actually different, or whether this is just the effect of the fitting. Maybe the map size is of influence, data on more cities are needed if one wants to establish that. For now it seems the weight factor for population must be determined separately for each mission.

Also data on more advanced missions are needed to investigate the rating effects, and possible offsets. I have not found any effects of starting funds or required population size (in Perwadjyt and Nekhen).

Assuming a similar equation to be valid for the other missions, it appears the score in Cleo for the longer missions is determined by the monthly income (money/time) and population size. Especially in a stable city, once the monuments are finished, it is quite simple to have a high monthly income, and with the high weight factor of 10, this still is the main term in determining the score.

[This message has been edited by joshofet (edited 06-25-2004 @ 07:06 AM).]

"Cheats are a good idea, but if I remember correctly the game won't calculate a score if you cheat."
You are right, this probably won't work. Seems some of the quick thoughts were a bit too quick

"[...] how I would go about in Nubt to change the KR, you really can't do very much in that mission.
IIRC, Nubt is the first of the tutorials: build houses, hunt ostrichs & wait a building to catch fire ...
If you like, I can modify a new or one of your Nubt.sav (or any other) to the effect, that there is for example a looping request for 1(00) game meat giving you monthly a fix or variable KR increase/decrease if you fulfill quick & doing nothing if you don't.
(With carpenters & masons turned on and gifts of wood & granite one can build there at least a small obelisk to give some MR.)

"[...] it does not matter for the population how old you city is, the effect on the score is just proportional to the population size and the difficulty level."
I think this discovery is a big step towards a clear and working score formula for Cleo.

"Anyhow the ratings are not very interesting, 99.9% of the score is determined by money and population."
That would seem to me somehow a step backward (from Pharaoh) in improving the score formula??? Maybe the achived ratings are irrelevant if the needed value is zero, but relative to the targets otherwise?

Reading through this, i just got an empirical idea how the formula for calculating the score can be found out. This idea is inspired by my chemistry lessons on chemical kinetics and i felt that the method i have learnt may apply in this case. But of course, if the formula is different from cities to cities, then finding out a general formula would be very tedious and, i think, quite impossible.

So here goes. In the screen where you are shown the score, there's population, city funds, culture, prosperity and kingdom ratings on it too. Obviously this implies that these are factors affecting the calculation of the score. (Monument ratings too i guess..) So what we have to do is just keep all of these factors constants and just change one of them at a time, so that we can find out how THAT factor alone can influence the score.

For example, keep population at 5000, prosperity at 60, culture 50, kingdom at 100, and changing the final city funds from let's say 50,000 to 52000. This means an increase by 1.04 times in city funds. Next check the increase in the final score, as a fraction of the original score. Let's say it increased from 15000 to 15900, then it's an increase by 1.06 times. 1.06 divided by 1.04 gives approximately 1.019. It then implies that the constant in front of the city fund factor is 1.019.

Repeating these procedures for the other factors, i think the we can find out all the constants for the factors, and thus we'll have our formula.

Edit: typing through the procedures, i realise that the above method may not work if the formula involves addition signs as well. For example, let's say score = 10*city funds + 100. Then, increasing the city funds by 100% will not result in an increase in score by 1000%.