While playing (and replaying and replaying...) the Bridges contest map, I stumbled over some interesting observations about the Pharaoh game model for production. The production rates information at Grumpus' site and other posts have given everyone the basic facts, but it has always bothered me that the "facts" are fairly messy. I mean, the game designer probably didnt sit down and pull the fact that (for example) a Brewery will produce exactly 47 beers a month out of his uhh.. hat. Therefore the "Law of Elegance" dictates that there must be something else that WAS chosen which as a secondary affect causes the 47 beers a month number. Hence I also live up to my forum handle.

For the Bridges map I needed a kind of in-game clock to help time some production of scaffolding at a carpenter's guild. What I used was the total number of stored granite blocks and the current % completion number of the granite quarry. So for example the time 88-36% exactly describes a time point during the game when 88 granite blocks are in storage and the current quarries are 36% done with the next blocks. I always had enough room for the granite and it was only being used only at very specific times which fit my need for a clock perfectly.

After playing with this for a time, some observations come to mind:

Theory #1: "The Tick Theory"
There is short time period which I call a "tick" which is the smallest period of time in which the game does production. All production building's % completions are increased once at the beginning of a tick and the % completions do not change during a tick.

Game Data #1: There are exactly 16 ticks per month.

Theory #2: "A Building's Production Step Value"
I will call the above increase the "step value" of a building. A building's % done is increased by the step value for each tick as long as the building has employees. Production always starts at zero and when % done becomes greater than 100% (always displayed as 100%) the building produces its product. The step value is set by the type of building and religious modifiers and I contend that THIS was the number chosen by the game designer.

The various building's basic production speeds are based on their step value:

2.00% = Carpenter's Guild
3.00% = Brewery, Brickworks, Cattle, Jeweler, Papyrus, Potter, Weapons, Weaver
4.00% = Clay Pit, Gemstone Mine
5.00% = Copper Mine
6.00% = Gold Mine, Granite, Limestone, Plainstone
6.25% = Shipwright
12.0% = Recruiter with Academy

When Ptah's Temple Complex and Amon's altar have been added, the step values of the respective production facilities are increased by 50%. In the below, [PTC] indicates the temple complex and [PTC-A] indicates the altar has been added to the temple complex. While the manual says that Shipwrights are increased by Ptah's Complex, the production speed stayed the same in the game I tested.

4.50% = Jeweler[PTC], Weaver[PTC], Brickworks[PTC-A]
6.00% = Clay Pit[PTC], Gemstone[PTC]
7.50% = Copper Mine[PTC]
9.00% = Gold Mine[PTC], Granite[PTC-A], Limestone[PTC-A], Plainstone[PTC-A]

As an example of how the above works, each tick of a normal granite quarry increases the % done by 6%. So the sequence is as follows:

Tick 00: 00% Done
Tick 01: 06% Done
Tick 02: 12% Done
Tick 03: 18% Done
...
Tick 14: 84% Done
Tick 15: 90% Done
Tick 16: 96% Done
Tick 17: 100% / 0% Done: Building produces a cart pusher.
Tick 18: 06% Done
Tick 19: 12% Done

Given the above I can derive the production rates described by Grumpus; remember that there are 16 ticks per month.

(stepValue -> total ticks to complete product -> calculated production/month)
2.00% -> 50 ticks -> 16/50 = 32.00% per month
3.00% -> 34 ticks -> 16/34 = 47.06% per month ( Grumpus = 47 )
4.00% -> 25 ticks -> 16/25 = 64.00% per month ( Grumpus = 64 )
4.50% -> 23 ticks -> 16/23 = 69.57% per month
5.00% -> 20 ticks -> 16/20 = 80.00% per month ( Grumpus = 80 )
6.00% -> 17 ticks -> 16/17 = 94.12% per month ( Grumpus = 94 )
6.25% -> 16 ticks -> 16/16 = 100.0% per month
7.50% -> 14 ticks -> 16/14 = 114.3% per month
9.00% -> 12 ticks -> 16/12 = 133.3% per month
12.0% -> 09 ticks -> 16/09 = 177.8% per month ( Grumpus = 2 )

Theory #3: "Walker/Pusher Speeds"
From watching the walkers/pushers moving around at speed 10% and correlating that to the above tick information I have basically two slightly different values for the speed of movement. The numbers come out as either 3.333 or 3.4 squares per tick or respectively 53.333 or 54.4 squares per month.

Some more info from close observation:
Game Data #2: There are 50 animation cycles ( uh microticks ?) per tick.
Game Data #3: There are 12 animations per walker type. After 12 they repeat.
Game Data #4: A walker moves 4 squares during 5 full animations = 60 microticks.

From Data #2 thru #4 a walker's speed could be calculated to be 4*50/(5*12) = 3.333 squares per tick. Or (16*3.333) = 53.333 squares per month.

The only problem here is that I set up a long road and did a different test with cart pushers. A cart pusher moved 17 squares in exactly 5 ticks which comes out to be (17/5) = 3.4 squares per tick or (16*3.4) = 54.4 squares per month. The cart pushers had the same 12 animations and seemed to move on the squares in the same fashion as the walkers used to get the above data.

For the rest of this message I will use the 3.333 number for calculations since it is a bit smaller.

Theory #4: "Distances from Source Building to Destinations"
If I take the production speed info and tie in the walker speed I can calculate the maximum distance that a production house can be from wherever the product needs to go ( storage yard, next production house in the chain, whatever...). The formula I use is (number of ticks per production * speed of cart / 2) where the divide by 2 is because the cart has to return to the production location.

2.00% -> 50 ticks -> 50*3.333/2 = 83.3 sq. [ Wood to carpenters ]
3.00% -> 34 ticks -> 34*3.333/2 = 56.7 sq. [ Beer, Bricks... to store ]
4.00% -> 25 ticks -> 25*3.333/2 = 41.7 sq. [ Clay, Gems to store/prod ]
4.50% -> 23 ticks -> 23*3.333/2 = 38.3 sq. [ Ptah Jewel,Linen,Bricks to store]
5.00% -> 20 ticks -> 20*3.333/2 = 33.3 sq. [ Copper Mine to store/weapsmith]
6.00% -> 17 ticks -> 17*3.333/2 = 28.3 sq. [ Gold,Quarry to palace/store ]
6.25% -> 16 ticks -> 16*3.333/2 = 26.7 sq. [ Wood to shipwright ]
7.50% -> 14 ticks -> 14*3.333/2 = 23.3 sq. [ Ptah Copper to store/weaponsmith]
9.00% -> 12 ticks -> 12*3.333/2 = 20.0 sq. [ Ptah Gold,Quarry to palace/store ]
12.0% -> 09 ticks -> 09*3.333/2 = 15.0 sq. [ Weapons to Recruiter ]

The above are probably maximum numbers because the cart pushers are not immediately spawned from the building (takes about 12 microticks from the 100% tick mark) and they usually have a small wait (about 4-8 microticks) at the destination to unload. So maybe knock off a square from the above.

Well thats it for now. Looking forward to your comments on this.
-Nerdicus (Andy Antoniewicz)

Wow, that looks interesting. As I'm too lazy to recalculate all these numbers, I just take them as they are.

Nerdicus but be some awfull number-cruncher.

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Marcus Germanicus
Veni, vidi, ludevi

Very impressive Nerdicus

I'm betting some of our local number-crunchers will be testing your theories and reporting their results. As for me, I'll just print out a copy of this gold mine and see how it might help me in my city layouts to be a bit more efficient. It would also be interesting if some of the Impressions wizards might comment on your observations and theories. I think I just felt the sum total IQ of Pharaoh Heaven increase a few more points!

Inkblot

Theory#4 is going to make us all better. I build a lot of SY, etc.. too close to my industries sometimes out of fear of slowing production. This will give me a bit of breathing room. Thanks for the great work. Your brain is scary

...SenetEr...
...playing Pharaoh till they bury me with my cats...

Great work Nerdicus!

I had suspected the existance of the 16th of a month "tick" as the monthly production rates were all close to multiples of 16. But I had assumed that the optimal rate was always a multiple of 16 and that the experimental results that were slightly lower were caused by something being less than optimal. Your explanation of losing a few percent of production in the tick that takes you over 100% makes perfect sense and exactly predicts the experimental results. That constitutes proof in my book.

Concerning the walker speeds, my own (not necessarily accurate) measurements are 54-55 squares per month, so I'm biased in favour of your 3.4 squares per tick calculation. You didn't say how you determined the number of animation cycles per tick. Is it possible that the number is 51 rather than 50? It seems unlikely as it's not a very round number, but it would result in a speed of 4*51/(5*12)=3.4 squares per tick.

The speed of people in the game is controlled by the "Figure" text file. The speed of cart pushers and most walkers is set to 6 for all difficulty levels. It seems likely that this number sets either the length of an animation cycle (a sixth of some unit of time) or the distance moved in one animation cycle (6 times some smaller unit). The second possibility seems more logical, but this can be verified by modifying the file and seeing if the animation runs faster or if the figure just covers more ground in a single animation cycle. If the speed is indeed the number of distance units (steps?) travelled per animation cycle, then the number of steps to a square (using your 4 squares per 5 full animations) is 6*5*12/4=90.
Perhaps setting the walker speed very high or very low would provide some useful experimental data (I'll try this over the weekend if I have time).

Thanks again for a great analysis.

This is outstanding work!! I'm going to print it out and start using it in laying out cities.

Great work, Nerdicus!
If you don't mind, I'll translate it into Czech and publish on my site, so that people who don't speak English can benefit from it.

I'm designing the city "by heart", just estimating the correct distances, but this will help me a lot. If I accidentally stumble over something new that supports your theory (or contradicts it), I'll let you know.

Thanks for sharing it!

Cherub Baltic

Astounding! Absolutely first-rate work! The pharaoh community is richer for your efforts and I commend you! (I'm also going to print this out and put it to work. *grin*)

Terrific stuff!

I once measured a clay pit cart pusher's speed, and came up with 55 squares/month. This was from the beta demo, and I've never had the time or inclination to follow up.

I think you have come pretty close to nailing this down, and much appreciate the time and effort you have put into it.

Nerdicus: Would you mind if I posted that as a strategy article in the Strat section?

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Angel Reckless Rodent
Caesar III Heaven & Pharaoh Heaven
reck@heavengames.com

Excellent catch Nero Would! You are exactly correct. I went back to double check and there ARE exactly 51 "microticks" per tick. So in summary the following are the updated tables and data from my original message.

Game Data #1 = 16 ticks per month
Game Data #2 = 51 microticks per tick
Game Data #3 = 12 animations playing at one per microtick
Game Data #4 = Walker moves 4 squares per 5 full animation cycles (60 microticks)

Therefore:
Walker speed = 4*51/(5*12) = 3.4 squares per tick.
or in months = 3.4*16 = 54.4 squares per month.

The maximum cart pusher distance table then becomes:

2.00% -> 50 ticks -> 50*(3.4)/2 = 85.0 sq. [ Wood to carpenters ]
3.00% -> 34 ticks -> 34*(3.4)/2 = 57.8 sq. [ Beer, Bricks,... *1 to store ]
4.00% -> 25 ticks -> 25*(3.4)/2 = 42.5 sq. [ Clay, Gems to store/shop ]
5.00% -> 20 ticks -> 20*(3.4)/2 = 34.0 sq. [ Copper Mine to store/weapsmith]
6.00% -> 17 ticks -> 17*(3.4)/2 = 28.9 sq. [ Gold, Quarries*2 to palace/store ]
6.25% -> 16 ticks -> 16*(3.4)/2 = 27.2 sq. [ Wood to shipwright ]
12.0% -> 09 ticks -> 09*(3.4)/2 = 15.3 sq. [ Weapons to Recruiter ]

With a Temple Complex to Ptah and an Altar of Amon
4.50% -> 23 ticks -> 23*(3.4)/2 = 39.1 sq. [ Jewel,Linen,Bricks to store]
6.00% -> 17 ticks -> 17*(3.4)/2 = 28.9 sq. [ Clay,Gems to store/shop ]
7.50% -> 14 ticks -> 14*(3.4)/2 = 23.8 sq. [ Copper to store/weaponsmith]
9.00% -> 12 ticks -> 12*(3.4)/2 = 20.4 sq. [ Gold, Quarries*2 to palace/store ]

*1 -> the entire list for the 3.0% entry is Brewery, Brickworks, Cattle Ranch, Jeweler, Papyrus Maker, Potter, Weaponsmith, and Weaver

*2 -> All Stone Quarries share the same values Granite, Limestone, and Plainstone.

I will repeat the note from my original message:
The above are probably maximum numbers because the cart pushers are not immediately spawned from the building (takes about 12 microticks from the 100% tick mark) and they usually have a small wait (about 4-8 microticks) at the destination to unload. So maybe knock off a square from the above.

Nero Would,
You asked about how I determined the numbers. Well, I did it the old fashioned way... I turned the game down to 10% and then repeatedly did a P-P command (unpause-pause) to step the game one animation at a time. I would then check a working building to see if the production value had changed yet. Damn tedious and I think I probably didnt double check when I originally counted 50. The number so nice and even that I didnt even question that it may not be correct. Measure twice and then cut once.

Angel Reckless Rodent,
Thanks! and go ahead and post it in the strategy section (with the new numbers from the above appended please)

-Nerdicus

Wow, thanks for the info, that'll be very useful.

Oh, wait, I already had that info. =)

Anyway, that's a great analysis. It all looks correct to me, though we all think you may have a little too much free time. FYI, For reasons that were never clear to me, the programmer lingo was 16 weeks per month, 51 ticks per week.

Here's a hint to get more info out of your numbers on production times. Look at employment numbers...

WOW! Very Impressive!

Your eyes are much better than mine!

Thanks a heap! This will go into my "Pharaoh Bible" as page one!

- Max

Nerdicus,
Once again, very nice! And once again, I have a tiny quibble. I hesitate to mention it, but I hate to see a flaw in such beautiful work. Under Theory #2, in the phrase "when % done becomes greater than 100%", "greater than" should be replaced with "greater than or equal" or "not less than" or something similar.

Production rates are briefly discussed in Baltic's thread "Rostja in 317 months - guide & download", where I use "(1/16 month) interval" instead of your "tick". (Reply #19 has some incorrect speculation which I corrected in reply #24.)

Now that Conan has pointed it out, I see that production rates are determined by the number of employees. Raw materials buildings produce 0.5% per employee per "week" (16th of a month), workshops and carpenters guilds produce 0.25% per employee per "week", Shipwrights and recruiters don't seem to fit the pattern).

I'm not sure what additional information Conan is hinting we can get from that. Perhaps the production rates of partially staffed buildings (e.g. copper mine with 2 employees does 1% production per "week")?

Hmm, you are correct again Nero Would. And thanks for the pointer Conan. I like the programmer's nomenclature a bit better than mine (though 16 "days" per month would seem better than "weeks"). Hehe the first 4 day work week you think?

What is the process here in forum land? Should I just go back and edit my two posts to use the new names or should I just re-post an updated copy of my original message with all of the suggested changes?

[This message has been edited by Nerdicus (edited 01-14-2000).]

It'd probably be best to post a new post with all the changes.

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Angel Reckless Rodent
Caesar III Heaven & Pharaoh Heaven
reck@heavengames.com

Just wanted to say, I'm impressed with the detail of the observations. I mean I normally end up placinfg somethign and finding out it's out of reach so I move it

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Homage to thee, Osiris, Lord of Eternity, King of the Gods, whose names are manifold, whose forms are holy, thou being of hidden form in the temples, whose Ka is holy."
-- Book of the Dead (1240 BC)

This is a repost with many changes from my original message (response#1). I have updated/added some new data (big thank you to Nero Would and Conan). And I have changed the naming convention so that it is a bit less confusing. What I called a "tick" before is now called a "day" and what I had called a "microtick" or an "animation" is now called a "step". I hope this makes the formulas and results a bit more intuitive.

While playing (and replaying and replaying...) the Bridges contest map, I stumbled over some interesting observations about the Pharaoh game model for production. The production rates information at Grumpus' site and other posts have given everyone the basic facts, but it has always bothered me that the "facts" are fairly messy. I mean, the game designer probably didnt sit down and pull the fact that (for example) a Brewery will produce exactly 47 beers a month out of his uhh.. hat. Therefore the "Law of Elegance" dictates that there must be something else that WAS chosen which as a secondary affect causes the 47 beers a month number. Hence I also live up to my forum handle.

For the Bridges map I needed a kind of in-game clock to help time some production of scaffolding at a carpenter's guild. What I used was the total number of stored granite blocks and the current % completion number of the granite quarry. So for example the time 88-36% exactly describes a time point during the game when 88 granite blocks are in storage and the current quarries are 36% done with the next blocks. I always had enough room for the granite and it was only being used only at very specific times which fit my need for a clock perfectly.

After playing with this for a time, some observations come to mind:

Theory #1: "The 4 Day Work Week Theory"
There is short time period which I will call a "day" which is the smallest period of time in which the game does production. All production building's % completions are increased once at the end of a day and the % completions do not change until the end of the next day.

Game Data #1: There are exactly 16 days per game month.

Theory #2: "A Building's Daily Gain"
I will call the above increase in production the "daily gain" of a building. Each day a building's percent done is increased by the daily gain as long as the building has employees. The daily gain is calculated as the number of employees multiplied by a rate depending upon the type of product produced. Production always starts at zero and when the percent done becomes greater than or equal to 100% (always displayed as 100%) the building produces its product.

Game Data #2: Raw materials are produced at a rate of 0.5% per worker per day.
Game Data #3: Manufactured products are produced at a rate of 0.25% per worker per day.
Game Data #4: Shipwrights produce ships at a rate of 0.3125% per worker per day.

With full employment the daily gains for various buildings are as follows:

2.00% = Carpenter's Guild
3.00% = Brewery, Brickworks, Cattle, Jeweler, Papyrus, Potter, Weapons, Weaver
4.00% = Clay Pit, Gemstone Mine
5.00% = Copper Mine
6.00% = Gold Mine, Granite, Limestone, Plainstone
6.25% = Shipwright
12.0% = Recruiter with Academy

When Ptah's Temple Complex and Amon's altar have been added, the daily gains of some production facilities are increased by 50%. In the below, [PTC] indicates the temple complex and [PTC-A] indicates the altar has been added to the temple complex. While the manual says that Shipwrights are increased by Ptah's Complex, the production speed stayed the same in the game I tested. With full employment the daily gains are as follows:

4.50% = Jeweler[PTC], Weaver[PTC], Brickworks[PTC-A]
6.00% = Clay Pit[PTC], Gemstone[PTC]
7.50% = Copper Mine[PTC]
9.00% = Gold Mine[PTC], Granite[PTC-A], Limestone[PTC-A], Plainstone[PTC-A]

As an example of how the above works, each day a fully staffed granite quarry will increases the % done by a daily gain of 6%. So the sequence is as follows:

Day 00: 00% Done
Day 01: 06% Done
Day 02: 12% Done
Day 03: 18% Done
...
Day 14: 84% Done
Day 15: 90% Done
Day 16: 96% Done
Day 17: 100% / 0% Done: Building produces a cart pusher.
Day 18: 06% Done
Day 19: 12% Done

Given the daily gains above, I can derive the production rates as described by Grumpus the Elder. Remember that there are 16 days per month and that these numbers are for full employment.

(Daily Gain -> Total days to complete product -> calculated production/month)
2.00% -> 50 days -> 16/50 = 32.00% per month ( Carpenter's Guild )
3.00% -> 34 days -> 16/34 = 47.06% per month ( Brewery, Brickworks,... *1 )
4.00% -> 25 days -> 16/25 = 64.00% per month ( Clay Pit, Gemstone Mine )
5.00% -> 20 days -> 16/20 = 80.00% per month ( Copper Mine )
6.00% -> 17 days -> 16/17 = 94.12% per month ( Gold Mine, Quarries *2 )
6.25% -> 16 days -> 16/16 = 100.0% per month ( Shipwright )
12.0% -> 09 days -> 16/09 = 177.8% per month ( Recruiter )

With a Temple Complex to Ptah and an Altar of Amon
4.50% -> 23 days -> 16/23 = 69.57% per month ( Brickworks,Jeweler,Weaver )
6.00% -> 17 days -> 16/17 = 94.12% per month ( Clay Pit, Gemstone Mine )
7.50% -> 14 days -> 16/14 = 114.3% per month ( Copper Mine )
9.00% -> 12 days -> 16/12 = 133.3% per month ( Gold Mine, Quarries *2 )

*1 -> the entire list for the 3.0% entry is Brewery, Brickworks, Cattle Ranch, Jeweler, Papyrus Maker, Potter, Weaponsmith, and Weaver

*2 -> All Stone Quarries (Granite, Limestone, and Plainstone) share the same values .

Theory #3: "Walker/Pusher Speeds"
From watching the walkers/pushers moving around at speed 10% and correlating that to the above day information I can calculate the speed of walker/cart pusher movement. The numbers come out as 3.4 squares per day or 54.4 squares per month.

Some more information from close observation:
Game Data #5: There are 51 animation "steps" per day.
Game Data #6: There are 12 different animation steps per walker type. After 12 they repeat.
Game Data #7: A walker moves 4 squares during 5 animation cycles = 60 steps.

From Data #5 thru #7 a walker's speed can be calculated to be 4*51/(5*12) = 3.4 squares per day or (16*3.4) = 54.4 squares per month.

This value was confirmed on a long road using a different test with cart pushers. A cart pusher moved 17 squares in exactly 5 days which comes out to be (17/5) = 3.4 squares per day or (16*3.4) = 54.4 squares per month.

Theory #4: "Distances from Source Building to Destinations"
If I take the production speed info and tie in the walker speed I can calculate the maximum distance that a production house can be from wherever the product needs to go ( storage yard, next production house in the chain, whatever...). The formula I use is (number of days per production * speed of cart / 2) where the divide by 2 is because the cart has to return to the production location.

Maximum cart pusher distance table (given full employment):

2.00% -> 50 days -> 50*(3.4)/2 = 85.0 sq. ( Wood to carpenters )
3.00% -> 34 days -> 34*(3.4)/2 = 57.8 sq. ( Beer, Bricks,... *1 to store )
4.00% -> 25 days -> 25*(3.4)/2 = 42.5 sq. ( Clay, Gems to store/shop )
5.00% -> 20 days -> 20*(3.4)/2 = 34.0 sq. ( Copper Mine to store/weapsmith )
6.00% -> 17 days -> 17*(3.4)/2 = 28.9 sq. ( Gold, Quarries*2 to palace/store )
6.25% -> 16 days -> 16*(3.4)/2 = 27.2 sq. ( Wood to shipwright )
12.0% -> 09 days -> 09*(3.4)/2 = 15.3 sq. ( Weapons to Recruiter )

With a Temple Complex to Ptah and an Altar of Amon
4.50% -> 23 days -> 23*(3.4)/2 = 39.1 sq. ( Bricks,Jewels,Linen to store )
6.00% -> 17 days -> 17*(3.4)/2 = 28.9 sq. ( Clay,Gems to store/shop )
7.50% -> 14 days -> 14*(3.4)/2 = 23.8 sq. ( Copper to store/weaponsmith )
9.00% -> 12 days -> 12*(3.4)/2 = 20.4 sq. ( Gold, Quarries*2 to palace/store )

*1 -> the entire list for the 3.0% entry is Brewery, Brickworks, Cattle Ranch, Jeweler, Papyrus Maker, Potter, Weaponsmith, and Weaver

*2 -> All Stone Quarries share the same values Granite, Limestone, and Plainstone.

The above are probably maximum numbers because the cart pushers are not immediately spawned from the building (takes about 12 steps from the 100% day mark) and they usually have a small wait (about 4-8 steps) at the destination to unload. So maybe knock off a square from the above.

-Nerdicus (Andy Antoniewicz)

Nerdicus/Andy,

Add me to the long list of your admirers. Thanks for spreading the knowledge.

Gunthebath