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)