I have noticed that whipping has become increasingly popular and it has reached the point that many people seem to believe that slavery should be an automatic civic selection. Voices in opposition seem to have been drowned out in what I believe to be an overstatement, or perhaps misunderstanding, of the pros and cons (and yes, there are cons) to the use of whipping. Though I do not pretend to be an expert on the subject, and welcome friendly discussion/criticism, my experience has shown that slavery is often not the best choice. My personal preference is the oft disparaged caste system and, if I have time, I will go into why. For now, here is my analysis of how slavery actually affects the game.
Initial Comparison - Ideal Steady State Hammers
The initial rules are simple. We will look at a steady state comparison of two cities. The size of the cities is irrelevant, as is the happiness cap, the terrain, the other workers in the city, and the growth time. All we do is look at the possible use of the last citizen to be born. The options are obvious, so none of this should be new. You either whip the citizen into 30 hammers, or you put him to work in the field. The field work can be conducted on either a mined grass hill or mined plains hill. The two scenarios are summarized in the following production schedule.
Turn SL GH PH
0-------0------0------0
1------30------3-----4
2------30------6-----8
3------30------9-----12
4------30-----12-----16
5------30-----15-----20
6------30-----18-----24
7------30-----21-----28
8------30-----24-----32
9------30-----27-----36
10----30-----30-----40
11----60-----33-----44
12----60-----36-----48
13----60-----39-----52
14----60-----42-----56
15----60-----45-----60
16----60-----48-----64
17----60-----51-----68
18----60-----54-----72
19----60-----57-----76
20----60-----60-----80
21----90-----63-----84
22----90-----66-----88
23----90-----69-----92
24----90-----72-----96
25----90-----75-----100
26----90-----78-----104
27----90-----81-----108
28----90-----84-----112
29----90-----87-----116
30----90-----90-----120
First 10 Turns
AHT--300---165----220
First 20 Turns
AHT--900---630----840
First 30 Turns
AHT-1800--1395--1860
There are a few things that need to be noted from this. The most important is that under no circumstances does whipping produce extra hammers. I will discuss non ideal steady state comparisons later. For the ideal steady state scenario, a mined grassland hill produces the same number of hammers as a single 10 turn whipping cycle. The benefit of whipping in this case is that all the hammers for a given 10 turn cycle are given up front. This means that the player will have had more hammers worth of stuff lying around for a longer time. I have coined the term Accumulated Hammer Turns (AHT), which is just the accumulated hammers a city has produced by a given turn, integrated over all turns of interest. You see that on turn 30, both the whipping cycle city and the mined grassland hill city have produced a total of 90 hammers. The whipping cycle city, however, has had 1800 AHT worth of stuff working for him, while the mined grassland hill city has only had 1395 AHT worth. This is the benefit of slavery, not faster building or more hammers. Note that as the integrated time increases from turn 10 to turn 30, the relative benefit of slavery decreases. Also note that if a mined plains hill is available, by turn 30 the whipping cycle city has produced less raw hammers and has less AHT worth of material. Whipping is not always best.
Further Comparison - “Yea but…..”
Alright, the above comparison was an ideal steady state comparison. So now we need to include the various factors that affect the comparison. I will use numbers whenever possible, but they will be for specific situations. The main point should be if a given specific situation is generally applicable or if it is conservative enough to be useful. The main factors that modify the ideal steady state comparison are available terrain, health caps, growth speed, and happiness caps.
The first main factor that needs discussion is terrain. The question here is whether the non slavery city has an available hill to work. If a city does not have hills or other 3 hammer tiles to work, then slavery is clearly beneficial in total hammers as well as AHT worth. Otherwise, the above hammer schedule applies on a per citizen basis.
The second factor, the health cap, is also a limiting factor for the non slavery city. While whipping breaks even on happiness because it yields -1 crowded unhappiness and +1 cruel oppression unhappiness, it does not have a similar balance with health. The unhealthiness caused by crowding goes down by one and is not replaces by anything else. This means that for a given whipping cycle, the comparative non slavery city will have 1 more unhealthiness. This equals a net effect of 1 less food production. Now, in the mined grassland hill scenario, this is made up with the 1 extra food produced from the grassland hill tile. In the mined grassland hill scenario, this represents a deficit that must be paid for some other way. So, taking both hammers and food into consideration, the most fair comparison is between the whipping cycle city and the mined grassland hill city. The hammer production schedule still applies.
The growth speed is effectively a limitation on the whipping cycle city. Make no mistake, the non slavery city is not “paying food” to work its tile. The whole issue is whether to use food to make hammers through a mine or to use it to produce hammers through population. A fair comparison assumes that a whipping city only has a 2 food per whipping cycle advantage over the non slavery city. If one has food resources, then the other has them as well. If the whipping cycle city is retooled for max growth, then the non slavery city should be retooled for max growth as well. The only differences should be in the use of the citizens being whipped. In these cases, the hammer production schedule applies.
So, that said, the real importance of growth speed is in how many whipping cycles can be run at once without altering your city size. If you can only grow 1 pop in 10 turns, then you can only whip once every ten turns without starting to see a decline in city size. If you can grow 5 pop in 10 turns, and you have enough happiness to support it, you can run 5 whipping cycles at a time without seeing your city size decrease. This is important because, together with the happiness, it creates an upper limit on the use of whipping in a given city.
The final factor is the already mentioned happiness cap. This affects a given whipping cycle and a worked tile in the same way. As mentioned, you either get crowding unhappiness or cruel oppression unhappiness. The key here, though, is that cities will have a base of 3 happiness of Emperor. So the number of whipping cycles that can be run will be low. This means it is easy to find city sites that can work hills instead of whipping. Most cities will be able to have 2 or three hills in range.
Actual Mechanics Comparison - How things really work
The reality of civ is one where difficulty makes early happiness caps around 5-7, the health cap will be around 7, a city can easily have 2-3 hills, and most cities will only have 2 food resources. These numbers can be disputed, but they are more or less on target and their accuracy does not affect the analysis much. If you have a city with a +4 and a +3 food resource tile, then you can achieve +9 food growth at size 2. This will allow you to grow/whip 2.5 times in 10 turns. So, over 20 turns, the effective size of your city is +2 crowded unhappiness and +3 cruel oppression unhappiness.
A non slavery city will work the same +9 food tiles but will work a mined grassland hill when it gets to size 3 (instead of whipping back to size 2). This city will now be at +8 food growth and will be producing hammers according to the schedule above. As you can see, it’s growth is not significantly slower than the whipping city. As the whipping city grows to its equilibrium 2.5 whipping cycles, the non-slavery city can keep up with the required growth rate while losing at most a few turn. This means that, again, slavery is not gaining you hammers, just AHT worth.
The tradeoff comes when at the point where the whipping cycle city has reached equilibrium. It is an effective size (unhappiness-wise) of 5. It must produce +9 food in order to keep the whipping going. The non-slavery city, however, has reached size 5 with 3 mined grassland hills and is still at +6 food. The three mined grassland hills are already keeping total hammer production even with the whipping cycle city, so the extra 6 food is no longer needed. The non-slavery city can now change one of its food resource squares to working another hill, if available, or turn it into a specialist. There is no significant time loss since growth for working hills keeps pace with growth for whipping. It is once equilibrium is reached that the non-slavery city can begin leveraging additional production. Once again, slavery does not get you more hammers…in practice it gets you less. What is does do is give you, in effect, a paycheck advance.
This scenario holds true even if you have enough food to run more whipping cycles at a time since happiness caps affect both cities in the exact same way. The difference comes when the non-slavery city becomes health limited or cannot find hills to work. At this point whipping does have an advantage. Please note, however, that this only starts to happen when you are running 3 or 4 whipping cycles at a time. This requires enough food to grow 3 or 4 times in ten turns (basically you must have a granary) and a happiness cap that allows for the larger effective city size. On average, whipping in smaller cities with low happiness caps will not cause the comparison non-slavery city to see any limitations.
Conclusions - What’s the deal?
In the end, the choice of using slavery is more difficult than people make it out to be. Terrain, growth rates, and happiness caps must be taken into consideration. The majority of situations will see a non-slavery city producing more than a comparable size whipping city once both reach equilibrium. In the end, what slavery gets you is a greater (though diminishing over time) AHT worth. Slavery will only lead in total hammer production when you are running enough whipping cycles to outstrip hill supply. If hills are scarce and you can find several food resources per city, Slavery will not only get you your paycheck advance, but it will outproduce as well. However, if your happiness caps are low (such as on higher difficulties) and/or there are many available hills, slavery is not the panacea it is often advertised as. The sacrificing of specialist commerce combined with the opportunity cost of other civics in the category can easily make it the wrong choice.
Initial Comparison - Ideal Steady State Hammers
The initial rules are simple. We will look at a steady state comparison of two cities. The size of the cities is irrelevant, as is the happiness cap, the terrain, the other workers in the city, and the growth time. All we do is look at the possible use of the last citizen to be born. The options are obvious, so none of this should be new. You either whip the citizen into 30 hammers, or you put him to work in the field. The field work can be conducted on either a mined grass hill or mined plains hill. The two scenarios are summarized in the following production schedule.
Turn SL GH PH
0-------0------0------0
1------30------3-----4
2------30------6-----8
3------30------9-----12
4------30-----12-----16
5------30-----15-----20
6------30-----18-----24
7------30-----21-----28
8------30-----24-----32
9------30-----27-----36
10----30-----30-----40
11----60-----33-----44
12----60-----36-----48
13----60-----39-----52
14----60-----42-----56
15----60-----45-----60
16----60-----48-----64
17----60-----51-----68
18----60-----54-----72
19----60-----57-----76
20----60-----60-----80
21----90-----63-----84
22----90-----66-----88
23----90-----69-----92
24----90-----72-----96
25----90-----75-----100
26----90-----78-----104
27----90-----81-----108
28----90-----84-----112
29----90-----87-----116
30----90-----90-----120
First 10 Turns
AHT--300---165----220
First 20 Turns
AHT--900---630----840
First 30 Turns
AHT-1800--1395--1860
There are a few things that need to be noted from this. The most important is that under no circumstances does whipping produce extra hammers. I will discuss non ideal steady state comparisons later. For the ideal steady state scenario, a mined grassland hill produces the same number of hammers as a single 10 turn whipping cycle. The benefit of whipping in this case is that all the hammers for a given 10 turn cycle are given up front. This means that the player will have had more hammers worth of stuff lying around for a longer time. I have coined the term Accumulated Hammer Turns (AHT), which is just the accumulated hammers a city has produced by a given turn, integrated over all turns of interest. You see that on turn 30, both the whipping cycle city and the mined grassland hill city have produced a total of 90 hammers. The whipping cycle city, however, has had 1800 AHT worth of stuff working for him, while the mined grassland hill city has only had 1395 AHT worth. This is the benefit of slavery, not faster building or more hammers. Note that as the integrated time increases from turn 10 to turn 30, the relative benefit of slavery decreases. Also note that if a mined plains hill is available, by turn 30 the whipping cycle city has produced less raw hammers and has less AHT worth of material. Whipping is not always best.
Further Comparison - “Yea but…..”
Alright, the above comparison was an ideal steady state comparison. So now we need to include the various factors that affect the comparison. I will use numbers whenever possible, but they will be for specific situations. The main point should be if a given specific situation is generally applicable or if it is conservative enough to be useful. The main factors that modify the ideal steady state comparison are available terrain, health caps, growth speed, and happiness caps.
The first main factor that needs discussion is terrain. The question here is whether the non slavery city has an available hill to work. If a city does not have hills or other 3 hammer tiles to work, then slavery is clearly beneficial in total hammers as well as AHT worth. Otherwise, the above hammer schedule applies on a per citizen basis.
The second factor, the health cap, is also a limiting factor for the non slavery city. While whipping breaks even on happiness because it yields -1 crowded unhappiness and +1 cruel oppression unhappiness, it does not have a similar balance with health. The unhealthiness caused by crowding goes down by one and is not replaces by anything else. This means that for a given whipping cycle, the comparative non slavery city will have 1 more unhealthiness. This equals a net effect of 1 less food production. Now, in the mined grassland hill scenario, this is made up with the 1 extra food produced from the grassland hill tile. In the mined grassland hill scenario, this represents a deficit that must be paid for some other way. So, taking both hammers and food into consideration, the most fair comparison is between the whipping cycle city and the mined grassland hill city. The hammer production schedule still applies.
The growth speed is effectively a limitation on the whipping cycle city. Make no mistake, the non slavery city is not “paying food” to work its tile. The whole issue is whether to use food to make hammers through a mine or to use it to produce hammers through population. A fair comparison assumes that a whipping city only has a 2 food per whipping cycle advantage over the non slavery city. If one has food resources, then the other has them as well. If the whipping cycle city is retooled for max growth, then the non slavery city should be retooled for max growth as well. The only differences should be in the use of the citizens being whipped. In these cases, the hammer production schedule applies.
So, that said, the real importance of growth speed is in how many whipping cycles can be run at once without altering your city size. If you can only grow 1 pop in 10 turns, then you can only whip once every ten turns without starting to see a decline in city size. If you can grow 5 pop in 10 turns, and you have enough happiness to support it, you can run 5 whipping cycles at a time without seeing your city size decrease. This is important because, together with the happiness, it creates an upper limit on the use of whipping in a given city.
The final factor is the already mentioned happiness cap. This affects a given whipping cycle and a worked tile in the same way. As mentioned, you either get crowding unhappiness or cruel oppression unhappiness. The key here, though, is that cities will have a base of 3 happiness of Emperor. So the number of whipping cycles that can be run will be low. This means it is easy to find city sites that can work hills instead of whipping. Most cities will be able to have 2 or three hills in range.
Actual Mechanics Comparison - How things really work
The reality of civ is one where difficulty makes early happiness caps around 5-7, the health cap will be around 7, a city can easily have 2-3 hills, and most cities will only have 2 food resources. These numbers can be disputed, but they are more or less on target and their accuracy does not affect the analysis much. If you have a city with a +4 and a +3 food resource tile, then you can achieve +9 food growth at size 2. This will allow you to grow/whip 2.5 times in 10 turns. So, over 20 turns, the effective size of your city is +2 crowded unhappiness and +3 cruel oppression unhappiness.
A non slavery city will work the same +9 food tiles but will work a mined grassland hill when it gets to size 3 (instead of whipping back to size 2). This city will now be at +8 food growth and will be producing hammers according to the schedule above. As you can see, it’s growth is not significantly slower than the whipping city. As the whipping city grows to its equilibrium 2.5 whipping cycles, the non-slavery city can keep up with the required growth rate while losing at most a few turn. This means that, again, slavery is not gaining you hammers, just AHT worth.
The tradeoff comes when at the point where the whipping cycle city has reached equilibrium. It is an effective size (unhappiness-wise) of 5. It must produce +9 food in order to keep the whipping going. The non-slavery city, however, has reached size 5 with 3 mined grassland hills and is still at +6 food. The three mined grassland hills are already keeping total hammer production even with the whipping cycle city, so the extra 6 food is no longer needed. The non-slavery city can now change one of its food resource squares to working another hill, if available, or turn it into a specialist. There is no significant time loss since growth for working hills keeps pace with growth for whipping. It is once equilibrium is reached that the non-slavery city can begin leveraging additional production. Once again, slavery does not get you more hammers…in practice it gets you less. What is does do is give you, in effect, a paycheck advance.
This scenario holds true even if you have enough food to run more whipping cycles at a time since happiness caps affect both cities in the exact same way. The difference comes when the non-slavery city becomes health limited or cannot find hills to work. At this point whipping does have an advantage. Please note, however, that this only starts to happen when you are running 3 or 4 whipping cycles at a time. This requires enough food to grow 3 or 4 times in ten turns (basically you must have a granary) and a happiness cap that allows for the larger effective city size. On average, whipping in smaller cities with low happiness caps will not cause the comparison non-slavery city to see any limitations.
Conclusions - What’s the deal?
In the end, the choice of using slavery is more difficult than people make it out to be. Terrain, growth rates, and happiness caps must be taken into consideration. The majority of situations will see a non-slavery city producing more than a comparable size whipping city once both reach equilibrium. In the end, what slavery gets you is a greater (though diminishing over time) AHT worth. Slavery will only lead in total hammer production when you are running enough whipping cycles to outstrip hill supply. If hills are scarce and you can find several food resources per city, Slavery will not only get you your paycheck advance, but it will outproduce as well. However, if your happiness caps are low (such as on higher difficulties) and/or there are many available hills, slavery is not the panacea it is often advertised as. The sacrificing of specialist commerce combined with the opportunity cost of other civics in the category can easily make it the wrong choice.
per turn (plus whatever you gain by working the tiles), because you can't regrow population any faster than that. This is the math behind the Globe Theater as a key military production wonder - you start whipping two population every other turn.
