Caution: This article is for true micromanagers.
Optimising the Globe Theatre Draft City
Contents
1. Introduction
2. Analysis
3. The data
4. Using the Data
5. Worked Example
6. Observations
1. Introduction
Many people are familiar with a particular tactic which makes use of the National Wonder the Globe Theatre and the draft feature of the civic Nationhood. Ordinarily drafting a military unit causes a loss of one population point and 1
for some number of turns. Using the Globe Theatre you eliminate the and so if you have a lot of food available you can draft units very frequently. A similar thing can be done using the whip, and you can read all about it in VoiceOfUnreason's excellent guide Vocum Sineratio: The Whip.
I will concentrate only on the Globe Theatre city with respect to the draft - not the whip. I will refer to it from here as the GTdraft city.
The GTdraft city tactic has great synery with empires which run a heavy espionage economy, because the Nationhood civic gives +25%
to every city. If you're using the Nationhood civic you really ought to take advantage of the GTdraft tactic. Since it does not depend on the Slavery civic, it can be used in the late game when you need to use Emancipation.
NOTE: For the moment we will focus on pre Infantry and pre Mech Infantry drafting. Infantry cost two pop points and Mech infantry cost 3 pop points, requiring minimum populations of 7 and 8 respectively. Before that everything costs 1 pop point. Riflemen are the best unit to draft as they give the highest hammer to food ratio.
Here are the questions I will attempt to answer.
Q1: Where is the best site for a GTdraft city?
Q2: At what population should I run my GTdraft city?
Another question which is mainly relevant to Quick and Normal speed is...
Q3: What is the minimum population I could run the GTdraft city, minimising the number of plots needed to work, to have the GTdraft city able to draft a unit every turn without losing population?
You can skim read over the next section if you prefer.
2. Analysis
Suppose we want to run our GTdraft city between the sizes X and X+1. In other words, repeatedly grow from size X to X+1 and then draft at X+1. We will look for the best size X to do this at.
Given a city of size X, the total food Y required to grow to size X+1 is given by
Quick: Y = int(13 + 1.5X)
Normal: Y = 20+2X
Epic: Y = 30+3X
Marathon Y = 60+6X
If there is a granary present in the city, it stores half the food, rounded down. i.e. The granary stores int(Y/2) food.
So with a granary, the amount of food G you would require to grow to size X+1 is int( (Y+1) / 2 ). (Here we have used the fact that for any integer x, x = int( x/2 ) + int( (x+1) / 2 ) .)
Quick: G = int( (13 + 1.5X + 1) / 2)
Normal: G = int( (20 + 2X) / 2)
Epic: G = int( (30 + 3X + 1) / 2)
Marathon: G = int( (60 + 6X) / 2)
Note that for normal and marathon speeds Y is always even and so no rounding is necessary when dividing by 2. (i.e. int(Y/2) = int((Y+1)/2).
A city of size X must feed X citizens whom each eat 2F. Therefore the food surplus S a city has available is #F - 2X, where #F is the amount of food collected from the city's BFC (big fat cross) including the city tile itself (usually 2F) minus the food lost due to unhealthiness. This surplus is used to either support specialists or put towards growing the city. For the moment we will assume we run no specialists in the GTdraft city. I will write about how you can use specialists as well, later on. I'll also assume there is no unhealthiness. If you anticipate unhealthiness then adjust your surplus accordingly - I'll give brief mention to how to do this later.
Define a function R(X) = G(X) / S(X). This will represent how often (in turns) the GTdraft city can draft its population. For example, R=1 would be every turn, R=2 would be every 2nd turn, R = 1.5 would be twice in every three turns. I could have defined a Frequency F(X) = 1/R(X) instead but I think it's a bit easier to read the values for R(X) because G is usually greater than S.
3. The Data
Next we tabulate the data.
You can either refer to the pdf, the MS Excel spreadsheet, or the ugly tables in the next post.
Please report any errors if you see any.
4. Using the Data
Q: Ok so what are all these numbers good for?
A: Answering the quesions from the Introduction of course!
Firstly, keep in mind that a city must be at least size 6 to be able to draft, so the GTdraft city cannot do the cycle below size 5-6.
Q1: Where is the best site for a GTdraft city?
A: Generally it would be best to pick a site where there is large amount of food available, and make it your objective to get the GTdraft city pumping out a unit every turn or as close to that as possible. Especially on Quick speed, and to some extent on Normal speed, you often won't need a huge amount of food to achieve this at a low population.
In the Analysis section I defined R(X) as how often you could draft from the GTdraft city. Our aim is to get R(X) as close to 1 as possible, preferably without going under 1. If we go under 1, which is likely at Quick speed, and possible at Normal speed, we could use the extra food surplus for specialists or else risk wasting food.
At Epic and Marathon speed, and often on Normal speed, getting R=1 is not achievable and instead we will do our best to reduce R to as close to 1 as possible.
At Normal, Epic and Marathon speeds picking a good site for your GTdraft city will usually require you to decide how much food you are willing to put into this city to exploit. At quick speed and sometimes on Normal speed, your city won't necessarily need to be very large so it would be wise to pick a site where you don't take more food than is necessary.
Q2: At what population should I run my GTdraft city?
A: The best population to run your city at, in a perpetuous cycle from X to X+1, will be the value of X for which R(X) is minimum. I will show you how to find this value in the worked example shortly.
Q3: What is the minimum population I could run the GTdraft city, minimising the number of plots needed to work, to have the GTdraft city able to draft a unit every turn without losing population?
A: Again I will show you in the worked example, but basically it will be the minimum city size X (but no less than 5 remember) for which R is 1 or less.
5. Worked Example
Assuming the age of riflemen is roughly the best time to employ the GTdraft city, it would be fair to assume Civil Service has been researched. This will be important for ensuring we count the correct amount of food from irrigated farmed resources etc. I'll also assume Biology has not been researched.
Here I will work through an example to show how you would find the values of S(X) and hence calculate R(X).
Here is where this city will be settled.
To aid us with finding the function S(X), let's see what the city will look like once it has a lighthouse and all the tiles are improved.
Let us count up the surplus for each size X by starting with the best tiles and working our way to the worst tiles. For the city at size 1, we must remember to include the 2
supplied by the city centre. For size 1, we choose the farmed corn, to get a surplus of 2+4 = 6. After the corn, the rice and two clams are the same, so for sizes X=2 through to X=4 we will add 3 to the surplus each time. For each of the grassland farms, we add 1 food to the surplus. After all those tiles, the rest are all either food neutral or food negative and so we discontinue counting.
Let's find the best R value, assuming we're playing Normal speed. To do this I refer to the table for Normal speed (you'll be way off if you accidentally look at the table for the wrong speed).
In the row for X=1, I start at S=6.
In row X=2, I move to S=9.
I continue along the rows until I get to X=9, where the last grassland farm was counted, marking each value of R(X) red along the way.
Notice the minimum value is 0.933 at city size X = 4. This is a problem because 5 is the minimum size for our GTdraft city (cycling between 5-6 population). Instead we look at the row for X=5 and see R would be 1 if S were 15. But at X=5, S is 16, so we have one food too many. If the city had exactly one unhealtiness (very unlikely at this population!) we would be set. We can't use the 1 to support an extra specialist. If we had 2 too much we could have supported exactly one specialist while running the draft every turn between 5-6 pop. What you could have done is put a windmill on the grass hill, and had your size 5 city simply work the 4 resources plus the windmill. That way every of the grassland farms would be freed up for another city. An alternative to putting a windmill on the hill is just working one of the coast tiles too, freeing up the grass hill for another city as well.
Since R would remain under 1 all the way to population 9, there would be no improvement in drafting speed above population 5-6. All you would get instead is food wasted and possibly a little bit more commerce for each extra tile.
So this is a good example of a city on Normal speed where you can run the draft every turn at a size of 5-6 using only 4 resource tiles plus a coast tile. It's probably a bit uncommon to have this much food available, and given the amount of food in the BFC that is not needed, this city would perhaps have been better as a GP farm, with another good (but slightly worse) food location being used for the GTdraft city.
What if this were Epic speed? Let's see what happens now.
Doing the same thing as we did before, going through marking red the R values in the table for Epic speed, we get
The minimum R is 1.400 at size X=4. Again though, this is lower than the required 5 population. The next best value is R=1.412 at X=6. It's important to note here that this is better than the R value at X=5 which is R = 1.438. The R values seem to be better at even values of X i.e. even populations. Remember I said this is because of the rounding that happens at Epic speed - a similar thing happens for Quick speed.
So let's run this city at size 6-7. Since the R value is greater than 1, we're not going to be able to force the draft on this city every turn while maintaining a constant population. Also, it's up to you whether running it at 6-7 instead of 5-6 pop is worth the gain in drafting efficiency - in this example the gain is very very small. Keep in mind that the higher the population you draft at, the more food you are turning into the military unit. At normal speed, the difference would be 1 extra per military unit.
For one final example, let's use the same setup but turn the grassland corn into a grassland resourceless farm. Now we have
and we get
This time the best R is 1.688 at X=8.
6. Observations
On Normal and Marathon speed, adding a grassland farm always improves the value R. In other words, in the tables for Normal and Marathon, moving down one row and right one column never increases the value of R. Because of the rounding for Epic and Quick speeds, sometimes R will increase, meaning it's slightly more efficient at a higher population. So referring to these tables is more important if you play Epic or Quick speed.
If your GTdraft city is above the population where it has its optimum R, you can be more agressive with the drafting until it reachs the ideal population. If the R value is less than or equal to 1 you should be drafting absolutely nonstop at or above the ideal population.
I mentioned at the beginning of the article that this is only for true micro managers. This may be true but at least this is something that only really needs to be done once in each game if at all (choosing a GTdraft city site and deciding what population to run it at).
As you would have seen, gamespeed has a large impact on how you should implement a GTdraft city. On Quick speed, you shouldn't aim to get much food at all in the city. On Epic speed you will probably never reach R=1 and you will need to decide how much food you're willing to commit to the GTdraft city.
At Marathon speed, since building military using hammers is effectively done at a discount compared to other speeds, you should probably consider whether it's even worth running a GTdraft city. Instead, making heavier use of the whip in the GT city would be wise, since using the whip allows you to take advantage of the production multiplier buildings like the forge and factory. Drafting ignores these multipliers.
I didn't mention it earlier but the granary is essential in the GTdraft city. All the maths above assumed a granary is present. Also, since drafting units gives only half the normal xp, a barracks will only ever give you 1xp. With this in mind, it's still worth it having a barracks due to the sheer volume of troops you will produce from the city.
On Quick speed, if you get a 5-6 pop GTdraft city, when you draft riflemen you will be converting 10 into 73
.
Optimising the Globe Theatre Draft City
Contents
1. Introduction
2. Analysis
3. The data
4. Using the Data
5. Worked Example
6. Observations
1. Introduction
Many people are familiar with a particular tactic which makes use of the National Wonder the Globe Theatre and the draft feature of the civic Nationhood. Ordinarily drafting a military unit causes a loss of one population point and 1
for some number of turns. Using the Globe Theatre you eliminate the and so if you have a lot of food available you can draft units very frequently. A similar thing can be done using the whip, and you can read all about it in VoiceOfUnreason's excellent guide Vocum Sineratio: The Whip.I will concentrate only on the Globe Theatre city with respect to the draft - not the whip. I will refer to it from here as the GTdraft city.
The GTdraft city tactic has great synery with empires which run a heavy espionage economy, because the Nationhood civic gives +25%
to every city. If you're using the Nationhood civic you really ought to take advantage of the GTdraft tactic. Since it does not depend on the Slavery civic, it can be used in the late game when you need to use Emancipation.NOTE: For the moment we will focus on pre Infantry and pre Mech Infantry drafting. Infantry cost two pop points and Mech infantry cost 3 pop points, requiring minimum populations of 7 and 8 respectively. Before that everything costs 1 pop point. Riflemen are the best unit to draft as they give the highest hammer to food ratio.
Here are the questions I will attempt to answer.
Q1: Where is the best site for a GTdraft city?
Q2: At what population should I run my GTdraft city?
Another question which is mainly relevant to Quick and Normal speed is...
Q3: What is the minimum population I could run the GTdraft city, minimising the number of plots needed to work, to have the GTdraft city able to draft a unit every turn without losing population?
You can skim read over the next section if you prefer.
2. Analysis
Suppose we want to run our GTdraft city between the sizes X and X+1. In other words, repeatedly grow from size X to X+1 and then draft at X+1. We will look for the best size X to do this at.
Given a city of size X, the total food Y required to grow to size X+1 is given by
Quick: Y = int(13 + 1.5X)
Normal: Y = 20+2X
Epic: Y = 30+3X
Marathon Y = 60+6X
If there is a granary present in the city, it stores half the food, rounded down. i.e. The granary stores int(Y/2) food.
So with a granary, the amount of food G you would require to grow to size X+1 is int( (Y+1) / 2 ). (Here we have used the fact that for any integer x, x = int( x/2 ) + int( (x+1) / 2 ) .)
Quick: G = int( (13 + 1.5X + 1) / 2)
Normal: G = int( (20 + 2X) / 2)
Epic: G = int( (30 + 3X + 1) / 2)
Marathon: G = int( (60 + 6X) / 2)
Note that for normal and marathon speeds Y is always even and so no rounding is necessary when dividing by 2. (i.e. int(Y/2) = int((Y+1)/2).
A city of size X must feed X citizens whom each eat 2F. Therefore the food surplus S a city has available is #F - 2X, where #F is the amount of food collected from the city's BFC (big fat cross) including the city tile itself (usually 2F) minus the food lost due to unhealthiness. This surplus is used to either support specialists or put towards growing the city. For the moment we will assume we run no specialists in the GTdraft city. I will write about how you can use specialists as well, later on. I'll also assume there is no unhealthiness. If you anticipate unhealthiness then adjust your surplus accordingly - I'll give brief mention to how to do this later.
Define a function R(X) = G(X) / S(X). This will represent how often (in turns) the GTdraft city can draft its population. For example, R=1 would be every turn, R=2 would be every 2nd turn, R = 1.5 would be twice in every three turns. I could have defined a Frequency F(X) = 1/R(X) instead but I think it's a bit easier to read the values for R(X) because G is usually greater than S.
3. The Data
Next we tabulate the data.
You can either refer to the pdf, the MS Excel spreadsheet, or the ugly tables in the next post.
Please report any errors if you see any.
4. Using the Data
Q: Ok so what are all these numbers good for?
A: Answering the quesions from the Introduction of course!
Firstly, keep in mind that a city must be at least size 6 to be able to draft, so the GTdraft city cannot do the cycle below size 5-6.
Q1: Where is the best site for a GTdraft city?
A: Generally it would be best to pick a site where there is large amount of food available, and make it your objective to get the GTdraft city pumping out a unit every turn or as close to that as possible. Especially on Quick speed, and to some extent on Normal speed, you often won't need a huge amount of food to achieve this at a low population.
In the Analysis section I defined R(X) as how often you could draft from the GTdraft city. Our aim is to get R(X) as close to 1 as possible, preferably without going under 1. If we go under 1, which is likely at Quick speed, and possible at Normal speed, we could use the extra food surplus for specialists or else risk wasting food.
At Epic and Marathon speed, and often on Normal speed, getting R=1 is not achievable and instead we will do our best to reduce R to as close to 1 as possible.
At Normal, Epic and Marathon speeds picking a good site for your GTdraft city will usually require you to decide how much food you are willing to put into this city to exploit. At quick speed and sometimes on Normal speed, your city won't necessarily need to be very large so it would be wise to pick a site where you don't take more food than is necessary.
Q2: At what population should I run my GTdraft city?
A: The best population to run your city at, in a perpetuous cycle from X to X+1, will be the value of X for which R(X) is minimum. I will show you how to find this value in the worked example shortly.
Q3: What is the minimum population I could run the GTdraft city, minimising the number of plots needed to work, to have the GTdraft city able to draft a unit every turn without losing population?
A: Again I will show you in the worked example, but basically it will be the minimum city size X (but no less than 5 remember) for which R is 1 or less.
5. Worked Example
Assuming the age of riflemen is roughly the best time to employ the GTdraft city, it would be fair to assume Civil Service has been researched. This will be important for ensuring we count the correct amount of food from irrigated farmed resources etc. I'll also assume Biology has not been researched.
Here I will work through an example to show how you would find the values of S(X) and hence calculate R(X).
Here is where this city will be settled.
To aid us with finding the function S(X), let's see what the city will look like once it has a lighthouse and all the tiles are improved.
Let us count up the surplus for each size X by starting with the best tiles and working our way to the worst tiles. For the city at size 1, we must remember to include the 2
supplied by the city centre. For size 1, we choose the farmed corn, to get a surplus of 2+4 = 6. After the corn, the rice and two clams are the same, so for sizes X=2 through to X=4 we will add 3 to the surplus each time. For each of the grassland farms, we add 1 food to the surplus. After all those tiles, the rest are all either food neutral or food negative and so we discontinue counting.
Code:
X=1 S=6
X=2 S=9
X=3 S=12
X=4 S=15
X=5 S=16
X=6 S=17
X=7 S=18
X=8 S=19
X=9 S=20Let's find the best R value, assuming we're playing Normal speed. To do this I refer to the table for Normal speed (you'll be way off if you accidentally look at the table for the wrong speed).
In the row for X=1, I start at S=6.
In row X=2, I move to S=9.
I continue along the rows until I get to X=9, where the last grassland farm was counted, marking each value of R(X) red along the way.
Notice the minimum value is 0.933 at city size X = 4. This is a problem because 5 is the minimum size for our GTdraft city (cycling between 5-6 population). Instead we look at the row for X=5 and see R would be 1 if S were 15. But at X=5, S is 16, so we have one food too many. If the city had exactly one unhealtiness (very unlikely at this population!) we would be set. We can't use the 1
to support an extra specialist. If we had 2 too much we could have supported exactly one specialist while running the draft every turn between 5-6 pop. What you could have done is put a windmill on the grass hill, and had your size 5 city simply work the 4 resources plus the windmill. That way every of the grassland farms would be freed up for another city. An alternative to putting a windmill on the hill is just working one of the coast tiles too, freeing up the grass hill for another city as well.Since R would remain under 1 all the way to population 9, there would be no improvement in drafting speed above population 5-6. All you would get instead is food wasted and possibly a little bit more commerce for each extra tile.
So this is a good example of a city on Normal speed where you can run the draft every turn at a size of 5-6 using only 4 resource tiles plus a coast tile. It's probably a bit uncommon to have this much food available, and given the amount of food in the BFC that is not needed, this city would perhaps have been better as a GP farm, with another good (but slightly worse) food location being used for the GTdraft city.
What if this were Epic speed? Let's see what happens now.
Doing the same thing as we did before, going through marking red the R values in the table for Epic speed, we get
The minimum R is 1.400 at size X=4. Again though, this is lower than the required 5 population. The next best value is R=1.412 at X=6. It's important to note here that this is better than the R value at X=5 which is R = 1.438. The R values seem to be better at even values of X i.e. even populations. Remember I said this is because of the rounding that happens at Epic speed - a similar thing happens for Quick speed.
So let's run this city at size 6-7. Since the R value is greater than 1, we're not going to be able to force the draft on this city every turn while maintaining a constant population. Also, it's up to you whether running it at 6-7 instead of 5-6 pop is worth the gain in drafting efficiency - in this example the gain is very very small. Keep in mind that the higher the population you draft at, the more food you are turning into the military unit. At normal speed, the difference would be 1 extra
per military unit.For one final example, let's use the same setup but turn the grassland corn into a grassland resourceless farm. Now we have
Code:
X=1 S=5
X=2 S=8
X=3 S=11
X=4 S=12
X=5 S=13
X=6 S=14
X=7 S=15
X=8 S=16
X=9 S=17and we get
This time the best R is 1.688 at X=8.
6. Observations
On Normal and Marathon speed, adding a grassland farm always improves the value R. In other words, in the tables for Normal and Marathon, moving down one row and right one column never increases the value of R. Because of the rounding for Epic and Quick speeds, sometimes R will increase, meaning it's slightly more efficient at a higher population. So referring to these tables is more important if you play Epic or Quick speed.
If your GTdraft city is above the population where it has its optimum R, you can be more agressive with the drafting until it reachs the ideal population. If the R value is less than or equal to 1 you should be drafting absolutely nonstop at or above the ideal population.
I mentioned at the beginning of the article that this is only for true micro managers. This may be true but at least this is something that only really needs to be done once in each game if at all (choosing a GTdraft city site and deciding what population to run it at).
As you would have seen, gamespeed has a large impact on how you should implement a GTdraft city. On Quick speed, you shouldn't aim to get much food at all in the city. On Epic speed you will probably never reach R=1 and you will need to decide how much food you're willing to commit to the GTdraft city.
At Marathon speed, since building military using hammers is effectively done at a discount compared to other speeds, you should probably consider whether it's even worth running a GTdraft city. Instead, making heavier use of the whip in the GT city would be wise, since using the whip allows you to take advantage of the production multiplier buildings like the forge and factory. Drafting ignores these multipliers.
I didn't mention it earlier but the granary is essential in the GTdraft city. All the maths above assumed a granary is present. Also, since drafting units gives only half the normal xp, a barracks will only ever give you 1xp. With this in mind, it's still worth it having a barracks due to the sheer volume of troops you will produce from the city.
On Quick speed, if you get a 5-6 pop GTdraft city, when you draft riflemen you will be converting 10
into 73.
and 10 
