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Optimising the Globe Theatre Draft City

Discussion in 'Civ4 Strategy Articles' started by PieceOfMind, Dec 8, 2008.

  1. PieceOfMind

    PieceOfMind Drill IV Defender Retired Moderator

    Joined:
    Jan 15, 2006
    Messages:
    9,319
    Location:
    Australia
    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:mad: for some number of turns. Using the Globe Theatre you eliminate the :mad: 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% :espionage: 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:food: 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:food: 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=20
    
    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:food: to support an extra specialist. If we had 2 :food: 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 :food: 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=17
    
    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:food: into 73:hammers:.
     

    Attached Files:

  2. PieceOfMind

    PieceOfMind Drill IV Defender Retired Moderator

    Joined:
    Jan 15, 2006
    Messages:
    9,319
    Location:
    Australia
    Spoiler :


    Quick
    Code:
    X	G(X)	S(X)-->	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
    1	7		7.000	3.500	2.333	1.750	1.400	1.167	1.000	0.875	0.778	0.700	0.636	0.583	0.538	0.500	0.467	0.438	0.412	0.389	0.368	0.350	0.333	0.318	0.304	0.292	0.280	0.269	0.259	0.250	0.241	0.233
    2	8		8.000	4.000	2.667	2.000	1.600	1.333	1.143	1.000	0.889	0.800	0.727	0.667	0.615	0.571	0.533	0.500	0.471	0.444	0.421	0.400	0.381	0.364	0.348	0.333	0.320	0.308	0.296	0.286	0.276	0.267
    3	9		9.000	4.500	3.000	2.250	1.800	1.500	1.286	1.125	1.000	0.900	0.818	0.750	0.692	0.643	0.600	0.563	0.529	0.500	0.474	0.450	0.429	0.409	0.391	0.375	0.360	0.346	0.333	0.321	0.310	0.300
    4	10		10.000	5.000	3.333	2.500	2.000	1.667	1.429	1.250	1.111	1.000	0.909	0.833	0.769	0.714	0.667	0.625	0.588	0.556	0.526	0.500	0.476	0.455	0.435	0.417	0.400	0.385	0.370	0.357	0.345	0.333
    5	10		10.000	5.000	3.333	2.500	2.000	1.667	1.429	1.250	1.111	1.000	0.909	0.833	0.769	0.714	0.667	0.625	0.588	0.556	0.526	0.500	0.476	0.455	0.435	0.417	0.400	0.385	0.370	0.357	0.345	0.333
    6	11		11.000	5.500	3.667	2.750	2.200	1.833	1.571	1.375	1.222	1.100	1.000	0.917	0.846	0.786	0.733	0.688	0.647	0.611	0.579	0.550	0.524	0.500	0.478	0.458	0.440	0.423	0.407	0.393	0.379	0.367
    7	12		12.000	6.000	4.000	3.000	2.400	2.000	1.714	1.500	1.333	1.200	1.091	1.000	0.923	0.857	0.800	0.750	0.706	0.667	0.632	0.600	0.571	0.545	0.522	0.500	0.480	0.462	0.444	0.429	0.414	0.400
    8	13		13.000	6.500	4.333	3.250	2.600	2.167	1.857	1.625	1.444	1.300	1.182	1.083	1.000	0.929	0.867	0.813	0.765	0.722	0.684	0.650	0.619	0.591	0.565	0.542	0.520	0.500	0.481	0.464	0.448	0.433
    9	13		13.000	6.500	4.333	3.250	2.600	2.167	1.857	1.625	1.444	1.300	1.182	1.083	1.000	0.929	0.867	0.813	0.765	0.722	0.684	0.650	0.619	0.591	0.565	0.542	0.520	0.500	0.481	0.464	0.448	0.433
    10	14		14.000	7.000	4.667	3.500	2.800	2.333	2.000	1.750	1.556	1.400	1.273	1.167	1.077	1.000	0.933	0.875	0.824	0.778	0.737	0.700	0.667	0.636	0.609	0.583	0.560	0.538	0.519	0.500	0.483	0.467
    11	15		15.000	7.500	5.000	3.750	3.000	2.500	2.143	1.875	1.667	1.500	1.364	1.250	1.154	1.071	1.000	0.938	0.882	0.833	0.789	0.750	0.714	0.682	0.652	0.625	0.600	0.577	0.556	0.536	0.517	0.500
    12	16		16.000	8.000	5.333	4.000	3.200	2.667	2.286	2.000	1.778	1.600	1.455	1.333	1.231	1.143	1.067	1.000	0.941	0.889	0.842	0.800	0.762	0.727	0.696	0.667	0.640	0.615	0.593	0.571	0.552	0.533
    13	16		16.000	8.000	5.333	4.000	3.200	2.667	2.286	2.000	1.778	1.600	1.455	1.333	1.231	1.143	1.067	1.000	0.941	0.889	0.842	0.800	0.762	0.727	0.696	0.667	0.640	0.615	0.593	0.571	0.552	0.533
    14	17		17.000	8.500	5.667	4.250	3.400	2.833	2.429	2.125	1.889	1.700	1.545	1.417	1.308	1.214	1.133	1.063	1.000	0.944	0.895	0.850	0.810	0.773	0.739	0.708	0.680	0.654	0.630	0.607	0.586	0.567
    15	18		18.000	9.000	6.000	4.500	3.600	3.000	2.571	2.250	2.000	1.800	1.636	1.500	1.385	1.286	1.200	1.125	1.059	1.000	0.947	0.900	0.857	0.818	0.783	0.750	0.720	0.692	0.667	0.643	0.621	0.600
    16	19		19.000	9.500	6.333	4.750	3.800	3.167	2.714	2.375	2.111	1.900	1.727	1.583	1.462	1.357	1.267	1.188	1.118	1.056	1.000	0.950	0.905	0.864	0.826	0.792	0.760	0.731	0.704	0.679	0.655	0.633
    17	19		19.000	9.500	6.333	4.750	3.800	3.167	2.714	2.375	2.111	1.900	1.727	1.583	1.462	1.357	1.267	1.188	1.118	1.056	1.000	0.950	0.905	0.864	0.826	0.792	0.760	0.731	0.704	0.679	0.655	0.633
    18	20		20.000	10.000	6.667	5.000	4.000	3.333	2.857	2.500	2.222	2.000	1.818	1.667	1.538	1.429	1.333	1.250	1.176	1.111	1.053	1.000	0.952	0.909	0.870	0.833	0.800	0.769	0.741	0.714	0.690	0.667
    19	21		21.000	10.500	7.000	5.250	4.200	3.500	3.000	2.625	2.333	2.100	1.909	1.750	1.615	1.500	1.400	1.313	1.235	1.167	1.105	1.050	1.000	0.955	0.913	0.875	0.840	0.808	0.778	0.750	0.724	0.700
    20	22		22.000	11.000	7.333	5.500	4.400	3.667	3.143	2.750	2.444	2.200	2.000	1.833	1.692	1.571	1.467	1.375	1.294	1.222	1.158	1.100	1.048	1.000	0.957	0.917	0.880	0.846	0.815	0.786	0.759	0.733
    
    Normal
    Code:
    X	G(X)	S(X)-->	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
    1	11		11.000	5.500	3.667	2.750	2.200	1.833	1.571	1.375	1.222	1.100	1.000	0.917	0.846	0.786	0.733	0.688	0.647	0.611	0.579	0.550	0.524	0.500	0.478	0.458	0.440	0.423	0.407	0.393	0.379	0.367
    2	12		12.000	6.000	4.000	3.000	2.400	2.000	1.714	1.500	1.333	1.200	1.091	1.000	0.923	0.857	0.800	0.750	0.706	0.667	0.632	0.600	0.571	0.545	0.522	0.500	0.480	0.462	0.444	0.429	0.414	0.400
    3	13		13.000	6.500	4.333	3.250	2.600	2.167	1.857	1.625	1.444	1.300	1.182	1.083	1.000	0.929	0.867	0.813	0.765	0.722	0.684	0.650	0.619	0.591	0.565	0.542	0.520	0.500	0.481	0.464	0.448	0.433
    4	14		14.000	7.000	4.667	3.500	2.800	2.333	2.000	1.750	1.556	1.400	1.273	1.167	1.077	1.000	0.933	0.875	0.824	0.778	0.737	0.700	0.667	0.636	0.609	0.583	0.560	0.538	0.519	0.500	0.483	0.467
    5	15		15.000	7.500	5.000	3.750	3.000	2.500	2.143	1.875	1.667	1.500	1.364	1.250	1.154	1.071	1.000	0.938	0.882	0.833	0.789	0.750	0.714	0.682	0.652	0.625	0.600	0.577	0.556	0.536	0.517	0.500
    6	16		16.000	8.000	5.333	4.000	3.200	2.667	2.286	2.000	1.778	1.600	1.455	1.333	1.231	1.143	1.067	1.000	0.941	0.889	0.842	0.800	0.762	0.727	0.696	0.667	0.640	0.615	0.593	0.571	0.552	0.533
    7	17		17.000	8.500	5.667	4.250	3.400	2.833	2.429	2.125	1.889	1.700	1.545	1.417	1.308	1.214	1.133	1.063	1.000	0.944	0.895	0.850	0.810	0.773	0.739	0.708	0.680	0.654	0.630	0.607	0.586	0.567
    8	18		18.000	9.000	6.000	4.500	3.600	3.000	2.571	2.250	2.000	1.800	1.636	1.500	1.385	1.286	1.200	1.125	1.059	1.000	0.947	0.900	0.857	0.818	0.783	0.750	0.720	0.692	0.667	0.643	0.621	0.600
    9	19		19.000	9.500	6.333	4.750	3.800	3.167	2.714	2.375	2.111	1.900	1.727	1.583	1.462	1.357	1.267	1.188	1.118	1.056	1.000	0.950	0.905	0.864	0.826	0.792	0.760	0.731	0.704	0.679	0.655	0.633
    10	20		20.000	10.000	6.667	5.000	4.000	3.333	2.857	2.500	2.222	2.000	1.818	1.667	1.538	1.429	1.333	1.250	1.176	1.111	1.053	1.000	0.952	0.909	0.870	0.833	0.800	0.769	0.741	0.714	0.690	0.667
    11	21		21.000	10.500	7.000	5.250	4.200	3.500	3.000	2.625	2.333	2.100	1.909	1.750	1.615	1.500	1.400	1.313	1.235	1.167	1.105	1.050	1.000	0.955	0.913	0.875	0.840	0.808	0.778	0.750	0.724	0.700
    12	22		22.000	11.000	7.333	5.500	4.400	3.667	3.143	2.750	2.444	2.200	2.000	1.833	1.692	1.571	1.467	1.375	1.294	1.222	1.158	1.100	1.048	1.000	0.957	0.917	0.880	0.846	0.815	0.786	0.759	0.733
    13	23		23.000	11.500	7.667	5.750	4.600	3.833	3.286	2.875	2.556	2.300	2.091	1.917	1.769	1.643	1.533	1.438	1.353	1.278	1.211	1.150	1.095	1.045	1.000	0.958	0.920	0.885	0.852	0.821	0.793	0.767
    14	24		24.000	12.000	8.000	6.000	4.800	4.000	3.429	3.000	2.667	2.400	2.182	2.000	1.846	1.714	1.600	1.500	1.412	1.333	1.263	1.200	1.143	1.091	1.043	1.000	0.960	0.923	0.889	0.857	0.828	0.800
    15	25		25.000	12.500	8.333	6.250	5.000	4.167	3.571	3.125	2.778	2.500	2.273	2.083	1.923	1.786	1.667	1.563	1.471	1.389	1.316	1.250	1.190	1.136	1.087	1.042	1.000	0.962	0.926	0.893	0.862	0.833
    16	26		26.000	13.000	8.667	6.500	5.200	4.333	3.714	3.250	2.889	2.600	2.364	2.167	2.000	1.857	1.733	1.625	1.529	1.444	1.368	1.300	1.238	1.182	1.130	1.083	1.040	1.000	0.963	0.929	0.897	0.867
    17	27		27.000	13.500	9.000	6.750	5.400	4.500	3.857	3.375	3.000	2.700	2.455	2.250	2.077	1.929	1.800	1.688	1.588	1.500	1.421	1.350	1.286	1.227	1.174	1.125	1.080	1.038	1.000	0.964	0.931	0.900
    18	28		28.000	14.000	9.333	7.000	5.600	4.667	4.000	3.500	3.111	2.800	2.545	2.333	2.154	2.000	1.867	1.750	1.647	1.556	1.474	1.400	1.333	1.273	1.217	1.167	1.120	1.077	1.037	1.000	0.966	0.933
    19	29		29.000	14.500	9.667	7.250	5.800	4.833	4.143	3.625	3.222	2.900	2.636	2.417	2.231	2.071	1.933	1.813	1.706	1.611	1.526	1.450	1.381	1.318	1.261	1.208	1.160	1.115	1.074	1.036	1.000	0.967
    20	30		30.000	15.000	10.000	7.500	6.000	5.000	4.286	3.750	3.333	3.000	2.727	2.500	2.308	2.143	2.000	1.875	1.765	1.667	1.579	1.500	1.429	1.364	1.304	1.250	1.200	1.154	1.111	1.071	1.034	1.000
    
    Epic
    Code:
    X	G(X)	S(X)-->	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
    1	17		17.000	8.500	5.667	4.250	3.400	2.833	2.429	2.125	1.889	1.700	1.545	1.417	1.308	1.214	1.133	1.063	1.000	0.944	0.895	0.850	0.810	0.773	0.739	0.708	0.680	0.654	0.630	0.607	0.586	0.567
    2	18		18.000	9.000	6.000	4.500	3.600	3.000	2.571	2.250	2.000	1.800	1.636	1.500	1.385	1.286	1.200	1.125	1.059	1.000	0.947	0.900	0.857	0.818	0.783	0.750	0.720	0.692	0.667	0.643	0.621	0.600
    3	20		20.000	10.000	6.667	5.000	4.000	3.333	2.857	2.500	2.222	2.000	1.818	1.667	1.538	1.429	1.333	1.250	1.176	1.111	1.053	1.000	0.952	0.909	0.870	0.833	0.800	0.769	0.741	0.714	0.690	0.667
    4	21		21.000	10.500	7.000	5.250	4.200	3.500	3.000	2.625	2.333	2.100	1.909	1.750	1.615	1.500	1.400	1.313	1.235	1.167	1.105	1.050	1.000	0.955	0.913	0.875	0.840	0.808	0.778	0.750	0.724	0.700
    5	23		23.000	11.500	7.667	5.750	4.600	3.833	3.286	2.875	2.556	2.300	2.091	1.917	1.769	1.643	1.533	1.438	1.353	1.278	1.211	1.150	1.095	1.045	1.000	0.958	0.920	0.885	0.852	0.821	0.793	0.767
    6	24		24.000	12.000	8.000	6.000	4.800	4.000	3.429	3.000	2.667	2.400	2.182	2.000	1.846	1.714	1.600	1.500	1.412	1.333	1.263	1.200	1.143	1.091	1.043	1.000	0.960	0.923	0.889	0.857	0.828	0.800
    7	26		26.000	13.000	8.667	6.500	5.200	4.333	3.714	3.250	2.889	2.600	2.364	2.167	2.000	1.857	1.733	1.625	1.529	1.444	1.368	1.300	1.238	1.182	1.130	1.083	1.040	1.000	0.963	0.929	0.897	0.867
    8	27		27.000	13.500	9.000	6.750	5.400	4.500	3.857	3.375	3.000	2.700	2.455	2.250	2.077	1.929	1.800	1.688	1.588	1.500	1.421	1.350	1.286	1.227	1.174	1.125	1.080	1.038	1.000	0.964	0.931	0.900
    9	29		29.000	14.500	9.667	7.250	5.800	4.833	4.143	3.625	3.222	2.900	2.636	2.417	2.231	2.071	1.933	1.813	1.706	1.611	1.526	1.450	1.381	1.318	1.261	1.208	1.160	1.115	1.074	1.036	1.000	0.967
    10	30		30.000	15.000	10.000	7.500	6.000	5.000	4.286	3.750	3.333	3.000	2.727	2.500	2.308	2.143	2.000	1.875	1.765	1.667	1.579	1.500	1.429	1.364	1.304	1.250	1.200	1.154	1.111	1.071	1.034	1.000
    11	32		32.000	16.000	10.667	8.000	6.400	5.333	4.571	4.000	3.556	3.200	2.909	2.667	2.462	2.286	2.133	2.000	1.882	1.778	1.684	1.600	1.524	1.455	1.391	1.333	1.280	1.231	1.185	1.143	1.103	1.067
    12	33		33.000	16.500	11.000	8.250	6.600	5.500	4.714	4.125	3.667	3.300	3.000	2.750	2.538	2.357	2.200	2.063	1.941	1.833	1.737	1.650	1.571	1.500	1.435	1.375	1.320	1.269	1.222	1.179	1.138	1.100
    13	35		35.000	17.500	11.667	8.750	7.000	5.833	5.000	4.375	3.889	3.500	3.182	2.917	2.692	2.500	2.333	2.188	2.059	1.944	1.842	1.750	1.667	1.591	1.522	1.458	1.400	1.346	1.296	1.250	1.207	1.167
    14	36		36.000	18.000	12.000	9.000	7.200	6.000	5.143	4.500	4.000	3.600	3.273	3.000	2.769	2.571	2.400	2.250	2.118	2.000	1.895	1.800	1.714	1.636	1.565	1.500	1.440	1.385	1.333	1.286	1.241	1.200
    15	38		38.000	19.000	12.667	9.500	7.600	6.333	5.429	4.750	4.222	3.800	3.455	3.167	2.923	2.714	2.533	2.375	2.235	2.111	2.000	1.900	1.810	1.727	1.652	1.583	1.520	1.462	1.407	1.357	1.310	1.267
    16	39		39.000	19.500	13.000	9.750	7.800	6.500	5.571	4.875	4.333	3.900	3.545	3.250	3.000	2.786	2.600	2.438	2.294	2.167	2.053	1.950	1.857	1.773	1.696	1.625	1.560	1.500	1.444	1.393	1.345	1.300
    17	41		41.000	20.500	13.667	10.250	8.200	6.833	5.857	5.125	4.556	4.100	3.727	3.417	3.154	2.929	2.733	2.563	2.412	2.278	2.158	2.050	1.952	1.864	1.783	1.708	1.640	1.577	1.519	1.464	1.414	1.367
    18	42		42.000	21.000	14.000	10.500	8.400	7.000	6.000	5.250	4.667	4.200	3.818	3.500	3.231	3.000	2.800	2.625	2.471	2.333	2.211	2.100	2.000	1.909	1.826	1.750	1.680	1.615	1.556	1.500	1.448	1.400
    19	44		44.000	22.000	14.667	11.000	8.800	7.333	6.286	5.500	4.889	4.400	4.000	3.667	3.385	3.143	2.933	2.750	2.588	2.444	2.316	2.200	2.095	2.000	1.913	1.833	1.760	1.692	1.630	1.571	1.517	1.467
    20	45		45.000	22.500	15.000	11.250	9.000	7.500	6.429	5.625	5.000	4.500	4.091	3.750	3.462	3.214	3.000	2.813	2.647	2.500	2.368	2.250	2.143	2.045	1.957	1.875	1.800	1.731	1.667	1.607	1.552	1.500
    
    Marathon
    Code:
    X	G(X)	S(X)-->	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26	27	28	29	30
    1	33		33.000	16.500	11.000	8.250	6.600	5.500	4.714	4.125	3.667	3.300	3.000	2.750	2.538	2.357	2.200	2.063	1.941	1.833	1.737	1.650	1.571	1.500	1.435	1.375	1.320	1.269	1.222	1.179	1.138	1.100
    2	36		36.000	18.000	12.000	9.000	7.200	6.000	5.143	4.500	4.000	3.600	3.273	3.000	2.769	2.571	2.400	2.250	2.118	2.000	1.895	1.800	1.714	1.636	1.565	1.500	1.440	1.385	1.333	1.286	1.241	1.200
    3	39		39.000	19.500	13.000	9.750	7.800	6.500	5.571	4.875	4.333	3.900	3.545	3.250	3.000	2.786	2.600	2.438	2.294	2.167	2.053	1.950	1.857	1.773	1.696	1.625	1.560	1.500	1.444	1.393	1.345	1.300
    4	42		42.000	21.000	14.000	10.500	8.400	7.000	6.000	5.250	4.667	4.200	3.818	3.500	3.231	3.000	2.800	2.625	2.471	2.333	2.211	2.100	2.000	1.909	1.826	1.750	1.680	1.615	1.556	1.500	1.448	1.400
    5	45		45.000	22.500	15.000	11.250	9.000	7.500	6.429	5.625	5.000	4.500	4.091	3.750	3.462	3.214	3.000	2.813	2.647	2.500	2.368	2.250	2.143	2.045	1.957	1.875	1.800	1.731	1.667	1.607	1.552	1.500
    6	48		48.000	24.000	16.000	12.000	9.600	8.000	6.857	6.000	5.333	4.800	4.364	4.000	3.692	3.429	3.200	3.000	2.824	2.667	2.526	2.400	2.286	2.182	2.087	2.000	1.920	1.846	1.778	1.714	1.655	1.600
    7	51		51.000	25.500	17.000	12.750	10.200	8.500	7.286	6.375	5.667	5.100	4.636	4.250	3.923	3.643	3.400	3.188	3.000	2.833	2.684	2.550	2.429	2.318	2.217	2.125	2.040	1.962	1.889	1.821	1.759	1.700
    8	54		54.000	27.000	18.000	13.500	10.800	9.000	7.714	6.750	6.000	5.400	4.909	4.500	4.154	3.857	3.600	3.375	3.176	3.000	2.842	2.700	2.571	2.455	2.348	2.250	2.160	2.077	2.000	1.929	1.862	1.800
    9	57		57.000	28.500	19.000	14.250	11.400	9.500	8.143	7.125	6.333	5.700	5.182	4.750	4.385	4.071	3.800	3.563	3.353	3.167	3.000	2.850	2.714	2.591	2.478	2.375	2.280	2.192	2.111	2.036	1.966	1.900
    10	60		60.000	30.000	20.000	15.000	12.000	10.000	8.571	7.500	6.667	6.000	5.455	5.000	4.615	4.286	4.000	3.750	3.529	3.333	3.158	3.000	2.857	2.727	2.609	2.500	2.400	2.308	2.222	2.143	2.069	2.000
    11	63		63.000	31.500	21.000	15.750	12.600	10.500	9.000	7.875	7.000	6.300	5.727	5.250	4.846	4.500	4.200	3.938	3.706	3.500	3.316	3.150	3.000	2.864	2.739	2.625	2.520	2.423	2.333	2.250	2.172	2.100
    12	66		66.000	33.000	22.000	16.500	13.200	11.000	9.429	8.250	7.333	6.600	6.000	5.500	5.077	4.714	4.400	4.125	3.882	3.667	3.474	3.300	3.143	3.000	2.870	2.750	2.640	2.538	2.444	2.357	2.276	2.200
    13	69		69.000	34.500	23.000	17.250	13.800	11.500	9.857	8.625	7.667	6.900	6.273	5.750	5.308	4.929	4.600	4.313	4.059	3.833	3.632	3.450	3.286	3.136	3.000	2.875	2.760	2.654	2.556	2.464	2.379	2.300
    14	72		72.000	36.000	24.000	18.000	14.400	12.000	10.286	9.000	8.000	7.200	6.545	6.000	5.538	5.143	4.800	4.500	4.235	4.000	3.789	3.600	3.429	3.273	3.130	3.000	2.880	2.769	2.667	2.571	2.483	2.400
    15	75		75.000	37.500	25.000	18.750	15.000	12.500	10.714	9.375	8.333	7.500	6.818	6.250	5.769	5.357	5.000	4.688	4.412	4.167	3.947	3.750	3.571	3.409	3.261	3.125	3.000	2.885	2.778	2.679	2.586	2.500
    16	78		78.000	39.000	26.000	19.500	15.600	13.000	11.143	9.750	8.667	7.800	7.091	6.500	6.000	5.571	5.200	4.875	4.588	4.333	4.105	3.900	3.714	3.545	3.391	3.250	3.120	3.000	2.889	2.786	2.690	2.600
    17	81		81.000	40.500	27.000	20.250	16.200	13.500	11.571	10.125	9.000	8.100	7.364	6.750	6.231	5.786	5.400	5.063	4.765	4.500	4.263	4.050	3.857	3.682	3.522	3.375	3.240	3.115	3.000	2.893	2.793	2.700
    18	84		84.000	42.000	28.000	21.000	16.800	14.000	12.000	10.500	9.333	8.400	7.636	7.000	6.462	6.000	5.600	5.250	4.941	4.667	4.421	4.200	4.000	3.818	3.652	3.500	3.360	3.231	3.111	3.000	2.897	2.800
    19	87		87.000	43.500	29.000	21.750	17.400	14.500	12.429	10.875	9.667	8.700	7.909	7.250	6.692	6.214	5.800	5.438	5.118	4.833	4.579	4.350	4.143	3.955	3.783	3.625	3.480	3.346	3.222	3.107	3.000	2.900
    20	90		90.000	45.000	30.000	22.500	18.000	15.000	12.857	11.250	10.000	9.000	8.182	7.500	6.923	6.429	6.000	5.625	5.294	5.000	4.737	4.500	4.286	4.091	3.913	3.750	3.600	3.462	3.333	3.214	3.103	3.000
    
     
  3. PieceOfMind

    PieceOfMind Drill IV Defender Retired Moderator

    Joined:
    Jan 15, 2006
    Messages:
    9,319
    Location:
    Australia
    I'll soon be adding the same tables for the infantry and mech infantry R values. In other words, for drafting 2 or 3 population instead of 1. Comes out as a fair bit less efficient in the food to hammer conversion (this is not new to anyone I know) but I will include it for completeness.

    I still want to check whether perpetual GTdrafting is worth it at infantry and mech infantry. If it is, you simply get your proper military cities to build the specialised units like tanks, marines, paratroopers etc. where promotions have more value, and have this city producing the basic troops. The window where infantry are available is pretty big, before mech inf. come so this will be an important consideration.

    By the way, it turns out I broke a few of the image links in one of my edits of the original post, so they would have been down for several hours. Sorry if this confused anyone reading it recently. They're fixed now of course.
     
  4. ventrue

    ventrue Warlord

    Joined:
    Nov 10, 2008
    Messages:
    139
    Location:
    Houston, Tx
    Thanks for the article. Is it possible to run the National Park and the Globe Theatre in the same city?

    Would it be best to run Theocracy while drafting out these units? Should you put all your great generals as specialists in the Globe City?
     
  5. UWHabs

    UWHabs Deity

    Joined:
    Oct 10, 2008
    Messages:
    4,182
    Location:
    Toronto
    Well, it depends what other cities you have. Since you only get 1/2 the XP, Theocracy/settled GG would only give 1 XP. I'd say it would be useful to run one, to at least draft units with 2XP to get the first promotion, but if you have another city as military pump, I'd expect your generals would be better settled there.
     
  6. JammerUno

    JammerUno King

    Joined:
    Aug 28, 2006
    Messages:
    850
    Location:
    Utrecht, Netherlands
    So basically you're looking for a citysite that will produce a set amount of food at a set level. Considering the usage of tiles, you want your GT city to take up as little land as possible. Considering I've seen starting locations with 3 fish (18 food) it's very doable to set up a city for continuous drafting through the ages.
    The question I'm interested in, is how this compares to setting up the city for something else. Say you've built your NE somewhere already, you're playing epic speed, and you find a location like the one above. You could also work 13 tiles and run an engineer if you workshop all the grasslands. That gets you hammers and good versatility in the output of units. Assuming chemistry, that would be 29 hammers without modifiers, 27 working the tiles and 2 from the engineer. That's still inferior to setting this up as a GT site, so I would put that down here.
    I feel there's a definite advantage of having the GT coastal. It usually gives the best food anyway, but having all those productionless tiles makes it an easy decision. The city you used as an example one tile south, now I would put the maoi there and workshop/watermill all the tiles making it an excellent production site for troops, and navy as well.
     
  7. PieceOfMind

    PieceOfMind Drill IV Defender Retired Moderator

    Joined:
    Jan 15, 2006
    Messages:
    9,319
    Location:
    Australia
    By the way, just so you know, the city site was a start when I generated a map. However I removed a gold from one of the hills and added the rice (I don't think you normally would start with two grain resources).

    In my mind my main conclusion was that particularly on quick speed, you should keep the globe theatre city as small as possible and place it in such a way that other cities have access to the tiles it doesn't need.

    JammerUno you're probably right that in this example the it would have been better to make the city something else.

    ventrue I'd never sugest putting great generals in this city. Considering they would only give 1xp they'd be far far more useful in your proper military cities.

    In this article I mainly wanted to answer the questions in the introduction - that is to see how fast you can pump units out of this city. Soon I'm going to be posting some more data on the food to hammer conversion rates for various city sizes.

    The conversion rate is always better at smaller city sizes, but at the slower speeds like normal and epic, you'd have to compromise between conversion rate and output speed.

    I think even when the city is fairly large the conversion is worth it, especially for riflemen and less so for the later units.
     
  8. Negator_UK

    Negator_UK King

    Joined:
    Nov 14, 2007
    Messages:
    758
    Nice article, although I'd say it wasn't finished yet - you need to distill the numbers down into something more manageable somehow.

    How about looking at it form the point of view of amount of food available. Take a min sized city for each speed and work out the steady state draft rate for a given food surplus. Your tables will have fewer numbers, and those will more likely be the numbers players want to use.
     
  9. PieceOfMind

    PieceOfMind Drill IV Defender Retired Moderator

    Joined:
    Jan 15, 2006
    Messages:
    9,319
    Location:
    Australia
    In my current Epic speed game, I have picked out a site for the GTdraft city. It will have 3 bananas, 1 sugar, and as many grassland farms as it wants.

    I could run this city between size 5 and 6, drafting Riflemen. At Epic speed, Riflemen cost 165:hammers:. Using the data in the first post, I find a value R(5) = 1.643 or R(6) = 1.600. This means I could draft a little bit more frequently running between size 6 and 7, but only slightly more.

    Running the city at size 5 to 6 means the footprint of the GTdraft city will be a total of 6 tiles (I have to include the city tile). So if I work out the hammers gathered per tile, it is as follows:

    165:hammers: / (1.643 turns * 7 tiles) = 16.739:hammers: per turn per tile.
    These cannot go through production modifiers but regardless this is an insane amount, and it comes well before factories and power plants can be built. If I do not include the city tile (so as to give better comparison with ordinary improvements), it is getting 20.095:hammers: per turn per tile! On top of this, it will get the 1:hammers: from the city tile for building things.

    Running it at size 6 to 7 would give 14.732:hammers: per turn per tile, or not counting the city tile 17.188:hammers: per turn per tile, but would be able to draft at a slightly faster rate. So there is a tradeoff - the faster you want it to draft units the less efficient it gets.

    I'm also playing a Protective leader, so the unit will start with the free promotions and probably enough xp for 1 or 2 more.
     
  10. PieceOfMind

    PieceOfMind Drill IV Defender Retired Moderator

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    This is the city site I was talking about in the above post. Notice how it uses up very few tiles to achieve its fast drafting rate. It does use several valuable tiles which could be used by the cities around it, but those bananas and sugar can be used by other cities while it is not drafting anyway.

    When it gets built it may take a while to get the Globe Theatre and a barracks built but at least it can take advantage of the whip for building those things, with all that food available.


     

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  11. royal62184

    royal62184 Prince

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    Great thread, I have a game going right now that will finish the globe in 30 turns and I plan on putting this to use :)
     
  12. Tecibbar

    Tecibbar unliving

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    I am more interested if it's worthwhile running nationhood. How many hammer can be earned per turn? In beauacracy, one can get around 100 :science: and 10 :hammers:.
     
  13. PieceOfMind

    PieceOfMind Drill IV Defender Retired Moderator

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    In post #9 above I treated one particular example at Epic speed. In that example, in the GTdraft city I was pulling 20:hammers: per tile from the tiles that could be worked by the city, but that was only during the time I could build riflemen (they are the most efficient hammer wise). This would total to approx 100:hammers: per turn I guess, but that is not the bonus measure over what you could do using slavery or using mines.

    It's probably not best to compare the hammer bonuses between Nationhood and Beauracracy IMO. It could be done but it will depend heavily on the size of your empire, your access to happiness resources, your ability to use the culture slider for happiness (eg. in a SE), the production output of your capital etc.

    Nationhood has several benefits including the no upkeep and the +25%:espionage: - very powerful in EEs - and the +2:) from barracks. All of these can be leveraged to different extents but I would imagine if used properly these can easily lead to more value than 100:science: and 10:hammers:.

    Also, you can draft units in cities other than the GTdraft city. And it's more powerful for Protective or Aggressive leaders since they get Drill I + City Garrison I or Combat I free .
     
  14. EmperorFool

    EmperorFool Deity

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  15. PieceOfMind

    PieceOfMind Drill IV Defender Retired Moderator

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    EF,

    A few comments.

    It's a bit hard for me to say how useful this will be in BUG. I know that each game I will go to these tables at most once. It's more of an interest's sake thing, to know how frequently one will be able to draft.

    Regarding the button that would automate drafting, that is what really got me interested. If I could have a button that when enabled automatically forced the city to draft at size 6 (or whatever number I entered somewhere) that would be incredibly useful in reducing micro management. At the moment I'm using the civ reminders to remind me at the end of every turn to draft.

    The actual values for S(x), G(x), R(x) etc. are what I use when picking the site for the city and I wouldn't use them once the city is built. Once the city is setup up my only interest is in the automation of the drafting.
     
  16. Wilhelmus

    Wilhelmus Chieftain

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    I have another optimisation suggestion:
    When spiritual, you may spend 5 turns in Nationhood, and then switch back to other civics. During these 5 turns, I'd like to whip consecutively in the GTdraft city, while growing back to original size during the 5 to 10 turns that I'm running other civics.

    My question would be; what is the minumum surplus food at size 5 you need to maintain such a cycle? I will assume that grassland farms are available for population above size 5 (if at size 5 further bonus food resources are still unworked, this city should be GP farm, not GTdraft).

    The 5 turn Nationhood + 5 turn Not cycle for Normal speed.
    The 5 turn Nationhood + 10 turn Not cycle for Epic speed.

    I had this idea, since I'm an Epic player, and at this speed, you will hardly ever find a city that allows for unlimited consecutive drafting, S(X) <= 1.000, however S(X) <= 2.000 or 3.000 are easy to find, and don't qualify as prime GPfarms. So then I asked myself, why run 100% Nationhood for 33% to 50% drafting efficiency?

    While in Nationhood, I also plan to draft in two non GT cities each of the five turns. At Epic speed these have an anger cooldown time of 15 turns, hence the 5 + 10 turn cycle. These cities I want to sustain at the population happiness allows.

    Edit
    Just realize that at epic, you can not only use 5+10 cycles, granting 15 draftees per cycle, but also 6+9, 7+8, 8+7, 9+6, and 10+5 cycles, granting 18, 21, 24, 27, and 30 draftees respectively. This depends on the food surpluss in the GTdraft city, and the number of other cities that can bre drafted from.
     
  17. Crusher1

    Crusher1 King

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    Damnit, LOL! Why always the math?! Seriously, I hate math - it gives me a headache - and I never understand a word you say, seriously - clueless.

    I simply enter WB, put down a city with random amounts of food and put the GT in the city. I then adjust techs accordingly so that I test it in each according era, I.E. drafting Mace compared to muskets, compared to Rifles, Etc.

    I do the same thing with whipping, lol. I suppose what I'm trying to say is all the really matters is the bottom line and what final number works best ^^. It's like using a television set. I have no clue how it works - but I can turn the power on and use it nonetheless.

    I was looking forward to reading the article too! But then all I saw was an alien language =/.
     
  18. PieceOfMind

    PieceOfMind Drill IV Defender Retired Moderator

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    Honestly, once I've done the math and automated it in the form of a spreadsheet, I find it far more time consuming to go and test things out by hand using the world-builder. Since I made these tables they are obviously presented in a way that is natural for me to use them, and maybe not so natural for others, but if you can get used to them it becomes very quick to check how the gtdraft city will go. I usually play Epic speed though so the information in this article is not all that important most of the time.

    I assure you the language of number is a wholely human creation. :p

    And by the way,... "Why always the math?" As a mathematician it's not unusual to find oneself breaking down all sorts of things into number, especially things as cold and logical as a turn-based computer game. Maths might give you a headache... for me it's the maths that keeps me interested. ;)
     
  19. Crusher1

    Crusher1 King

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    I don't know how to read your graph though - it is very confusing to me. Can't you use something that is easy to understand, lol?

    Why not just say something like,

    Optimizing the Globe Theater on normal speed to get 1 unit every turn with regrowth:

    Size 10 city - 19F surplus
    Size 11 city - 20F surplus
    Size 12 city - 21F surplus
    Size 13 city - 22F surplus
    Size 14 city - 23F surplus

    I'm just guessing and have no idea if the numbers are right. The point is I understand that ;) while I have no clue what your graphs are saying ^^.
     
  20. PieceOfMind

    PieceOfMind Drill IV Defender Retired Moderator

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    At Normal speed,

    it's 15 surplus food for a cycle between size 5 and 6.

    For every extra pop point, it's 1 extra food. If you refer to the table, it'll be all the values where you see 1.000.

    The problem is, it's very difficult to get 15 surplus food at size 5-6 so I wanted to show the two dimensions of information so it can be worked out in non-ideal circumstances. If you can't stand doing a bit of math it's probably not worth your time using the table anyway. I might make an addition with some very limited information about how much food you need in ideal cases, but I think this was already covered in the linked article at the top of the thread.
     

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