Linear-time GP generation with merchants?

ig2r

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Hi there,

I'd like you to comment on this strategy, since I haven't yet found the time to try it in practice.

Let's suppose we're philosophical, running caste system, and have a city with enough food to run a specialist.
1. Run a merchant in this city.
2. When a great merchant pops, settle him in this city (+6G, +1F).
3. For every two great merchants settled, run an additional merchant specialist off their extra food. Repeat.

Now for the math behind it. For the sake of simplicity, let's assume that we will have popped only GMs, and they have all been settled in our merchant city. Let's further assume that the GP threshold will increase by 100 for each great person, ignoring the +200 change in increase at 1000 GPP.

Let n denote the number of great people we have generated so far. Thus, we will be able to run at least
M(n) := 1 + (n/2)
merchant specialists in the city. Generating the next great person will cost
requiredGPP(n) := 100 * (n + 1)
points, and our merchant specialists will generate
producedGPP(n) := 6 * (1 + n/2)
points per turn.

Now, we can estimate the number of turns it takes to pop the next GM:

rounds(n) = requiredGPP(n) / producedGPP(n) = (100*(n+1)) / (6 * (1 + n/2)) = 100/3 * ((n + 1) / (n + 2)).

As you can see, for an increasing n, the second term ((n + 1) / (n + 2)) will tend to cancel out, leaving us with a near-constant number of turns (roughly 33 turns) to the next GP throughout the game. What's more, even if we assume that roughly one in two generated great persons is not a GM, or is a GM which we don't settle, this linear-time property still holds (although the turn count 'rounds(n)' will differ, obviously). Other effects (threshold increase by 200 GPP past 1000 GPP, being non-PHI, pacifism, golden ages, parthenon, national epic...) will also only impact the turn count, not the underlying model.

So much for the theory anyway. Does this sound feasible in a real game, am I missing something, have I only managed to re-state common knowledge?
 
Welcome to the forums :)

This has certainly been suggested in the past as far back as vanilla (about 2 years ago now :eek: ) I can't remember all the details but some games were posted a long time ago using this idea. It can be a moderately successful economic strategy if you have a good starting city with plenty of food and decent hammers.

The real benefit comes from the gold the settled GMs and the food driven ones generate. That gold allows for the research slider to be raised and indirectly funds research. Obviously it is important to build all the economic buildings and Wall Street in the city to maximise the gold output. Getting the Pyramids for Representation would benefit from the settled GMs and the food ones.

The problems are as the extra food causes the city grows so it needs more happiness and health buildings as well as economic buildings to boost gold and research (from Representation beakers and commerce). A good enemy capital with a shrine and plenty of food and hammers is the ideal site for this strategy.

In BtS this strategy is somewhat superceded by corporations where Sid's Sushi can easily introduce a lot of extra food into all cities in the late game. The chosen city with good original food and settled GMs plus Sushi does not look so different from many other cities with farms (post Biology) and Sushi ... apart from the settled GMs and Wall Street of course ;) ... but its food and population will not be so different.

Several effects limit this strategy. One is the increasing cost of GPPs which you've acknowledged. The other is the amount of food required to grow a large city. At size 10 with a granary it takes 20 food to grow to size 11, at size 40 it takes 50 food to grow to size 41. Large cities often have health problems and that means each extra pop costs 3 food to feed instead of the normal 2. Only in very late in the game when you're researching Future Techs can these health problems be solved for very large cities.
 
^^National Park - Removes :yuck: from population... far earlier than future techs

But the reasoning is good: this strat will have diminuishing returns as the GP are generated....
 
It could solve the health problems.

I had assumed that we would build the NE (for more GPPs) and Wall Street (for more gold) so there wouldn't be room :(
 
Your math is incomprehensible, but did you consider that settled merchants don't generate GPP?

I don't think linear-time GP generation is obtainable.

I agree, I think the maths are flawed. Using your example, you have a +2:food: surplus to begin with to run the initial merchant, during which time the city growth is stagnated. Once the 1st GM is popped and settled, you have only a +1:food: surplus and can't run your second merchant without starving the city. If you could run "half a merchant", then you could get your linear GP progression, but as far as I can see you need to find food from elsewhere.
 
If you could run "half a merchant", then you could get your linear GP progression, but as far as I can see you need to find food from elsewhere.

Why not? You can just run a merchant 1/2 of the time. If you go to the extreme you can swich a citizen between a 2:food: tile (even an unimproved plain grassland will do it) and a merchant every turn.



Nice concept, but I see 2 problems here:
1. The increase in the the GPP costs isn't linear; the slope of your linear regression will incrase after every 10th GM and has a tendency to go to the infinite, which means you can only make a regression line in a finite range.

2. In your estimation you come to about 1 GM/33 turns. This means that in an averge game you will only get about 10 GM who will produce a total of 60 raw :gold:, which isn't that spectacular.
 
I made a simulation. I thought about a GP farm with 15 pop and 7 specialists (3 working food resources 15 food, plus 5 working grassland farms . When I join a merchant, I don't try to grow up the city but take one of the workers of one grassland farm). I made simulation with merchants and priests. For the priests I took into account the Angkor Walt and a Shrine.

Here are the results:
Code:
Great Merchant Simulation (Shrine)

Turn: 5 Great Merchant: 1 Raw Gold/Turn: 21 Raw Gold: 105

Turn: 14 Great Merchant: 2 Raw Gold/Turn: 27 Raw Gold: 354

Turn: 26 Great Merchant: 3 Raw Gold/Turn: 36 Raw Gold: 774

Turn: 42 Great Merchant: 4 Raw Gold/Turn: 42 Raw Gold: 1449

Turn: 62 Great Merchant: 5 Raw Gold/Turn: 48 Raw Gold: 2427

Turn: 84 Great Merchant: 6 Raw Gold/Turn: 54 Raw Gold: 3657

Turn: 109 Great Merchant: 7 Raw Gold/Turn: 63 Raw Gold: 5235

Turn: 136 Great Merchant: 8 Raw Gold/Turn: 72 Raw Gold: 7125

Turn: 167 Great Merchant: 9 Raw Gold/Turn: 78 Raw Gold: 9510

Turn: 199 Great Merchant: 10 Raw Gold/Turn: 84 Raw Gold: 12201



Great Prophet Simulation (Shrine+Angor Walt+1 temple)

Turn: 5 Great Priest: 1 Raw Gold/Turn: 7 Raw Gold: 35 Raw Production 14 Total Production 70

Turn: 13 Great Priest: 2 Raw Gold/Turn: 12 Raw Gold: 131 Raw Production 16 Total Production 198

Turn: 25 Great Priest: 3 Raw Gold/Turn: 17 Raw Gold: 335 Raw Production 18 Total Production 414

Turn: 42 Great Priest: 4 Raw Gold/Turn: 22 Raw Gold: 709 Raw Production 20 Total Production 754

Turn: 63 Great Priest: 5 Raw Gold/Turn: 27 Raw Gold: 1276 Raw Production 22 Total Production 1216

Turn: 88 Great Priest: 6 Raw Gold/Turn: 32 Raw Gold: 2076 Raw Production 24 Total Production 1816

Turn: 117 Great Priest: 7 Raw Gold/Turn: 37 Raw Gold: 3149 Raw Production 26 Total Production 2570

Turn: 150 Great Priest: 8 Raw Gold/Turn: 42 Raw Gold: 4535 Raw Production 28 Total Production 3494

Turn: 188 Great Priest: 9 Raw Gold/Turn: 47 Raw Gold: 6321 Raw Production 30 Total Production 4634



Great Merchant Simulation (Shrine) - Philo or Pacisfism

Turn: 3 Great Merchant: 1 Raw Gold/Turn: 21 Raw Gold: 63

Turn: 7 Great Merchant: 2 Raw Gold/Turn: 30 Raw Gold: 174

Turn: 14 Great Merchant: 3 Raw Gold/Turn: 36 Raw Gold: 417

Turn: 22 Great Merchant: 4 Raw Gold/Turn: 42 Raw Gold: 756

Turn: 32 Great Merchant: 5 Raw Gold/Turn: 51 Raw Gold: 1245

Turn: 43 Great Merchant: 6 Raw Gold/Turn: 57 Raw Gold: 1860

Turn: 56 Great Merchant: 7 Raw Gold/Turn: 63 Raw Gold: 2679

Turn: 70 Great Merchant: 8 Raw Gold/Turn: 72 Raw Gold: 3660

Turn: 85 Great Merchant: 9 Raw Gold/Turn: 75 Raw Gold: 4812

Turn: 101 Great Merchant: 10 Raw Gold/Turn: 84 Raw Gold: 6159

Turn: 121 Great Merchant: 11 Raw Gold/Turn: 90 Raw Gold: 7977

Turn: 142 Great Merchant: 12 Raw Gold/Turn: 99 Raw Gold: 10035

Turn: 166 Great Merchant: 13 Raw Gold/Turn: 105 Raw Gold: 12558

Turn: 192 Great Merchant: 14 Raw Gold/Turn: 111 Raw Gold: 15468



Great Prophet Simulation (Shrine+Angor Walt+1 temple) - Philo or Pacifism

Turn: 3 Great Priest: 1 Raw Gold/Turn: 7 Raw Gold: 21 Raw Production 14 Total Production 42

Turn: 7 Great Priest: 2 Raw Gold/Turn: 12 Raw Gold: 69 Raw Production 16 Total Production 106

Turn: 13 Great Priest: 3 Raw Gold/Turn: 17 Raw Gold: 171 Raw Production 18 Total Production 214

Turn: 21 Great Priest: 4 Raw Gold/Turn: 22 Raw Gold: 347 Raw Production 20 Total Production 374

Turn: 32 Great Priest: 5 Raw Gold/Turn: 27 Raw Gold: 644 Raw Production 22 Total Production 616

Turn: 44 Great Priest: 6 Raw Gold/Turn: 32 Raw Gold: 1028 Raw Production 24 Total Production 904

Turn: 59 Great Priest: 7 Raw Gold/Turn: 37 Raw Gold: 1583 Raw Production 26 Total Production 1294

Turn: 75 Great Priest: 8 Raw Gold/Turn: 42 Raw Gold: 2255 Raw Production 28 Total Production 1742

Turn: 94 Great Priest: 9 Raw Gold/Turn: 47 Raw Gold: 3148 Raw Production 30 Total Production 2312

Turn: 115 Great Priest: 10 Raw Gold/Turn: 52 Raw Gold: 4240 Raw Production 32 Total Production 2984

Turn: 140 Great Priest: 11 Raw Gold/Turn: 57 Raw Gold: 5665 Raw Production 34 Total Production 3834

Turn: 169 Great Priest: 12 Raw Gold/Turn: 62 Raw Gold: 7463 Raw Production 36 Total Production 4878



Great Merchant Simulation (Shrine) - Philo + Pacisfism

Turn: 2 Great Merchant: 1 Raw Gold/Turn: 21 Raw Gold: 42

Turn: 5 Great Merchant: 2 Raw Gold/Turn: 27 Raw Gold: 123

Turn: 9 Great Merchant: 3 Raw Gold/Turn: 36 Raw Gold: 264

Turn: 15 Great Merchant: 4 Raw Gold/Turn: 42 Raw Gold: 516

Turn: 21 Great Merchant: 5 Raw Gold/Turn: 48 Raw Gold: 810

Turn: 29 Great Merchant: 6 Raw Gold/Turn: 57 Raw Gold: 1257

Turn: 38 Great Merchant: 7 Raw Gold/Turn: 63 Raw Gold: 1827

Turn: 47 Great Merchant: 8 Raw Gold/Turn: 69 Raw Gold: 2454

Turn: 57 Great Merchant: 9 Raw Gold/Turn: 78 Raw Gold: 3225

Turn: 68 Great Merchant: 10 Raw Gold/Turn: 84 Raw Gold: 4149

Turn: 81 Great Merchant: 11 Raw Gold/Turn: 90 Raw Gold: 5331

Turn: 96 Great Merchant: 12 Raw Gold/Turn: 99 Raw Gold: 6801

Turn: 111 Great Merchant: 13 Raw Gold/Turn: 105 Raw Gold: 8379

Turn: 129 Great Merchant: 14 Raw Gold/Turn: 111 Raw Gold: 10392

Turn: 148 Great Merchant: 15 Raw Gold/Turn: 120 Raw Gold: 12654

Turn: 168 Great Merchant: 16 Raw Gold/Turn: 126 Raw Gold: 15174

Turn: 189 Great Merchant: 17 Raw Gold/Turn: 132 Raw Gold: 17967



Great Prophet Simulation (Shrine+Angor Walt+1 temple) - Philo + Pacifism

Turn: 2 Great Priest: 1 Raw Gold/Turn: 7 Raw Gold: 14 Raw Production 14 Total Production 28

Turn: 5 Great Priest: 2 Raw Gold/Turn: 12 Raw Gold: 50 Raw Production 16 Total Production 76

Turn: 9 Great Priest: 3 Raw Gold/Turn: 17 Raw Gold: 118 Raw Production 18 Total Production 148

Turn: 14 Great Priest: 4 Raw Gold/Turn: 22 Raw Gold: 228 Raw Production 20 Total Production 248

Turn: 21 Great Priest: 5 Raw Gold/Turn: 27 Raw Gold: 417 Raw Production 22 Total Production 402

Turn: 30 Great Priest: 6 Raw Gold/Turn: 32 Raw Gold: 705 Raw Production 24 Total Production 618

Turn: 39 Great Priest: 7 Raw Gold/Turn: 37 Raw Gold: 1038 Raw Production 26 Total Production 852

Turn: 50 Great Priest: 8 Raw Gold/Turn: 42 Raw Gold: 1500 Raw Production 28 Total Production 1160

Turn: 63 Great Priest: 9 Raw Gold/Turn: 47 Raw Gold: 2111 Raw Production 30 Total Production 1550

Turn: 77 Great Priest: 10 Raw Gold/Turn: 52 Raw Gold: 2839 Raw Production 32 Total Production 1998

Turn: 94 Great Priest: 11 Raw Gold/Turn: 57 Raw Gold: 3808 Raw Production 34 Total Production 2576

Turn: 113 Great Priest: 12 Raw Gold/Turn: 62 Raw Gold: 4986 Raw Production 36 Total Production 3260

Turn: 135 Great Priest: 13 Raw Gold/Turn: 67 Raw Gold: 6460 Raw Production 38 Total Production 4096

Turn: 160 Great Priest: 14 Raw Gold/Turn: 72 Raw Gold: 8260 Raw Production 40 Total Production 5096

Turn: 188 Great Priest: 15 Raw Gold/Turn: 77 Raw Gold: 10416 Raw Production 42 Total Production 6272

If you are running Representation, the specialists give you beakers. With the production of the priests, you can build a market, grocer, bank, wall street, library, university and observatory fast. I'm not taking this into account. The gold/production is just from specialists, the shrine should give you gold as well.

I'm adding the code, of course I did it quite fast ;):
Code:
/*
 * Main.java
 *
 * Created on 16 de Maio de 2008, 13:42
 *
 * To change this template, choose Tools | Template Manager
 * and open the template in the editor.
 */

package greatpeople;

/**
 *
 * @author AnitaGaribaldi
 */
public class Main {
    
    /** Creates a new instance of Main */
    public Main() {
    }
    
    /**
     * @param args the command line arguments
     */
    public static void main(String[] args) {
        
        System.out.println("");
        System.out.println("Great Merchant Simulation (Shrine)");
        merchant_simulation (1); 
        
        System.out.println("");
        System.out.println("Great Prophet Simulation (Shrine+Angor Walt+1 temple)");
        priest_simulation (1);
        
        
        System.out.println("");
        System.out.println("Great Merchant Simulation (Shrine) - Philo or Pacisfism");
        merchant_simulation (2); 
        
        System.out.println("");
        System.out.println("Great Prophet Simulation (Shrine+Angor Walt+1 temple) - Philo or Pacifism");
        priest_simulation (2);
        
        
        System.out.println("");
        System.out.println("Great Merchant Simulation (Shrine) - Philo + Pacisfism");
        merchant_simulation (3); 
        
        System.out.println("");
        System.out.println("Great Prophet Simulation (Shrine+Angor Walt+1 temple) - Philo + Pacifism");
        priest_simulation (3);        
    }
    
    // mult_gpp - gpp multiplier
    static void merchant_simulation (int mult_gpp) {
                int merc = 7; //merchant
        int priest = 7; //prophet
        int gm = 0; //grea merchant
        int gp = 0; //great prophet
        int gpp = 0;
        int gold = 0;
        int tot_gold = 0;
        int extra_food = 0;
        int tot_food = 0;
        int next_gp = 100;
        int raw_prod = 0;
        int tot_prod = 0;
        
        
        
        for (int i=0; i < 200; i++) {
            /* check if we have a new great merchant */
            if (gpp >= next_gp ) {
                gm ++; extra_food ++;
                gpp -= next_gp;
                if (next_gp < 1000) next_gp += 100;
                else next_gp += 200;
                if (extra_food == 3) {
                    merc++; extra_food = 0;
                }
                System.out.println("Turn: "+i+" Great Merchant: "+gm+
                        " Raw Gold/Turn: "+gold+" Raw Gold: "+tot_gold);
            }
            gold = gm * 6 + merc * 3;
            gpp += (merc * 3 + 1) * mult_gpp;
            /* check if we can run one merchant for one turn*/
            if (tot_food >= 3) {
                gold += 3;
                gpp += 3;
                tot_food -= 3;
            }
            tot_food += extra_food;
            tot_gold += gold;
        }
    }

   // gpp multiplier
    static void priest_simulation (int mult_gpp) {
        int priest = 7; //priest
         int gp = 0; //great prophet
        int gpp = 0;
        int gold = 0;
        int tot_gold = 0;
        int extra_food = 0;
        int tot_food = 0;
        int next_gp = 100;
        int raw_prod = 0;
        int tot_prod = 0;
        
        
       

               
        for (int i=0; i < 200; i++) {
            /* check if we have a new great merchant */
            if (gpp >= next_gp ) {
                gp ++;
                gpp -= next_gp;
                if (next_gp < 1000) next_gp += 100;
                else next_gp += 200;
                System.out.println("Turn: "+i+" Great Priest: "+gp+
                        " Raw Gold/Turn: "+gold+" Raw Gold: "+tot_gold+
                        " Raw Production " + raw_prod + " Total Production " + tot_prod);
            }
            gold = gp * 5 + priest * 1;
            tot_gold += gold;
            raw_prod = (priest + gp) * 2;
            tot_prod += raw_prod;
            gpp += (priest * 3 + 3)*mult_gpp; //Angor Walt + Shrine            
        }        
    }
}
 
LOL I was just thinking about this yesterday. :crazyeye:

I was wondering if a settled GM strategy could allow you to run 100% sci. (thinking of using Fredrick as Org would help with this.). The problem I ran into is it would be too successful. As already pointed out your city would start growing too big by the end game as well as diminishing returns of settling the GM. However I did come up with a very weird halfway strategy.

The city obviously gets Wall street, but I couldn't decide on which other NW to build. I thought it must be ether the NE, Globe, or Park. But none of these seemed to fix all the problems that come late game. then I figured it out, Iron Works!

Aim to settle 12-18 GM in the city. Run as many merchants as you can. Build a sister GP farm with the NE that also runs GM and run Pacifism so both will produce but settle all of the GM in the main city. Once you reach endgame Workshop over the whole city. Aim to be able to workshop every square plus run all Engineers. For Germany with the UB thats a pop of 28. My city had around 400 production non-goldage! Obsoletes mega production city will still be a bit better but the best part is the city is an economic city until you need a mega production center at end game for Space race or Domination.

After you have produced about 12 or so GM keep the first city running Merchants to take advantage of wall street. Switch the second over to Eng/prophets/sci whatever else you want. You could also aim for some GP for a could golden ages in the endgame. GProphets are good to settle in the city after the merchants.

The best way to start up this strategy would be Orical->CoL. First GP is a prophet for the shrine then run a scientist to pop Philosophy. Switch to pacifism and start the GM Production! The fun part is the watch the endgame total city conversion. :)
 
Why not? You can just run a merchant 1/2 of the time. If you go to the extreme you can swich a citizen between a 2:food: tile (even an unimproved plain grassland will do it) and a merchant every turn.

Haha, that's true, I've done similar things before, usually when I'm trying to avoid growth in the late game I sometimes starve the city every few turns by running an extra specialist. In this sense, you're right, you can get a pseudo-linear progression this way, albeit a painfully slow one (without NE, Parthenon etc). It still seems very unpractical to pull off though; besides the need to MM every turn, the city will not grow naturally and this to me is the real killer -- the city would simply not be performing to its potential and I'd bet I could do more with it than run a merchant every other turn. Seems like a wasted GM as well :crazyeye:. I'll take a traditional GP farm any day, thanks. Interesting idea though :P
 
LOL I was just thinking about this yesterday. :crazyeye:

I was wondering if a settled GM strategy could allow you to run 100% sci. (thinking of using Fredrick as Org would help with this.). The problem I ran into is it would be too successful. As already pointed out your city would start growing too big by the end game as well as diminishing returns of settling the GM. However I did come up with a very weird halfway strategy.

The city obviously gets Wall street, but I couldn't decide on which other NW to build. I thought it must be ether the NE, Globe, or Park. But none of these seemed to fix all the problems that come late game. then I figured it out, Iron Works!

Aim to settle 12-18 GM in the city. Run as many merchants as you can. Build a sister GP farm with the NE that also runs GM and run Pacifism so both will produce but settle all of the GM in the main city. Once you reach endgame Workshop over the whole city. Aim to be able to workshop every square plus run all Engineers. For Germany with the UB thats a pop of 28. My city had around 400 production non-goldage! Obsoletes mega production city will still be a bit better but the best part is the city is an economic city until you need a mega production center at end game for Space race or Domination.

After you have produced about 12 or so GM keep the first city running Merchants to take advantage of wall street. Switch the second over to Eng/prophets/sci whatever else you want. You could also aim for some GP for a could golden ages in the endgame. GProphets are good to settle in the city after the merchants.

The best way to start up this strategy would be Orical->CoL. First GP is a prophet for the shrine then run a scientist to pop Philosophy. Switch to pacifism and start the GM Production! The fun part is the watch the endgame total city conversion. :)

I think it's better to start with Prophets, Merchants later. By the time you research Philosophy there will be soon a lot of good buildings/wonders to build. Why should we wait until the end of game for a production/gold city? If you are running philosophy a religious path is OK. Your shrine/Angkor Wat city will have good production because of the priests/great prophet settled. You can compensate the lost of gpp from specialists with Wonders: University of Sankor, Spiral Miranet and SoL. Wonders don't get unhappy or unhealthy. Soon there will be buildings: grocer, bank and university. I guess Ramses or Gandhi goes well with this. Cheap powerful temples nationwide.
 
Just one remark: GPP points required per new Great person is essentially quadratic in the number of previous great people (it only looks linear for the first few persons). Hence linear number of GPP generated/ quadratic number of GPP necessary gives a 1/ the number of GP's before number of turns before the next GP.

Still, I once used this method to get a 50+ city in vanilla (with something like 25 settled great persons).
 
I agree a prophet/wonder city is powerful. This is along Obsoletes style. THe mega production allows you to grab a lot of wonders which really boosts your economy/denies the computer. However that stratagy is suited to spiritual/industrious leaders more (Ramses is an excellent choice).

Here however I was looking for something different. As I said the original goal was to run a 100% sci economy, regular merchants produce 3x as much gold as prophets. The benefits of this is your library's/etc make full use. Your commerce city's will produce more net science (or at least in theory). Otherwise you will need both sci and gold modifying buildings in every commerce city to get the same benefit. With this plan you would have philosophy well before the AD's anyway. I agree though it would mean you need to found a solid production city to compensate for the loss of a production heavy capital.

Also I don't hold this to be a top/max optimum stratagy, just an interesting one that does work.
 
I can run 100% sci with priests/great prophets too. A priest with Angkor Wat is a engineer that gives you gold. A settled great prophet gives you 5 gold, a great merchant 6, but with the high production you can get the buildings that increases gold much faster and this increases your gold. Just look at
this thread. I have only a problem when I do this with my capital, I don't know what national wonder to build.
 
I didnt read your math, I just finished finals my head might explode if I have to think in the next two months, but I get the basic principle.

I've been experimenting with a number of different leaders lately, trying to get a better feel for the game in preparation for leaving Immortal and moving up to Diety, so Ill give this strategy a go.

Typically, I like to whore scientists (the idea of building a market in a gp farm just makes me cringe). Now obviously early in the game, this merchant strategy will be somewhat useless, IE, the first 4 or so great people (with philisophical) really cant be much else asides from scientists / priests (unless you build some wonders or something).

Regardless, I see some problems entering the arena, first, with that much gold you probably wont need many banks, meaning you wont actually end up ever building a wall street... unless you want to build a lot of banks in cities which are running at 100 percent research, which kinda makes this strategy bad in my book.

Second, with representation, merchants will give science as well as gold, so you really need universities + libraries to make those gp farms as effective as scientists, further waste of hammers.

Those are just some inefficiencies I see, but Im going to give it a go today and see what I can do. I think Ill try as Peter of Russia, Expansive + philisophical (both traits should help in this strat), and regen map until I get a nice freshwater gp farm on the coast for my capitol. Harbor with freshwater and expansive means with any luck Ill have 20+ health very early.
 
As qwertz pointed out the initial generation rate is rather slow even if it does give roughly linear time growth for the first 10. However the "linear time" really breaks down if you consider just one real-game condition. We're trying to do nothing but generate endless GM's but start with only one merchant? If you were going to pick a city to be this GP farm it seems reasonable to assume we'd pick the highest food site available and on any normal map a site that can support at least 4 specialists should be findable. Then the GPP generator goes as (n=number of GM's already born and merged) 4 + n/2 instead of 1 + n/2 which ends the linear time relation (of course in flat # of turns they will come out way faster). Going from n=0 to n=8 doubles the GP generation rate while the cost of the GP has increased ninefold. Now if the cost only ever incremented by 100 the generation rate would eventually still converge to a linear slope but not until a huge number have been generated (and the game probably over).
 
I've played a few games with this kind of economy. It works well. I'd say it's the optimal teching method for any leader that is Financial but isn't looking to build many wonders (with wonders+Financial it's better to use priests and prophets, IMO).

That said, I don't see reason for all that math... Just run as many merchants as you can. 100% science slider isn't that hard with this tactic.
 
Let's suppose we're philosophical, running caste system, and have a city with enough food to run a specialist.
1. Run a merchant in this city.
2. When a great merchant pops, settle him in this city (+6G, +1F).
3. For every two great merchants settled, run an additional merchant specialist off their extra food. Repeat.

I think you've missed one important point...

Every time you want to run a new Merchant specialist, it will require not only extra Food, but also extra Population. If you don't have the extra Population, then it means you would have to take one worked tile away in order to activate the Merchant.

Some reasons for not having the extra Population would be:

1) There's not enough time to grow the city to gain the extra Population.

2) You want to use the extra Population as fuel for whipping.

3) Your Happiness cap is not high enough.


Assuming you try to meet the extra population requirement (and do meet it), there's still a tradeoff between working an extra tile vs. an extra Merchant, or vs. an extra non-Merchant specialist. So the issue of which type of extra specialist to run still must be considered.


If you assume that your city is in a Stagnant food supply state while running the single Merchant specialist, then in order to grow the city to 1 pop higher you would first need to use the surplus food from your new Great Merchants to help grow the city. Only after the city has grown to 1 pop higher, does the extra Merchant specialist become available without sacrificing something else.
 
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