How fast to expand?

[elmurcis]

Reason why I use 0 and 100% research (and I stick to some 10-90% rate only in mid-late game), is that I can choose what tech I go for.. and complete it in 1 single 100% research run... If check F4 techs info and focus espionage on best techer, its much easier to get better tech trade with this style. Sometimes I even can research something I actually don't need right now, but I see that it could be nice tech to trade against something more useful that somebody already research. And after that you can trade this tech for other techs and also some gold.. and that let run 100% research again for some time...

 

[Bellringer]

Yudishtira

I have zipped my EXCEL spreadsheet and introductory notes into a zip file. Please check if it works. I can then put it in a separate thread for discussion.

 

[Htadus]

I reply to this yesterday agreeing to play forward but seem to have not completed the process. So here goes again.

Htadus

snip

So why is my Gold so much less than yours? Extra gold is from the extra trade routes and the grown cottages.
You get 30 gold from trade routes (14 internal+16 foreign) and I get 4 internal only. Why? I knew from the beginning that GLH would be very beneficial and having access to foreign trade routes would get me a lot of gold. That is the reason for building it.
Game does not allow me to connect to the foreign trade network so how do I do that? The game determines how trade routes are assigned based on size of the city, having a harbor and others. But you need to have a line of site to one of the AI coastal cities that is connected to the AI capital (or the city is the capital) and sailing or a road connected to the AI city to get foreign trade routes.
I have not built villages in my capital and second city as I thought I would specialise my capital for specialists and the second city for production, so that is a big loss also. This capital is a poor specialist city due to lack of any good food sources and it is not a really good Buro capital hammer wise. But it is a decent cottage city and so I did cottage many of its tiles.
How many cottages do you recommend per city? You need to play the map but the early cities definitely need a few cottages. But with a financial leader, you should have a bit more cottages than with other leaders and particularly on river tiles. After about 500 AD and based on the type of victory you are going for, cottages are no longer a good investment.

How do you defend 7 cities against barbarians with only 6 warriors? As someone already said, by using spawn busters. 2 warriors did the entire north and I used 2 more as early warning units in the south. Archers and even axemen appear near various improvements. Yup but with any war resources connected and have access to build units, all you need is the early warning systemYou have 69K soldiers against rival best of 119K so what if they attack?With Monty so close and not giving into his demands I knew he will declare. But I had a plan to limit his threat with caravals. Also at a max, AI will bring 2 galleys worth of units and if I sink both in the water, then no problem. Just need to have a plan.

I wonder if you can play further and show me how you can tackle Monti.

Thanks.

You are welcome.

I did play to 1000 AD.

After finishing Machinary, the tech path was toward Optics. But before that I realized that not using the whip was hurting the game and the cities were growing unhappy. So I traded Monty CoL for Monarchy and gold and switch to slavery and HR and whip up a few infrastructure. I was low on workers and still is. Bad habits die hard.

A several turns after building a few caravals, I saw 2 galleys filled with Jags heading our way. Something tell me it has nothing to do with a goodwill mission. So I demanded the gold he had and declared war on him and sank one of the galleys. By this time I was on my way toward completing Guild and had access to LB's and built one in the southern most city that he will likely attack. The LB killed while defending and the HA killed the remaining Jag. Monty had a city founded on our continent before the war and when it grew to size 2, we captured it and now waiting for the second city he planted to grow to size to so we can capture it.

Mean while the capital built the GLib and the GLH city built the Colosus. So I will not hurry to Astro for a while. English sailors proved the world is round also.

The plan is to go after Monty and Alex once we have MT liberated and the currently built mounted units are upgraded to Cavs with the money from the GM trade mission to one of the large . I know it is an overkill but I like efficient wars. After that may be more of the same.

BTW, this game would have been a long ways ahead had I chopped and whipped from the moment slavery was available.

 

[Shaandore]

50% slider would make 5 and 5 per turn, would it not? How are you getting 40 then? Shouldn't it be 20 ? Likewise with . Am I missing something?

I agree with all of your points, though.



Are you certain about beakers decaying? I was quite convinced that only hammers could decay.

True; sorry, I calculated with 20 base commerce. (That was my first example. Later I mixed it up)

But my point still stands:
With fixed multipliers (and no trades) binary and normal research produce the same output in the long run.

If we add multipliers (usually science, and in the beginning) it is useful to get some money to run through them.

EDIT: Corerctly:
Let's assume that you are building your first library in your capital, which is your only city, and has 10 20 commerce. The library gets built in 2 turns.
50% slider for 4 turns gets you
40 gold and 20 + 20 x 1.25 = 45 beakers
0% for first two turns and then 100% for two turns gets you
40 gold and 40 x 1,25 = 50 beakers

 

[Soirana]

True; sorry, I calculated with 20 base commerce. (That was my first example. Later I mixed it up)

But my point still stands:
With fixed multipliers (and no trades) binary and normal research produce the same output in the long run.

If we add multipliers (usually science, and in the beginning) it is useful to get some money to run through them.

EDIT: Corerctly:
Let's assume that you are building your first library in your capital, which is your only city, and has 10 20 commerce. The library gets built in 2 turns.
50% slider for 4 turns gets you
40 gold and 20 + 20 x 1.25 = 45 beakers
0% for first two turns and then 100% for two turns gets you
40 gold and 40 x 1,25 = 50 beakers

How about using more realistic numbers - about time I get to library it seems way more likely 13 base and 70 or 80% slider...

 

[pepe26]

lol who cares about realistic?! ^^ it just makes it more difficult to make a point comprehensively

 

[RJM]

...
With fixed multipliers (and no trades) binary and normal research produce the same output in the long run.
...

Not true - there is a tiny benefit to binary research. With research at 0% you get 1 anyway so binary research gives you 1 extra for every turn that the slider ist set at zero. That won't win the game for you, but it's nice to have in the early game.

 

[Bellringer]

I am now in the Modern era in my game and after building a few Banks etc. I did switch to the 0 research occasionally when I wanted plenty of gold to promote my military units. I found that the time saved in not building new units could be used to build further improvements in my cities. Even at 0 I was still producing some research from the contributions of Specialists. So I think I have benefited from this technique used appropriately.

 

[Shaandore]

Not true - there is a tiny benefit to binary research. With research at 0% you get 1 anyway so binary research gives you 1 extra for every turn that the slider ist set at zero. That won't win the game for you, but it's nice to have in the early game.

Yes, I intended that more like a rule of thumb. There are also rounding errors, that can be quite serious in the early game, especially pre-BTS.

In the OP's situation (mid-late game) there should be no significant difference if the circumstances are right.

 

[Shaandore]

How about using more realistic numbers - about time I get to library it seems way more likely 13 base and 70 or 80% slider...

You asked for it

13 base commerce. 10 turn interval. 80% science slider. Library ready on turn 2.
10,4 bpt before library
13 bpt after library
2,6 gpt

Total: 26 gold, 124,8 beakers

13 base commerce. 10 turn interval. 0% science slider for 2 turns, then 100% for 8 turns. Library ready on turn 2.

0 bpt before library
13 gpt before library
0 gpt after library
16,25 bpt after library

Total: 26 gold, 130 beakers

Due to rounding errors, depending on the output of your other city/cities, there would most likely be 1 gold or 1 beaker deficit on the first two turns if you are not running binary research. After that both methods are sensitive to rounding errors.

 

[kossin]

But my point still stands:
With fixed multipliers (and no trades) binary and normal research produce the same output in the long run.

There are hidden beaker multipliers which will get truncated (each tech pre-requisite is 20%, each AI knowing tech gives a % - on standard map it's 4%).

Not true - there is a tiny benefit to binary research. With research at 0% you get 1 anyway so binary research gives you 1 extra for every turn that the slider ist set at zero. That won't win the game for you, but it's nice to have in the early game.

You get the free beaker no matter where the slider is.

~~~

When in doubt, run binary research

 

[pepe26]

I am now in the Modern era in my game and after building a few Banks etc. I did switch to the 0 research occasionally when I wanted plenty of gold to promote my military units. I found that the time saved in not building new units could be used to build further improvements in my cities. Even at 0 I was still producing some research from the contributions of Specialists. So I think I have benefited from this technique used appropriately.

dude, thats a problem in itself! banks suck baaalls! only if you go for space and most of the time only in your capitol, a bank makes sense. if you wanna go for wallstreet, you obviously need more but since it comes even later than the much criticized Oxford, its gonna be even worse...

build something else instead... units for war, or at wealth... banks are really not what you wnna go for in less than premium cities (big shrines make an exception, too)

 

[Soirana]

You asked for it

13 base commerce. 10 turn interval. 80% science slider. Library ready on turn 2.
10,4 bpt before library
13 bpt after library
2,6 gpt

Total: 26 gold, 124,8 beakers

13 base commerce. 10 turn interval. 0% science slider for 2 turns, then 100% for 8 turns. Library ready on turn 2.

0 bpt before library
13 gpt before library
0 gpt after library
16,25 bpt after library

Total: 26 gold, 130 beakers

Due to rounding errors, depending on the output of your other city/cities, there would most likely be 1 gold or 1 beaker deficit on the first two turns if you are not running binary research. After that both methods are sensitive to rounding errors.

there is no such thing as 2.6 GPT as far as I know. First part gets only 20 gold.

 

[Shaandore]

there is no such thing as 2.6 GPT as far as I know. First part gets only 20 gold.

It is possible, these numbers are added in the whole empire, and the sum is rounded only after that (at least in BTS). I only calculated the output of the capital. There are most likely other cities, generating non-integer amount of gold.

Eg if you have 1 more city generating 0.4 GPT (quite possible if the city has 2 commerce), then you will get exactly 2.6+0.4=3 GPT. Thus the Capital's output is exactly 2,6 GPT, or 26 gold in 10 turns.

You are right about the fact that you would get only 2 GPT if you have no more cities. In some cases, one might end up losing 0.9 GPT due to rounding errors, if running non-binary research.

But as I said, it all depends on your other cities. I wrote a paragraph about rounding errors. With normal research, you most likely lose ~1 gold/beaker of income every turn. With binary, you might lose at most 1 beaker but only after the library is ready. (In this case, you would lose 0.25 bpt after the library is ready if you have no more libraries in other cities.)

 

[Shaandore]

There are hidden beaker multipliers which will get truncated (each tech pre-requisite is 20%, each AI knowing tech gives a % - on standard map it's 4%).

You would get those multipliers when running non-binary too. So assuming that the AIs knowledge of the tech(s) we research doesn't change in the interval, wouldn't the two outputs be the same?

I understand that under other circumstances, binary is better, since while we accumulate gold, the others might research the tech, giving us better multipliers when we run 100% slider. Again, binary is better because of the way multipliers are added over time.

When in doubt, run binary research

Agreed
I didn't want too make a case for non-binary research. I'm just trying to convince the OP that binary is not worse than normal research under any circumstances. With tech trading on (assuming some tech race) it is clearly superior.

 

[Soirana]

It is possible, these numbers are added in the whole empire, and the sum is rounded only after that (at least in BTS). I only calculated the output of the capital. There are most likely other cities, generating non-integer amount of gold.

Eg if you have 1 more city generating 0.4 GPT (quite possible if the city has 2 commerce), then you will get exactly 2.6+0.4=3 GPT. Thus the Capital's output is exactly 2,6 GPT, or 26 gold in 10 turns.

Since original calculation didn't showed any sort of extra cities....

Well, in there I am from that is called a lie. The more polite point is you and Mr. Belingar are working very hard to bend the numbers in your so called "calculations".

 

[RJM]

There are hidden beaker multipliers which will get truncated (each tech pre-requisite is 20%, each AI knowing tech gives a % - on standard map it's 4%).



You get the free beaker no matter where the slider is.

~~~

When in doubt, run binary research

The OP asked about expansion rate, which is only slightly related to the question of binary research vs break-even research. I am about to open a new thread where I will post a worked example from a real game.

 

[Shaandore]

You asked for it

13 base commerce. 10 turn interval. 80% science slider. Library ready on turn 2.
10,4 bpt before library
13 bpt after library
2,6 gpt

Total: 26 gold, 124,8 beakers

13 base commerce. 10 turn interval. 0% science slider for 2 turns, then 100% for 8 turns. Library ready on turn 2.

0 bpt before library
13 gpt before library
0 gpt after library
16,25 bpt after library

Total: 26 gold, 130 beakers

Due to rounding errors, depending on the output of your other city/cities, there would most likely be 1 gold or 1 beaker deficit on the first two turns if you are not running binary research. After that both methods are sensitive to rounding errors.

Since original calculation didn't showed any sort of extra cities....

Well, in there I am from that is called a lie. The more polite point is you and Mr. Belingar are working very hard to bend the numbers in your so called "calculations".

I'm sorry if you feel like I withheld information, that was not my intention. As a mathematician, my experience tells me that the more mathematics I use, the less people understand what I'm trying to say. That's why I try to show only the relevant details in these calculations. Makes them easier to comprehend/follow for people whose field of expertise is far from mathematics. This of course leads to slight differences compared to in-game numbers. As you see, I tried to address the question of rounding errors (bold text), and I did indicate that there will be differences due to rounding errors, and that they depend on the output of your other cities, I even gave the magnitude of those differences.

After that I agreed that with only 1 city, you are right about the fact that the 2,6 gpt would be rounded down to 2 gpt and we would generate only 20 gold in the interval.

Calling Bellringer and me liars was a rude thing to do, and I will ignore that.

By the way it seems to me that we agree on many things about binary research.

The points I have tried to make in this thread:
- Binary research under most circumstances is better than running fractional slider, and it is always better in the early game
- This is mostly because of tech trades, and partly because the way science multipliers are added during the game
- In mid-late game with no chance for tech trades and fixed multipliers (eg. in tech lead or as absolute last in tech <-thanks, Kossin!) there is no significant difference between running fractional slider and binary research.

Let me know if you disagree with any of the above, or you feel like I overlooked something. That is what Kossin did, and it worked.

The intent of my first posts was to convince Bellringer that in the long run, fractional slider is not better than binary, then the next post was to show an example which is closer to ingame numbers per your request. (If you check the total numbers, you see that binary was the winner.)

It is possible that I didn't express myself clearly enough, in which case I'm sorry, but I hope that in this post I did better

 

[Soirana]

Calling Bellringer and me liars was a rude thing to do, and I will ignore that.

For the record I never calle Bellringer lier.

By the way it seems to me that we agree on many things about binary research.

Let me know if you disagree with any of the above, or you feel like I overlooked something.

I'll give damn simple math sample.

5 city empire 35 raw commerce per turn, 0 gold in bank. At 40% slider breaks even.

Teching writing [so no library] one prerequisite - Animal Husbandry, no city growth planned on next ten turns.

In this ten turn period which approach steady or binary [4 at 100% 6 at zero]wins and by how much?

As for bringing points:
Mine is if you bend numbers enough in complicated matter truth might hide very far away. Very very far away.

p.s. in example above you are isolated. Too save the counting problem naturally.

 

[ben-jammin]

I thought we had along ago determined that the "rounding error" aspect of binary research is virtually nonexistent now that the entire empire is calculated together and you can't actually benefit more than a fraction of a beaker per turn.

Great technique for best taking advantage of new multiplier buildings, though. It works both ways, too. If you're about to get a bank/market (or a number of banks/markets), best to empty your treasury teching and then run the slider at 0% once the building is complete. The biggest efficiency is likely found in the early game leading up to your first GScienists, if you have a strong academy site.