Any Songhai fans yet?

[Thyrwyn]

I have to agree with others that say that their UB is awesome (experimenting with Songhai now). Basically, every city can build a mini-Stonehenge? Sign me up! +5 Culture, no maintenance, 2 artist slots. . . What's not to like. The UB alone can be used to leverage so many different strategies - it is especially handy for picking up the late game Social Policy trees, since you have to wait until Philosophy. The UB alone, more than negates the +30% increase that each city adds to Policy costs.

And extra gold. . . .

 

[Udey1]

I have to agree with others that say that their UB is The UB alone, more than negates the +30% increase that each city adds to Policy costs.

And extra gold. . . .

5+5+5+5... > (new culturecostbase) *(.3)(num cities) I'm not sure that's always true or even mostly.
But nevertheless. it is a good UB.

 

[vontos]

I just tried Songhai out for the first time and easily won a cultural victory in 1888. King difficulty, standard map and speed, on a continents map. I had been having trouble winning on king before this game but won easily. I could have gotten a domination victory much sooner but had already put the time into cultural and wanted to finish it out, haha. Science or diplomatic would not have been difficult either.

 

[Paeanblack]

5+5+5+5... > (new culturecostbase) *(.3)(num cities) I'm not sure that's always true or even mostly.

n = number of cities
c = cost for the next policy.

(5 * n) versus (c + 0.3 * c * (n - 1))

that is the same as:

(50) versus (c * (7/n + 3) )

The key factor is (7/n + 3). This starts at 10 and drops quickly to a value between 3 and 4. This means that as long as your cities are producing the same culture, more cities will give you policies faster. However, the first few cities provide the biggest improvement to getting policies more quickly. Your second city boosts your policy generation speed by 54%. Your 7th city boosts it by 4%.

However, your cities don't all produce the same culture. To simplify things, let's assume the capital produces some static amount of extra culture. This is palace + wonders + CS allies, etc.

b = capital bonus

b + (5 * n) versus (c + 0.3 * c * (n - 1))

or

(10 * b/n + 50) versus (c * (7/n + 3) )

Now you also need to take into account the (10 * b/n) factor. This also drops with every city you add, but unfortunately, it does not bottom out like the (7/n + 3) factor. Every city you add is cutting this bonus down. The effect this has on your policy generation speed depends on how big the static bonus is compared to the per-city generation. If you've just built a few wonders, getting that chopped down is not a big deal...the (7/n+3) factor will outweigh it. If you've built Stonehenge, allied with all the Cultural CSs, and are running Artists in your capital, then adding the second and third city will hurt.

The way puppets factor in is by increasing b slowly over time. This will mitigate increases in n.

In a nutshell:

--If you have ignored extra culture sources, then adding more cities (settlements/annexes) will speed up your policy generation as long as you build the basic monument/temple in each one. At ~10 cities, you've tripled the rate you get policies, but additional cities after that have negligible effect. The first few contribute the bulk of the speed-up.

--If you have built a couple wonders, or just Stonehenge, or allied with a cultural state, then additional cities, even the first few, will have little effect on your policy generation.

--If you have really pushed hard for early culture generation, then the first few additional cities will hurt your policy generation speed.


Some timing issues come into play...try to settle/annex right after getting a policy instead of right before, but apart from that, extra cities don't really have much impact on social policies as long as each new one gets the basic culture buildings and you aren't pursuing an extremely high or low culture strategy.

The 30% penalty may look scary and shy people away from expansion, but it is actually really balanced.

 

[Guardian_PL]

Its clear that this game is going to be based around gimmicky slingshots. Can anyone think of good ones for the Songhai? Barbarian farming can give a good gold income for fast building (library for Scientist specialists) or for paying off city states. Mosques give a lot of flexibility for picking up a few midgame social policies. What would good targets be? Chivalry for Mandekalu cav? Steel for longswords?

On my previous Emperor game I mopped my entire continent with standard Horsemen (like 4 of them), no need for slingshots when AI is so lame

 

[Vordeo]

I just tried starting a quick game as the Songhai, and this looks like a very good civ. Early game, so the only thing I've really seen is the extra gold from the UA, and that is massive. The UBs are very good for culture (and free!), and the UUs look like monsters. Think this'll be one of my favourite civs this game!

 

[Udey1]

n = number of cities
c = cost for the next policy.

(5 * n) versus (c + 0.3 * c * (n - 1))

that is the same as:

(50) versus (c * (7/n + 3) )

The key factor is (7/n + 3). This starts at 10 and drops quickly to a value between 3 and 4. This means that as long as your cities are producing the same culture, more cities will give you policies faster. However, the first few cities provide the biggest improvement to getting policies more quickly. Your second city boosts your policy generation speed by 54%. Your 7th city boosts it by 4%.

However, your cities don't all produce the same culture. To simplify things, let's assume the capital produces some static amount of extra culture. This is palace + wonders + CS allies, etc.

b = capital bonus

b + (5 * n) versus (c + 0.3 * c * (n - 1))

or

(10 * b/n + 50) versus (c * (7/n + 3) )

Now you also need to take into account the (10 * b/n) factor. This also drops with every city you add, but unfortunately, it does not bottom out like the (7/n + 3) factor. Every city you add is cutting this bonus down. The effect this has on your policy generation speed depends on how big the static bonus is compared to the per-city generation. If you've just built a few wonders, getting that chopped down is not a big deal...the (7/n+3) factor will outweigh it. If you've built Stonehenge, allied with all the Cultural CSs, and are running Artists in your capital, then adding the second and third city will hurt.

The way puppets factor in is by increasing b slowly over time. This will mitigate increases in n.

In a nutshell:

--If you have ignored extra culture sources, then adding more cities (settlements/annexes) will speed up your policy generation as long as you build the basic monument/temple in each one. At ~10 cities, you've tripled the rate you get policies, but additional cities after that have negligible effect. The first few contribute the bulk of the speed-up.

--If you have built a couple wonders, or just Stonehenge, or allied with a cultural state, then additional cities, even the first few, will have little effect on your policy generation.

--If you have really pushed hard for early culture generation, then the first few additional cities will hurt your policy generation speed.


Some timing issues come into play...try to settle/annex right after getting a policy instead of right before, but apart from that, extra cities don't really have much impact on social policies as long as each new one gets the basic culture buildings and you aren't pursuing an extremely high or low culture strategy.

The 30% penalty may look scary and shy people away from expansion, but it is actually really balanced.

heh- my post was sarcastic. Despite all this math I think I had it right the first time. It would be totally true but you forgot that each policy costs more than the last one. Since that also gets multiplied in the .3 is much larger than linear growth of +5 after a short time. Thus the UB bonus does not in fact weigh in a positive direction vs the founding of a new city (except for the first couple policies early game- which is why i said its only partly true)

 

[Show]

Regarding the deity/high difficulty stuff. I play pretty much only Greece on deity but you have to understand that CC/horsemen rush, and any early game strategy for that matter(sling-shots and what not) are just openers like in chess it makes sure oyu don't screw up on the first 100 turns or so, maybe you have other projects after the rush and another civ may be better suit for this project, it maybe not be the best for the opener you chose but it will compensate later on. For example the riflery slingshot is viable and can be put to great use by other civs(such as greece as a followup), not only babylon, it just needs to be adapted.

Askia can without a doubt make use of an horseman rush, especially with all the extra gold from barbs and pillaging, it might be a bit harder, but Askia has it's own UU later one and can keep making a lot of gold throughout the entire game, which can take aprt in later strategies.

 

[Paeanblack]

heh- my post was sarcastic. Despite all this math I think I had it right the first time. It would be totally true but you forgot that each policy costs more than the last one.

No, the whole point is that the increasing policy costs are irrelevant.

The question at hand is "will adding another city help me get the next policy faster, or will it take longer", with the assumption that each new settlement/annex produces ~5 culture.

The equation to answer that is:

( (c * (7/n + 3) ) / (c * (7/(n+1) + 3) ) * ( (b/(n+1) + 5) / (b/n + 5) )

The c factor drops out of the equation. I suppose I should have actually spelled that out; since it's not necessarily obvious.

 

[alpaca]

As a rule of thumb (Paeanblack: I understand the maths but not everyone likes math ), additional cities will slow your policy speed after the first three cities or so are in place. For a large number of cities, what determines your policy speed is roughly your average amount of culture per city. Since the average will always go down when you found a new city due to culture from wonders or cultured city states not scaling with the number of cities, you will get a lower policy speed by getting more cities.

What the Songhai building does for me, then, is increasing the average culture per city from something like 4-5 (I rarely even build a temple in most cities) to something like 8-9, almost twice as much.

 

[duxup]

My first game was the Songhai. I kept thinking "Man you really don't have to worry much about this culture thing in Civ V, this is crazy." Then I played as another Civ and realized how spoiled I was.

 

[Paeanblack]

As a rule of thumb (Paeanblack: I understand the maths but not everyone likes math ), additional cities will slow your policy speed after the first three cities or so are in place. For a large number of cities, what determines your policy speed is roughly your average amount of culture per city.

OK, perhaps trying without math would help. What the math shows is that many of the "intuitive" suppositions are not correct. Your "rule of thumb" is just not true.

The question everyone wants answered is "Will making another city slow down or speed up the time it takes to get the next policy?"

Much of the intuition revolves around statements like "it depends on the current policy cost", or "it depends on how much culture per turn your expansion cities make". When doing the math, these factors are irrelevant. They appear in both the numerator and denominator and cancel out. They have no effect on the answer.

There are only three variables that survive:

- Current number of cities
- The culture that your standard expansion cities generate.
- The bonus culture produced by things that don't occur in every city (palace, wonders, CS allies, etc)

The equations can be further simplified to only two variables

- Current number of cities
- The ratio between bonus culture and per-city culture

I realize this is highly non-intuitive, but it just doesn't matter if your "average amount of culture per new city" is 2 or 17 or 550. Sure, it determines whether your polices come quickly or slowly, but it doesn't matter when asking if those policies will come /more/ quickly or /more/ slowly if you expand.

 

[alpaca]

OK, perhaps trying without math would help. What the math shows is that many of the "intuitive" suppositions are not correct. Your "rule of thumb" is just not true.

The question everyone wants answered is "Will making another city slow down or speed up the time it takes to get the next policy?"

Much of the intuition revolves around statements like "it depends on the current policy cost", or "it depends on how much culture per turn your expansion cities make". When doing the math, these factors are irrelevant. They appear in both the numerator and denominator and cancel out. They have no effect on the answer.

There are only three variables that survive:

- Current number of cities
- The culture that your standard expansion cities generate.
- The bonus culture produced by things that don't occur in every city (palace, wonders, CS allies, etc)

The equations can be further simplified to only two variables

- Current number of cities
- The ratio between bonus culture and per-city culture

I realize this is highly non-intuitive, but it just doesn't matter if your "average amount of culture per new city" is 2 or 17 or 550. Sure, it determines whether your polices come quickly or slowly, but it doesn't matter when asking if those policies will come /more/ quickly or /more/ slowly if you expand.

You have to consider the non-equilibrium case, however. Your assumption of each city having the same culture doesn't make too much sense to me. But you're right, under your assumptions the question of whether expansion will increase your policies per turn only depends on the ratio of base culture over culture per city.

Let's talk about mathematics again, just between us

Spoiler :

y is the average amount of culture per city, the rest is like in your example. As an equation for when you get your next policy you have

(1 + 0.3(n-1))*p = y*n*k

We can solve that for k and get k = p/y * (0.7/n + 0.3). Assuming a large number of cities the 0.7/n term vanishes and you're left with 0.3 p/y, so the average amount of culture is the only relevant factor in determining the speed of getting new policies.

The average culture then can be calculated from y = b/n + c, again like in your example .

k = p(0.7 + 0.3n)/(b + cn) = p/3c *(7/3 + n)/(b/c + n)

This function is monotonously increasing if b/c > 7/3 but monotonously decreasing if b/c < 7/3, which means that if the amount of culture you get from city states and wonders is greater than twice the average culture of your cities, expanding will slow your policy growth. If it's lower, it will always increase it.

I can do the same analysis with my equation by assuming that going from n to n+1 your average culture per city drops. This drop basically depends on b/c so we're essentially saying the same thing.

Since b/c is usually pretty large if you have at least one city state, expanding isn't a good idea from this vantage point. Increasing c does make expanding better policy-wise so it does depend on the average amount of culture per city, which is proportional to c.

 

[Paeanblack]

You have to consider the non-equilibrium case, however. Your assumption of each city having the same culture doesn't make too much sense to me. But you're right, under your assumptions the question of whether expansion will increase your policies per turn only depends on the ratio of base culture over culture per city.

...

I can do the same analysis with my equation by assuming that going from n to n+1 your average culture per city drops. This drop basically depends on b/c so we're essentially saying the same thing.

Yeah, we seem to be on the same path.

For everyone else following along, alpaca and I used 'c' for different things. I used it for the cost of the next policy, alpaca used it for average expansion city culture.

We seem to be in agreement on the two key variables:

n - number of cities
r - ratio between bonus culture and typical city culture. You called this b/c, I called it b/5 (since this thoroughly hijacked thread was about Songhai)

I'm using "typical city culture" instead of "average city culture", since I don't mean total culture divided by number of cities. I mean the typical culture a new city will be producing.

I am under the impression that many players are likely to build a monument as the first build in a newly settled city, possibly followed by a temple. (Songhai probably goes straight for the temple)

So, at any given tech level, the amount of per-city culture from buildings that you generally build immediately in a new city goes into the denominator of r. (France's +2 bonus gets included here)

The sum total of every other culture source gets added up and put into the numerator: wonders, landmarks, artists, allies, buildings you don't/can't/won't soon build in your expansion cities, etc. Things like monuments/temples/etc in your capital that you do build everywhere do not count in the numerator. If you are going to rush a temple and run an artist in your expansion city, then either don't count an artist in your capital or subtract that from the numerator of r.

As you said, if r > 7/3 then expansion slows down policies. If r < 7/3, it speeds things up.

The question now, is what is the realistic value of r in various scenarios, across various strategies, and at various points in time?

 

[Show]

n = number of cities
c = cost for the next policy.

(5 * n) versus (c + 0.3 * c * (n - 1))

that is the same as:

(50) versus (c * (7/n + 3) )

Umm, no ? (c + 0.3 * c * (n - 1)) = (c * (7/n + 3) ) is only true for n= -2.33 or 10

In this case (5 * n) versus (c + 0.3 * c * (n - 1))

is the same as

(50) versus (c * (7/10 + 3) )

Following your logic I could say it's the same as (50) vs any function that returns 3.7c for n=10, which function can follow any kind of pattern imaginable.

And to the question of "Is adding this new city increasing the speed at which I get new social policies ?" , if it produces at least 30% of the culture produced by your best culture producing city or if it's a puppet city, yes.

 

[Stefanskantine]

Songhai are one of my favorites so far. I'd rank all their uniques as among the best on there own, and together they are just excellent. All that extra gold from barb camps in the early game is awesome. With gold you can do many things- befriend all city states, rush buy some key early buildings, hire a huge army to conquer the continent. = early game power

The Mandeleku is powerful too. Sometimes you can DW and rush right in and take a city with 2 or 3 of them before the ai even has a chance to put troops in defensive position. = mid game power

Then if you need to launch an invasion of other continents for mopping up your domination victory, you have embarked units that don't need complete support by naval units to make the trip. = late game power

 

[alpaca]

The thing is, even a monument in a new city will take 20 turns or so which is roughly on the scale of time it should take for you to get a new policy.

Sorry for the c-onfusion

I think realistic values for c (typical city culture) is something between 2 and 5. I personally don't tend to build many temples, but will build monasteries, so for me it's pretty close to 2, or 3 if I go with representation. b will usually be something like 15 if you have a single cultured city state ally and aren't actively wonder building but can be much higher. So typical values for r are > 3 which means expanding is almost always a bad idea policy-wise. If I play Songhai, I'll always build the Mud Pyramid which means c is much closer to 7 - so expanding can even speed up policy speed for the Songhai if you have a city state ally.

However, we should keep in mind that things can be interpreted the other way around: If you want to expand, you want to minimize b so city state allies and culture wonders aren't actually worth so much for you. Also, in the modern era things tend to become a little more complicated because we have more disposable income to sink into culture buildings and more social policies to screw around with things.

So, thread hijacked but it's useful to show that the Songhai unique building is a very good one

 

[Paeanblack]

The thing is, even a monument in a new city will take 20 turns or so which is roughly on the scale of time it should take for you to get a new policy.

Hmm...I usually hard-rush the monument, either by chopping or just buying the damn thing...even for my first expansion. I'll usually have it up in either 1 or 4 turns. I have no idea whether that is common strategy or not...or even optimal, but the extra 30-40 culture from getting it earlier seems worthwhile to me. A city-state would return slightly more culture for the gold, but the initial entry fee is painful if I couldn't do any missions for them. Buying the monument doesn't commit my entire coffers, and usually saves me from a tile purchase or two later on.

If you are slow-building the monument, yeah...that would really change things. That city is just dead-weight culturally.

I've been thinking about that 7/3rds threshold. That's based on the assumption that one settles and rushes the culture building immediately after starting a new policy cycle. In reality there is some delay, and in your case, it's pretty significant.

I have a hunch that the 7/3rds can be discounted by some function f of n, r, and k, where k is the fraction of time towards the next policy that the new city will spend without full culture generation. I'm pretty sure it will simplify to just a multiplicative factor.

That means we are looking at:

r >? 7/3 * f(n,r,k)

Which is clearly not as much fun to deal with, since r appears on both sides, and we know that it won't appear in a way that would allow it to be factored out from both sides. I'm not going to take a crack at defining f() at 2am, but feel free to weigh in

 

[alpaca]

I'd propose we start a new thread to continue our culture expansion discussion. We have seriously derailed the Songhai thread.

Buying monuments is a bad idea in my opinion, for two reasons: Firstly, buying cheap things is less efficient than buying expensive things and monuments are especially bad, costing 380/60 = 6.33 while for example colloseums cost 680/150 = 4.53. So I usually hammer build the monument. Secondly, you lose a lot of opportunity cost for not buying something with a higher yield, like a library or market.

For the non-equilibrium case we probably have to do a time-dependent analysis which is a lot more complex. This is at least what you usually end up doing in physics

Can't send PMs to you, otherwise I'd have done that.