The fact about hurry production cost (a bug?)

I was referring to the fact that if you build too many cottage cities early in the game, your production may be low enough to make you vulnerable to attack. I'm very much aware that once the necessary civics are in place, everything, including unit production, skyrockets. I use gold rushing myself once it becomes available. I was attempting to argue that there is a tradeoff for using too many cottages in the form of being weaker in the early game- you have to spend a lot of time building infastructure rather than units to optimize later rushbuying and your military would likely be weak.

Roland does point out that even a villiage with full bonuses is superior to a workshop or lumbermill given a financial civilization, which only takes 15 turns to develop, significantly less than the 35 turn lag changing a workshop to a mine. Lumbermills you might be able to argue for due to the fact that lumbermills on rivers produce gold and provide +.5 health, but would definitely fall behind towns even so. A watermill is probably better overall for a financial civ- a watermilled grassland provides 3/2/4. That's not really an argument against goldrushing being too powerful, just possibly a better way to implement it.

The reason why farms are important is that they can fuel city growth to work non-farm tiles. I suppose after you've reached optimum size they're not that useful, and are probably worth converting to cottages then.

I suppose since even a village provides better production than workshops with full benefits, something probably should be done to alleviate the imbalance. I think negating the benefits of bonuses to hammer production while rush-buying would probably fix it.

Actually, the more I think about it, the Kremlin is probably better off reworked somehow, although just how I'm not sure. It's really by far the most powerful wonder in the modern era- you just rush all your modern armor at ridiculous speeds and basically double your production. Maybe if the Kremlin halved your upgrade costs instead. I kind of like that idea.

I agree that you shouldn't over prepare for the late game cash rushing by building only cottages in the beginning of the game. You should play the beginning of the game according to what you think is optimal and then change some terrain improvements to cottages when universal suffrage is about to be invented. If you build only cottages for the entire game, then you will hurt your civilization.

I like that idea for the Kremlin. Krikkitone also posted some ideas a few pages back that were far more balanced than the present Kremlin effects.

Maybe it will be changed in a patch. A lot of people seem to like the power of cash rushing (judging by the number of posters that post arguments that support cash rushing). So maybe, the people from Firaxis don't want to change it to appease these posters. We'll see.

What is the logic about the Kremlin effect?

Why does it decrease rushcost? Is it because it is a big red castle? Or because it is where Sovjet HQ was? Or?

Please explain

I think it's kind of the whole Soviet "We know what's best for the state. Now, go build X. Immediately. Or we'll shoot you." deal. At least, that's kind of how I interpreted it.

Spammurabi said:

I'm very much aware that once the necessary civics are in place, everything, including unit production, skyrockets. I use gold rushing myself once it becomes available.

Click to expand...

Sorry I forgot you said that.

Spammurabi said:

I was attempting to argue that there is a tradeoff for using too many cottages in the form of being weaker in the early game- you have to spend a lot of time building infastructure rather than units to optimize later rushbuying and your military would likely be weak.

Click to expand...

Of course play a balanced game early on. Too many or too little cottages is a bad thing. I don't think you have to spend a lot of time building infrastructure in the late-game for this strategy to work though. Just change a few things here and there to cottages. Of course the decision whether to change a particular improvement depends on the city and it's current state of growth etc., but it's assumed the player uses his/her judgement in this matter. Sometimes I will change a watermill to a cottage - it depends on the city.

Spammurabi said:

Roland does point out that even a villiage with full bonuses is superior to a workshop or lumbermill given a financial civilization, which only takes 15 turns to develop, significantly less than the 35 turn lag changing a workshop to a mine. Lumbermills you might be able to argue for due to the fact that lumbermills on rivers produce gold and provide +.5 health, but would definitely fall behind towns even so. A watermill is probably better overall for a financial civ- a watermilled grassland provides 3/2/4. That's not really an argument against goldrushing being too powerful, just possibly a better way to implement it.

The reason why farms are important is that they can fuel city growth to work non-farm tiles. I suppose after you've reached optimum size they're not that useful, and are probably worth converting to cottages then.

Click to expand...

I haven't done the analysis on the overall yields on each improvement so I can't say whether watermills are better than towns in certain situations, but in general, a town is the most useful improvement for a person using this strategy. I don't intend to debate the relative uses of farms/towns/watermills though. An experienced player will understand how to use them properly. There are many other threads that go into hammer yields of improvements through cash-rushing.

I might have missed this point in the discussion thread. But it does not hurt to say it once more. When you are pop-rushing with a production bonus in normal game, you may get a higher (or lower) expected number of hammers when there is more than 30 hammers left for the current product. Hopefully Firaxis have fixed this one in the final patch. It is the same bug that haunted the quick, epic and marathon games which are discussed previously in this thread.

Everything may be off-by-1 but the basic idea is there.

The pop cost of whiping in a normal game is
ceiling((h+1)/30/(1+b)) where
h is the number of remaining hammer and
b = production bonus

For example:
If your product has 36 hammers left, and you have a 25% production bonus,
you need to whip only 1 pop to finish the building.

However, the actual production yield for whipping is (c+ceiling(t-c)*30)
where
c is the current production yield and
t = hammers needed to produce the building or unit

To put it simply, you add 30 hammers each time up to the point that the production is complete.

To micro-manage production using this BUG (It's a bug!),
at 25% bonus, try rushing with 31-36 hammers left. You will lose 1 pop and gain 60 hammers, where the expected gain is 37 hammers.
at 50% bonus, try rushing with 31-44 hammers left. You will lose 1 pop and gain 60 hammers. where the expected gain is 45 hammers.

I've not checked the overflow but I believe that it is already discussed to death in other threads.

As slavery and organized religion can be acquired pretty early, (most of us beeline for bronze and some will go for the monotheism route), you can whip and gain quite a bit if you get a religion early. If you have the pyramid and switch to Police State, you can whip out 1.7 axeman with 1 pop provided that you can keep your production overflow to 1-4.

Imagine the following. There is a jungle. A huge jungle. Some hundret men with equipment walking days and month to cross the wilderness. An then - founding a city.

There again, one year later. Nobody knows how but the Empire State building has been built there.

Again one year later - you guess it - there is a large factory. And soon there are tanks all over the place.

Welcome to the world of Civilization 4! Generally I like it .
Now what's that all about? In the real world you can't just take a lot of money and make Central Africa a second United States within 10 years. No matter how much money you have. In Civ 4 you can - using the US rush function for building. There is no concern about infrastructure or anything.

At least they could restrict rushing to cities that are connected to one's capital (without enemy territory between). Conquer a city deep within enemy territory. It takes some turns to suppress the rioting citizens but then you can produce tanks every turn (or at half cost every other turn). How that? Where to take the supply from?

Besides that ... there are other computer games that offer production speedup, too. What about Alpha Centauri? I don't know the numbers but there is a non-linear function to determine the cost of production speedup: Say you produce something that costs 1000 hammers. You still need 900. The first 100 hammers (10%) will cost 1 gold each. The second 100 hammers will cost 2 gold each and so on. Rushing at this point (for 4000 gold) is much more expensive per hammer than rushing when there are only 500 hammers left (for 1500 gold).

Rushing a wonder early would be almost impossible and so it should be (my opinion). It's well known that you can't speedup projects beyond some factor without wasting a lot of resources. Take twice the number of workers and you get a speedup of 1.5 - triple the number and it will be 1.8 and with four times the number you may reach 2. Buying parts instead of building them yourself will enable you to get to factor 3 or 4, but that's it. In Civ 4 you can reach factor 10 or 20 easily (at linear cost) - thats so far from reality ...

In contrast to my previous speakers I think that forges and factories should give a bonus on hurrying production. What is easier? Building a tank when there is a factory or when there is nothing, not even a forge?

So maybe you should pay 10 coins per hammer when there is nothing built in the city. -1 for a forge, additional -2 for a factory with power and maybe -2 if the size of the city is more than 8 (and +2 if the size is below 5).
This is easy to implement and the effect should be that rushing is a good option in industrial cities and a very expensive one in the pampas.

Another possibility could be to compare the city's production (hammers) with the hammers needed. The cost may be read from the table below:

city hammers/turn divided by
missing hammers......................gold per missing hammer
1-2%....................................................25
3-5%....................................................15
6-10%...................................................10
11-25%...................................................7
26-99%...................................................5

Maybe the cost can be cut down by 1/3 when at peace because there is always a region in the world that can produce needed parts cheaper than your nation ...

As I play the game in MP 95% of the time it can be that I launch an attack on some hardly defended cities but the time it needs to move my army there they build about 30 riflemen or so to defend (not in one city - in all cities together, moving is not a problem - for the enemy). You don't need to have a large number of units when you know you can build them this way. All you need is to save a lot of money. Building units is - as stated before - cheaper than upgrading. And with less units one can use pacifism quite easily.

I hope I got it to the point. Rushing production everywhere even in size 1 cities isn't a feature I want to have in the game. There has been a mp game where one destroyed one of my cities (I didn't have the money to rush defence units), built a new city there and after that had a base producing infantry all the time (yes one per turn).

Changing rush cost calculation to a non-linear function would take down this mess a lot. Additionally there should be modifiers depending on the city, whether it has a production capability or not.

PS: Isn't that the wrong place for the discussion anyway?

well to properly balance it,
1. poprushing should be treated like chop rushing.. say limit it to one pop removed per turn, each 'whip' removes one pop adds ?6? turns of unhappiness and then adds 30 production (modified by game speed+bonuses.. possibly change the base yield if a Wonder/unit is being Worked on.. techs could also change the bonus)

2. Gold rushing could be the same.... it could have a maximum hammers added to the build each time you rushed (50?+10 per population? modified by game speed)... and you could rush once per turn. (Cost modifiers: *1.5 cost for units, *2 for National Wonders, * 4 for Wonders... Cost could either be the current 3 per turn with No benefit from production bonuses OR ~7 modified by bonuses... I'd favor the former, makes US more unique and valuable between Banks and Factories)


Then I'd say make the Kremlin remove the limit on number of times 'rushing' can be done in a city in one turn, and removing the Cost penalties for units and Wonders

as for making central Africa the second United States... in civ 4 terms that requires cottage growth time... There are banks, etc. in Central Africa and Tanks can be assembled there rapidly, but the terrain surrounding it is continually being razed.. and therefore doesn't yield much commerce (there is more to a city than what is in it/ coming out of it)

Although I do think that limiting the amount that can be rushed in a turn balances the power of gold-rushing and pop rushing and makes it more realistic, I don't think it is that good for gameplay. You have to rush each turn in some cities and that makes it tedious and you might forget to do it. It actually adds micromanagement.

It is actually very difficult to make a game resemble real life without adding massive amounts of micromanagement. I have some different ideas though.

Maybe universal suffrage should allow you to change a setting in a city called 'government funding'. The upkeep of the city would go up with an amount dependent on the production level of the city (x times the production level of the city, x being subject to balancing issues) and the city would get double the normal production level. The setting should be available on the main map next to all the preference settings for a city and maybe in the domestic advisor. Maybe another very expensive setting to quadruple the production level.

Slavery could do something similar, transmuting food to production directly with a similar setting on a city. Effects would be similar to when you're building a settler or worker and the setting would cause 1 level of unhappiness until you remove the setting.

What do you think?

I do like that idea for U.S., show a little Gold Bar instead of a brown one (although I might make the amount of 'Funding' allowed based on Population instead of Production.. )... for Slavery I'm a bit uncertain. [if it was, then slave unhappiness should increase each turn in 'whipping' and only decrease when whipping is off]

There should be some type of Rush ability in the Game. Perhaps the city can rush something (up to X hammers per population) unit in the City... but if it does, the city is shut down [no production of any kind] for some number of turns (where the turns= Hammers rushed / population of City... round Up)

Kremlin could drop That type of rushing's cost.

Krikkitone said:

I do like that idea for U.S., show a little Gold Bar instead of a brown one (although I might make the amount of 'Funding' allowed based on Population instead of Production.. )

Click to expand...

Oh, my idea was if you mouse over the production of the city then it shows a + 100% from government funding. And if you mouse over the city upkeep, then it shows that part of the city upkeep is from government funding (not to be reduced by the courthouse effect).

Krikkitone said:

... for Slavery I'm a bit uncertain. [if it was, then slave unhappiness should increase each turn in 'whipping' and only decrease when whipping is off]

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The idea was to make the unhappiness be just 1, but the food -> hammer conversion is also a bit less advantageous than in the present version. Especially since the granary doesn't offer any bonus.

Krikkitone said:

There should be some type of Rush ability in the Game. Perhaps the city can rush something (up to X hammers per population) unit in the City... but if it does, the city is shut down [no production of any kind] for some number of turns (where the turns= Hammers rushed / population of City... round Up)

Kremlin could drop That type of rushing's cost.

Click to expand...

That could also work. There are many ways to change it. I however don't think that a production rush is needed that much in this game. I would like a production speedup more as it is more natural (realistic) and less powerful.

Are there games out there that have a production speedup but not a production rush? I know that the production rushing in Master of Orion I was limited to doubling the production output of a planet. That's quite similar to what I'm saying. But you still had to enable it every turn.

Roland Johansen said:

Oh, my idea was if you mouse over the production of the city then it shows a + 100% from government funding. And if you mouse over the city upkeep, then it shows that part of the city upkeep is from government funding (not to be reduced by the courthouse effect)

Click to expand...

See now that would be the problem it could either be
1. A % bonus to production with a gold penalty added After the courthouse bonus is applied
OR
2. A bonus added to production After the production bonuses are applied

Actually, is the food bonus for settlers added before or after production % bonuses are applied... if it is before, then adding anything after the % bonuses may be complicated.


In any case, Rushing, (as opposed to boosting) has an advantage to it. In the current design that advantage is due to the fact that they require a civic (and 'boosting' can only be done by redesigning a city's terrain.)

I'd say the mechanism for doing Gold rushing should be the same, but Slavery would be best like forest chopping (no limit to number of times per turn... but each time gives you extra unhappiness... so you could whip a city down to 1 pop (or maybe only down to 1/2 its highest population)... but you would acquire massive amounts of unhappiness.

For Gold rushing, First you need to eliminate any production bonuses from the calculation.. then, if fully developed towns are to be marginally better than say a farm/workshop mix (assuming Bio but Not State Property) [which they should be under US]
2 Workshop+1 Farm= 6 Hammers (12 with Factory)
3 Windmills/Watermills=6 Hammers (12 with Factory) +6 Commerce (12 Gold)
2 Mines+1 Farm= 8 Hammers (16 with Factory)
3 SP Workshops/Lumbermills=9 (18 with Factory)
3 Towns=3 Hammers (6 with Factory) +21 commerce (42 Gold with Banks)

42 Gold should buy more than 6 production but less than 12 (so that State Property workshops beat it in production)
so it should cost 6 at most...and 4 at least.

I'd say 5 since then it beats Workshops but not Mines/Lumbermills
[for a Pyramid US it does well too]
1 Mine+1 Farm=3 hammers
2 Towns=2 Hammers +8 Gold (divide by 5... and it beats everything in the early period.. of course Towns are really hard to get early on so its worth it.)

I would eliminate the "Just started" penalty though (keep the World/National Wonder Penalty.. and maybe add a unit one ~50% like the National Wonder)

At that point a Kremlin wouldn't be too overpowered (at least at -33% Gold rush costs.. which could add a -50% whip unhappiness.. because slavery is hard to maintain late game)

That way the Main benefit of US would be
1. a Rush ability (Defense/Wonders)
2. Development of production poor regions (or ones that you want focused on something besides production.. ie, growing more towns or specialists)

Using it for primary production (in a Wonder City/unit pumping city) would be foolish... However, for those production poor regions, eliminating the "just started" penalty would allow you not to worry about micromanaging it... want building X in production poor city.. just add it to the top of the queue and rush it...

Government Funding would probably be nice as a similar thing made available to everyone (with some Renaissance-Industrial tech) that adds the +100% production at the cost of 5 Gold per base Hammer.. not available for Wonders/Units (Give it its own separate line on the budget so it isn't influenced by inflation.)... of course if this was done every time there was Carryover you would have to get a refund (of course if ther next turn was Also Government Funded, then you would be charged a large amount to Government Fund that new level)

Krikkitone said:

See now that would be the problem it could either be
1. A % bonus to production with a gold penalty added After the courthouse bonus is applied
OR
2. A bonus added to production After the production bonuses are applied

Click to expand...

Oh, yes. That was a bit vague of me. I wouldn't like to see the production bonus be subject to production bonuses from buildings (and civics, resources) and I wouldn't like to see the gold cost be subject to the courthouse reduction. In this way, you always get the some conversion rate between the gold that you pay and the production that you gain. That would be the easiest thing to balance.

Krikkitone said:

Actually, is the food bonus for settlers added before or after production % bonuses are applied... if it is before, then adding anything after the % bonuses may be complicated.

Click to expand...

That is a strange one. The production from food doesn't get a production bonus unlike the production from food through pop-rushing.

In any case, Rushing, (as opposed to boosting) has an advantage to it. In the current design that advantage is due to the fact that they require a civic (and 'boosting' can only be done by redesigning a city's terrain.)

Click to expand...

I fully agree that rushing is more powerful than boosting, but that's not a problem to me. I don't see the necessity for a strong rushing ability (from a philosophical game developers point of view). I also think that boosting is more natural in a game like civ. It would resemble real life a bit better, because it is dependent on the amount of production already present in the city. It would eliminate the rushed defender in low production cities, which is a good thing in my opinion. And of course, it only has a low level of micromanagement, something that is important to me.

Krikkitone said:

I'd say the mechanism for doing Gold rushing should be the same, but Slavery would be best like forest chopping (no limit to number of times per turn... but each time gives you extra unhappiness... so you could whip a city down to 1 pop (or maybe only down to 1/2 its highest population)... but you would acquire massive amounts of unhappiness.

For Gold rushing, First you need to eliminate any production bonuses from the calculation.. then, if fully developed towns are to be marginally better than say a farm/workshop mix (assuming Bio but Not State Property) [which they should be under US]
2 Workshop+1 Farm= 6 Hammers (12 with Factory)
3 Windmills/Watermills=6 Hammers (12 with Factory) +6 Commerce (12 Gold)
2 Mines+1 Farm= 8 Hammers (16 with Factory)
3 SP Workshops/Lumbermills=9 (18 with Factory)
3 Towns=3 Hammers (6 with Factory) +21 commerce (42 Gold with Banks)

42 Gold should buy more than 6 production but less than 12 (so that State Property workshops beat it in production)
so it should cost 6 at most...and 4 at least.

I'd say 5 since then it beats Workshops but not Mines/Lumbermills
[for a Pyramid US it does well too]
1 Mine+1 Farm=3 hammers
2 Towns=2 Hammers +8 Gold (divide by 5... and it beats everything in the early period.. of course Towns are really hard to get early on so its worth it.)

I would eliminate the "Just started" penalty though (keep the World/National Wonder Penalty.. and maybe add a unit one ~50% like the National Wonder)

At that point a Kremlin wouldn't be too overpowered (at least at -33% Gold rush costs.. which could add a -50% whip unhappiness.. because slavery is hard to maintain late game)

That way the Main benefit of US would be
1. a Rush ability (Defense/Wonders)
2. Development of production poor regions (or ones that you want focused on something besides production.. ie, growing more towns or specialists)

Using it for primary production (in a Wonder City/unit pumping city) would be foolish... However, for those production poor regions, eliminating the "just started" penalty would allow you not to worry about micromanaging it... want building X in production poor city.. just add it to the top of the queue and rush it...

Click to expand...

I do think that you know how to balance the gold rushing ability (which is at present overpowered as we both know). We talked about that before and kind of agreed (if I recall correctly). I also agree that the 'just started' penalty is not really good for anything. It increases the cost of the rushed defending unit, which might be a good thing.

Krikkitone said:

Government Funding would probably be nice as a similar thing made available to everyone (with some Renaissance-Industrial tech) that adds the +100% production at the cost of 5 Gold per base Hammer.. not available for Wonders/Units (Give it its own separate line on the budget so it isn't influenced by inflation.)... of course if this was done every time there was Carryover you would have to get a refund (of course if ther next turn was Also Government Funded, then you would be charged a large amount to Government Fund that new level)

Click to expand...

You're correct about inflation as that should not influence it. I don't know about the carryover production though. I see it as buying a turn of extra production, not as buying production for a certain project. And the amount of production that is bought is based on the basic production in a city so it isn't influenced by changes in bonuses that are dependent on the project that is being constructed. So the carryover production from this should be added independently and not be subject to production bonuses. You might see two lines of carryover in a city screen. One of the normal production subject to production bonuses and one government funding overflow not subject to production bonuses.

By the way, adding government funding as an ability might not be the most difficult part, but making the AI use it in a sensible way might be challenging. You might make it pretty basic like:
1) Only in cities with a production level lower than x or who risk being captured and the government funding finishes a unit,
2) Only y% of income is available for it (like with trading, where the AI also only uses a limited amount of gold for it),
3) If more cities can use it and not enough gold is available, then apply it to the city with the least amount of buildings. If still in a tie, apply at random.

Some sort of coding like this is probably already in place for gold rushing. It's probably a weak point of the AI as I can't see an AI use something that needs a 'larger picture of your empire' in a sensible way.

Roland Johansen said:

That is a strange one. The production from food doesn't get a production bonus unlike the production from food through pop-rushing..

Click to expand...

Well in that case the easiest might be applying your suggestion to both of them.

1. Slavery allows the "Whip" setting where all a cities food is put into production (ala Settlers) ie brown bar added

2. US allows the "Funding" setting where X amount of Gold is put into production (ie ~10 production=50 Gold cost per population unit per turn) ie Yellow bar added


if it is a +100% bonus to production, it would have to be treated the same as all other +% bonuses to production (ie remove with Carry over, re-add if you continue 'Funding' etc.)... I think the "Yellow Bar" might be simpler.

The problem with the 'Yellow bar' is determining how much cash to put into it, and how it gets cut off if you run out of money, etc [not an issue with Settlers/Workers or a food bar]... This makes the 'Rushing' model much simpler.

For limiting MM, you could have an auto rush, where when you hit end turn, each city with 'Auto-Rush' on takes its turn where it
1. checks to see if there is enough $ in the treasury
2. if there is rushes whatever it is building (if the defense unit rushing was a reason to keep the 'just started' penalty, you could have it Not auto-rush if the build was just started)... of course I'd prefer a general 'Unit penalty'

As for the reason for a Rush... I think it makes the game more interesting to have a Rush than just a Food/$->Production setting.

How the game exactly shows the production addition and the internal calculations should not be big problems I think. And if the government funding goes up, then the gold per turn costs go up and the game will automatically adjust your tax rate to meet the higher costs.

An auto rush command could be useful, but as rushing is far more powerful then the 'funding' option and also more expensive, I don't think you'll use it all that much. If you're talking about the limited form of rushing as in your post 88, then an auto rush option would remove the micromanagement and would be a very good option.
In that case, the differences between 'funding' and 'limited autorushing' are only graphical in nature, buttons are at different points and the mouseover information might be at a different location. All, not very important for me as long as it is clear what is happening.
I'd like to see the autorush costs added to the gold per turn summary so that you can see what will happen with your income when you hit end turn.

Roland Johansen said:

I'd like to see the autorush costs added to the gold per turn summary so that you can see what will happen with your income when you hit end turn.

Click to expand...

Yeah that would be necessary
(perhaps in the middle portion and not the 'expenses' portion... Perhaps that could be done with upgrades too, when you alt-upgrade it could put all those units on 'auto upgrade' if you don't have the cash right now.)

So you could have...Income , Expenses, and "Planned Spending" ie auto upgrade/rushing (if planned spending was greater than Current Treasury+Income-Expenses, then you would know your Treasury would drop to near 0, and the Planned Spending would be put off for another turn.)

This would eliminate the necessity of the switch to 0% Science for X turns make sure you had enough cash to get all of 'unit X' upgraded.... Just hit alt-upgrade on one of them, make sure you run a slight surplus and eventually they all get upgraded.)

Yes, that planned spending idea sounds good. I think we've got some nice ideas here in general. They might even be implementable with the SDK, although I don't know the capabilities of the SDK and have not experimented with it yet.

I hope that rush buying of any sort gets some streamlining in the next installment of civ, maybe along the lines we're suggesting right here.

well with the next installment a number of things will be substantially rejiggered so I wouldn't be surprised to see a 'Government Funding' and 'Rush' setting being seperate.


Reply to below.. just a general guess

Do you know more than I or is this just a general guess that the next installment will probably again be different? Civ 1 and Civ 2 were very much alike, not a lot of change then.

malekithe said:

I was reading over this thread and thought I’d do some experimenting myself. I wound up deriving the formulas for all of the values involved in rushing production. Most of these have been hinted at in other posts, but I thought I'd post my findings. Feel free to try any of these formulas out in-game and let me know if they produce an incorrect result. I'd like to fix them if that's the case.

First I’ll explain my variable names:

H – Total hammers remaining in production
S – Game speed multipler – 0.66... = quick, 1.0 = normal, 1.5 = epic, 3.0 = marathon

Bonuses:
B – Sum of all production bonuses (eg. 0.5 if you have a forge and Organized Religion is applicable)
K – Kremlin Modifier – 0.5 for Kremlin, 1.0 otherwise

Penalties:
W – The wonder modifier – 2.0 for a world wonder, 1.5 for national wonder, 1.0 for everything else
Z – Zero Hammers modifier – 1.5 if this is the first turn of production

Now, the formula for the modified cost of whatever it is you’re rushing ([…] denotes the “floor” operation)

C = [ H / ( 1+B) * K * W * Z ]

Basically, you just multiply everything together, divide by 1+B, and then take the floor.

Now, if you want to convert that cost into a population or gold quantity you simply use one of the two simple formulas below.

Pop Rush:
P = [ C / ( 30 * S) + 1 ]

Gold Rush:
G = 3 * S * C

Also, a formula for the number of hammers of overflow you can expect (‘%’ represent the modulo operation)

O = ( 30 – (H % 30) ) % 30

And then, if you really want to know your total output per population point, you need to use one last formula (can’t really reduce it any more because of all the flooring and modulos that took place):

PP = (H + O) / P

The ramifications of all of this have already been hinted at in this thread and others. Namely:

• You don’t want to rush when the number of hammers remaining is a multiple of 30.

• There are additional jump points on other games speeds where your hammers per pop point can change considerably (on epic, no bonuses, 44 hammers remaining requires 1 pop and nets 60 hammers, 45 hammers remaining requires 2 pop and nets the same 60 hammers. That’s a whole second pop point resulting in no additional hammers.)

• You can significantly reduce the rush cost (in population or gold) through city buildings and the Kremlin.

• The Kremlin is the equivalent of a forge, factory, and power in every city (for rushing purposes).

• With the Kremlin and simply another 50% city bonus (or just a total city bonus of 200%), you can buy 1 hammer for 1 gold.

• Others, but it’s late and my mind is cloudy… I want to say something along the lines of “In the late-middle-thru-end game, hammers might be next to useless, or, at best, very inefficient”. But, then again, most of my games are over by the time I get grenadiers and cavalry

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I know this thread is really old but I think there's a slight error in malekithe's formula as written, which I corrected in the quote. The gold cost for hurrying should be 3*C*S, not 3*C.