Originally Posted by malekithe View Post
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
/pop for wonders. I think I read that somewhere but I can't find it.
